# Research Area B

## Project B2

### Tracking the surface atomic motion in a coherent phonon oscillation

*Davide Curcio, Klara Volckaert, Dmytro Kutnyakhov, Steinn Ymir Agustsson, Kevin Bühlmann, Federico Pressacco, Michael Heber, Siarhei Dziarzhytski, Yves Acremann, Jure Demsar, Wilfried Wurth, Charlotte E. Sanders, and Philip Hofmann*

X-ray photoelectron diffraction is a powerful tool for determining the structure of clean and adsorbate-covered surfaces. Extending the technique into the ultrafast time domain will open the door to studies as diverse as the direct determination of the electron-phonon coupling strength in solids and the mapping of atomic motion in surface chemical reactions. Here we demonstrate time-resolved photoelectron diffraction using ultrashort soft x-ray pulses from the free electron laser FLASH. We collect Se 3*d* photoelectron diffraction patterns over a wide angular range from optically excited Bi_{2}Se_{3} with a time resolution of 140 fs. Combining these with multiple scattering simulations allows us to track the motion of near-surface atoms within the first 3 ps after triggering a coherent vibration of the A1* _{g}* optical phonons. Using a fluence of 4.2mJ/cm

^{2}from a 1.55 eV pump laser, we find the resulting coherent vibrational amplitude in the first two interlayer spacings to be on the order of 0.01 Å.

### Multispectral time-resolved energy–momentum microscopy using high-harmonic extreme ultraviolet radiation

*Michael Heber, Nils Wind, Dmytro Kutnyakhov, Federico Pressacco, Tiberiu Arion, Friedrich Roth, Wolfgang Eberhardt, and Kai Rossnagel*

A 790-nm-driven high-harmonic generation source with a repetition rate of 6 kHz is combined with a toroidal-grating monochromator and a high-detection-efficiency photoelectron time-of-flight momentum microscope to enable time- and momentum-resolved photoemission spectroscopy over a spectral range of 23.6–45.5 eV with sub-100 fs time resolution. Three-dimensional (3D) Fermi surface mapping is demonstrated on graphene-covered Ir(111) with energy and momentum resolutions of ≲100 meV and ≲0.1 Å^{−1}, respectively. The tabletop experiment sets the stage for measuring the k* _{z}*-dependent ultrafast dynamics of 3D electronic structure, including band structure, Fermi surface, and carrier dynamics in 3D materials as well as 3D orbital dynamics in molecular layers.

### Ultrafast orbital tomography of a pentacene film using time-resolved momentum microscopy at a FEL

*Kiana Baumgärtner, Marvin Reuner, Christian Metzger, Dmytro Kutnyakhov, Michael Heber, Federico Pressacco, Chul-Hee Min, Thiago R. F. Peixoto, Mario Reiser, Chan Kim, Wei Lu, Roman Shayduk, Manuel Izquierdo, Günter Brenner, Friedrich Roth, Achim Schöll, Serguei Molodtsov, Wilfried Wurth, Friedrich Reinert, Anders Madsen, Daria Popova-Gorelova & Markus Scholz*

Time-resolved momentum microscopy provides insight into the ultrafast interplay between structural and electronic dynamics. Here we extend orbital tomography into the time domain in combination with time-resolved momentum microscopy at a free-electron laser (FEL) to follow transient photoelectron momentum maps of excited states of a bilayer pentacene film on Ag(110). We use optical pump and FEL probe pulses by keeping FEL source conditions to minimize space charge effects and radiation damage. From the momentum microscopy signal, we obtain time-dependent momentum maps of the excited-state dynamics of both pentacene layers separately. In a combined experimental and theoretical study, we interpret the observed signal for the bottom layer as resulting from the charge redistribution between the molecule and the substrate induced by excitation. We identify that the dynamics of the top pentacene layer resembles excited-state molecular dynamics.

### Coexisting ferromagnetic component and negative magnetoresistance at low temperature in single crystals of the VdW material GaGeTe

*A. Roychowdhury, T.K. Dalui, P.K. Ghose, S.K. Mahatha, N. Wind, K. Rossnagel, S. Majumdar, S. Giri*

We report magnetoresistance and magnetization studies of single-crystal GaGeTe, which has been proposed as a Van der Waals material. Semi-metallic character is observed in the temperature (*T*) variation of resistivity (*ρ*), following *ρ*(*T*) ∝* T*^{2} at low temperature with a slope compatible with the usual spin-fluctuating system. Magnetoresistance (MR) at 2 K is negative and strongly dependent on the direction of the magnetic field (*H*) with respect to the crystallographic *c*-axis. MR changes sign with increasing temperature above ∼ 100 K, when H is applied along the *c*-axis. Hall measurements indicate the *p*-type conductivity with a considerable hole concentration of ∼ 8.7 × 10^{19} cm^{−3}. Angle-resolved photoemission spectroscopy reproduces the reported results and confirms a peculiar dispersion shape of the hole-like band at the bulk high-symmetry T point near the Fermi energy indicating band inversion. Magnetic hysteresis measurement at 2 K shows diamagnetic behaviour at high-*H*, whereas a ferromagnetic (FM)-like magnetic hysteresis loop is observed at low-*H* in between ± 4 kOe. The FM component disappears close to 3 K. Signature of spin-fluctuation in *ρ*(*T*), negative MR, and low-*T* FM component without 3*d* or 4*f* impurities in GaGeTe is attractive for the fundamental interest.

### Ultrafast MHz-Rate Burst-Mode Pump–Probe Laser for the FLASH FEL Facility Based on Nonlinear Compression of ps-Level Pulses from an Yb-Amplifier Chain

*Marcus Seidel, Federico Pressacco, Oender Akcaalan, Thomas Binhammer, John Darvill,Nagitha Ekanayake, Maik Frede, Uwe Grosse-Wortmann, Michael Heber,Christoph M. Heyl, Dmytro Kutnyakhov, Chen Li, Christian Mohr, Jost Müller,Oliver Puncken, Harald Redlin, Nora Schirmel, Sebastian Schulz, Angad Swiderski,Hamed Tavakol, Henrik Tünnermann, Caterina Vidoli, Lukas Wenthaus, Nils Wind,Lutz Winkelmann, Bastian Manschwetus, and Ingmar Hartl*

The Free-Electron Laser (FEL) FLASH offers the worldwide still unique capability to study ultrafast processes with high-flux, high-repetition rate extreme ultraviolet, and soft X-ray pulses. The vast majority of experiments at FLASH are of pump–probe type. Many of them rely on optical ultrafast lasers. Here, a novel FEL facility laser is reported which combines high average power output from Yb:YAG amplifiers with spectral broadening in a Herriott-type multipass cell and subsequent pulse compression to sub-100-fs durations. Compared to other facility lasers employing optical parametric amplification, the new system comes with significantly improved noise figures, compactness, simplicity, and power efficiency. Like FLASH, the optical laser operates with 10-Hz burst repetition rate. The bursts consist of 800-μs long trains of up to 800 ultrashort pulses being synchronized to the FEL with femtosecond precision. In the experimental chamber, pulses with up to 50-*μ*J energy, 60-fs full-width half-maximum duration and 1-MHz rate at 1.03-μm wavelength are available and can be adjusted by computer-control. Moreover, nonlinear polarization rotation is implemented to improve laser pulse contrast. First cross-correlation measurements with the FEL at the plane-grating monochromator photon beamline are demonstrated, exhibiting the suitability of the laser for user experiments at FLASH.

### Ultrafast electronic linewidth broadening in the C 1s core level of graphene

*Davide Curcio et al.*

We show that the presence of a transiently excited hot electron gas in graphene leads to a substantial broadening of the C 1*s* line probed by time-resolved x-ray photoemission spectroscopy. The broadening is found to be caused by an exchange of energy and momentum between the photoemitted core electron and the hot electron gas, rather than by vibrational excitations. This interpretation is supported by a quantitative line-shape analysis that accounts for the presence of the excited electrons. Fitting the spectra to this model directly yields the electronic temperature of the system, in good agreement with electronic temperature values obtained from valence band data. Furthermore, we show how the momentum change of the outgoing core electrons leads to a detectable but very small change in the time-resolved photoelectron diffraction pattern and to a nearly complete elimination of the core level binding energy variation associated with the presence of a narrow σ band in the C 1*s* state.

### Subpicosecond metamagnetic phase transition in FeRh driven by non-equilibrium electron dynamics

*F. Pressacco et al.*

Femtosecond light-induced phase transitions between different macroscopic orders provide the possibility to tune the functional properties of condensed matter on ultrafast timescales. In first-order phase transitions, transient non-equilibrium phases and inherent phase coexistence often preclude non-ambiguous detection of transition precursors and their temporal onset. Here, we present a study combining time-resolved photoelectron spectroscopy and ab-initio electron dynamics calculations elucidating the transient subpicosecond processes governing the photoinduced generation of ferromagnetic order in antiferromagnetic FeRh. The transient photoemission spectra are accounted for by assuming that not only the occupation of electronic states is modified during the photoexcitation process. Instead, the photo-generated non-thermal distribution of electrons modifies the electronic band structure. The ferromagnetic phase of FeRh, characterized by a minority band near the Fermi energy, is established 350 ± 30 fs after the laser excitation. Ab-initio calculations indicate that the phase transition is initiated by a photoinduced Rh-to-Fe charge transfer.

### Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

*G. Schönhense et. al.*

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the *e–e* Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from −20 to −1100 V/mm for E_{kin} = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 *μ*m above the sample surface for E_{kin} = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E_{kin} = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm2 (retarding field −21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm2, it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E_{kin} = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

Review of Scientific Instruments 92, 053703 (2021)

### Magnetic order and surface state gap in (Sb0.95Cr0.05)2 Te3

*T. K. Dalui, P. K. Ghose, S. Majumdar, S. K. Mahatha, F. Diekmann, K. Rossnagel, R. Tomar, S. Chakraverty, A. Berlie, and S. Giri*

Magnetic transition element doping in topological insulators, which breaks the time-reversal symmetry, gives rise to the diverse range of exotic consequences, though proper understanding of the magnetic order has rarely been attempted by using any microscopic experiments. We report the occurrence of the magnetic order in (Sb_{0.95}Cr_{0.05})2Te_{3} using the muon spin relaxation studies. The asymmetry curve at low temperature (*T*) shows an evidence of a damped oscillation, providing a clue about the internal magnetic field (*H*_{int}), which follows *H*_{int}(*T*)=*H*_{int}(0)[1−*T*/*T*_{C}]^{β} with ordering temperature *T _{C}*≈6.1 K and critical exponent

*β*≈0.22. The critical exponent is close to the two-dimensional XY-type interaction. The magnetization curves at low

*T*exhibit a ferromagnetic behavior at low field (

*H*) and the de Haas–van Alphen (dHvA) effect at high

*H*. The analysis of the dHvA oscillation proposes the charge carrier that acts like a massive Dirac fermion. The Berry phase, as obtained from the Landau-level fan diagram, suggests a surface state gap at the Dirac point. The complex electronic structure is discussed by correlating the magnetic order attributed to the Cr doping in Sb

_{2}Te

_{3}.

### An open-source, end-to-end workflow for multidimensional photoemission spectroscopy

*R. Patrick Xian , Yves acremann, Steinn Y. agustsson, Maciej Dendzik, Kevin Bühlmann, Davide Curcio, Dmytro Kutnyakhov, Federico Pressacco, Michael Heber, Shuo Dong, Tommaso Pincelli, Jure Demsar, Wilfried Wurth, Philip Hofmann, Martin Wolf, Markus Scheidgen, Laurenz Rettig & Ralph Ernstorfer*

Characterization of the electronic band structure of solid state materials is routinely performed using photoemission spectroscopy. Recent advancements in short-wavelength light sources and electron detectors give rise to multidimensional photoemission spectroscopy, allowing parallel measurements of the electron spectral function simultaneously in energy, two momentum components and additional physical parameters with single-event detection capability. Efficient processing of the photoelectron event streams at a rate of up to tens of megabytes per second will enable rapid band mapping for materials characterization. We describe an open-source workflow that allows user interaction with billion-count single-electron events in photoemission band mapping experiments, compatible with beamlines at 3rd and 4rd generation light sources and table-top laser-based setups. The workflow offers an end-to-end recipe from distributed operations on single-event data to structured formats for downstream scientific tasks and storage to materials science database integration. Both the workflow and processed data can be archived for reuse, providing the infrastructure for documenting the provenance and lineage of photoemission data for future high-throughput experiments.

### Observation of an Excitonic Mott Transition Through Ultrafast Core-cum-Conduction Photoemission Spectroscopy

*Maciej Dendzik, R. Patrick Xian, Enrico Perfetto, Davide Sangalli, Dmytro Kutnyakhov, Shuo Dong, Samuel Beaulieu, Tommaso Pincelli, Federico Pressacco, Davide Curcio, Steinn Ymir Agustsson, Michael Heber, Jasper Hauer, Wilfried Wurth, Günter Brenner, Yves Acremann, Philip Hofmann, Martin Wolf, Andrea Marini, Gianluca Stefanucci, Laurenz Rettig, and Ralph Ernstorfer*

Time-resolved soft-x-ray photoemission spectroscopy is used to simultaneously measure the ultrafast dynamics of core-level spectral functions and excited states upon excitation of excitons in **WSe _{2}**. We present a many-body approximation for the Green’s function, which excellently describes the transient core-hole spectral function. The relative dynamics of excited-state signal and core levels clearly show a delayed core-hole renormalization due to screening by excited quasifree carriers resulting from an excitonic Mott transition. These findings establish time-resolved core-level photoelectron spectroscopy as a sensitive probe of subtle electronic many-body interactions and ultrafast electronic phase transitions.

### Time- and momentum-resolved photoemission studies using time-of-flight momentum microscopy at a free-electron laser

*D. Kutnyakhov, R. P. Xian, M. Dendzik, M. Heber, F. Pressacco, S. Y. Agustsson, L. Wenthaus, H. Meyer, S. Gieschen, G. Mercurio, A. Benz, K. Bühlman, S. Däster, R. Gort, D. Curcio, K. Volckaert, M. Bianchi, Ch. Sanders, J. A. Miwa, S. Ulstrup, A. Oelsner, C. Tusche, Y.-J. Chen, D. Vasilyev, K. Medjanik, G. Brenner, S. Dziarzhytski, H. Redlin, B. Manschwetus, S. Dong, J. Hauer, L. Rettig, F. Diekmann, K. Rossnagel, J. Demsar, H.-J. Elmers, Ph. Hofmann, R. Ernstorfer, G. Schönhense, Y. Acremann, and W. Wurth*

Time-resolved photoemission with ultrafast pump and probe pulses is an emerging technique with wide application potential. Real-time recording of nonequilibrium electronic processes, transient states in chemical reactions, or the interplay of electronic and structural dynamics offers fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction for electronic, chemical, and structural analyses requires few 10 fs soft X-ray pulses with some 10 meV spectral resolution, which are currently available at high repetition rate free-electron lasers. We have constructed and optimized a versatile setup commissioned at FLASH/PG2 that combines free-electron laser capabilities together with a multidimensional recording scheme for photoemission studies. We use a full-field imaging momentum microscope with time-of-flight energy recording as the detector for mapping of 3D band structures in (*k _{x}, k_{y}, E*) parameter space with unprecedented efficiency. Our instrument can image full surface Brillouin zones with up to 7 Å

^{−1}diameter in a binding-energy range of several eV, resolving about 2.5 × 10

^{5}data voxels simultaneously. Using the ultrafast excited state dynamics in the van der Waals semiconductor WSe

_{2}measured at photon energies of 36.5 eV and 109.5 eV, we demonstrate an experimental energy resolution of 130 meV, a momentum resolution of 0.06 Å

^{−1}, and a system response function of 150 fs.

### Ultrafast charge redistribution in small iodine containing molecules

* M. Hollstein, K. Mertens, S. Klumpp, N. Gerken, S. Palutke, I. Baev, G. Brenner, S. Dziarzhytski, M. Meyer, W. Wurth, D. Pfannkuche1, M. Martins*

We present studies on intra-molecular charge redistribution in iodine containing molecules upon iodine-4d photoionization. For this, we employed an XUV-pump-XUV-probe scheme based on time-delayed femtosecond pulses delivered by the free-electron laser at DESY in Hamburg (FLASH). The experimental results show delay dependent and molecule-specific iodine charge state distributions that arise upon multiple iodine-4d photoionization. Using the example of CH_{3}I and CH_{2}I_{2}, we compare the delay-dependent yields of I^{3+}. We model the involved processes using advanced ab initio electronic structure calculations which include electron correlations combined with a classical model of the nuclear motion. The qualitative agreement of our model with the experimental results allows us to relate the observed, strongly molecule-specific efficiencies of the intra-molecular charge rearrangement not only to molecule-specific fragmentation timescales but also to molecule-specific electronic structure and molecular environment.

### Direct observation of spin-orbit-induced 3d hybridization via resonant inelastic extreme ultraviolet scattering on an edge-sharing cuprate

*M. Malvestuto, A. Caretta, B. Casarin, R. Ciprian, M. Dell'Angela, S. Laterza, Y. Chuang, W. Wurth, A. Revcolevschi, L. A. Wray, and F. Parmigiani*

Using high resolution resonant inelastic x-ray scattering measurements, we have observed that the orbital excitations of the quasi-1D spin chain compound **CuGeO3** has nontrivial and noticeable orbital mixing effects from **3 d** valence spin-orbit coupling. In particular, the SOC leads to a significant correction of

**d**state, which has a direct interplay with the low energy physics of cuprates. Guided by atomic multiplet based modeling, our results strongly support a

_{z}2**3**spin-orbit mixing scenario and explore in detail the nature of these excitations.

*d*### 4D texture of circular dichroism in soft-x-ray photoemission from tungsten

*O. Fedchenko, K. Medjanik, S. Chernov, D. Kutnyakhov, M. Ellguth, A. Oelsner, B. Schönhense, T.R.F. Peixoto, P. Lutz, C.-H. Min , F. Reinert, S. Däster, Y. Acremann, J. Viefhaus, W. Wurth, J. Braun, J. Minár, H.Ebert, H.J. Elmers, and G. Schönhense*

Photoemission-intensity distributions I _{RCP/LCP} (*E* _{B} ,** k** ) measured for right- and left-circularly polarized soft x-rays revealed a large circular dichroism in angular distribution (

*CDAD*) in the 4D parameter space (

*E*

_{ B}binding energy,

**momentum vector). Full-field**

*k***-imaging combined with time-of-flight energy recording at a high-brilliance soft x-ray beamline allowed mapping the**

*k**CDAD*in the bulk Brillouin zone of tungsten and the entire d-band complex within a few hours.

*CDAD*-asymmetries are very high (up to 90%), persist throughout the whole photon-energy range (300–1300 eV) and show a pronounced dependence on momentum k and binding energy

*E*

_{B}, visualized as movies or sequences of cuts through the 4D object. One-step photoemission calculations for the same photon energies show fair agreement with the measured results. In addition to the requirement of a 'handed' experimental geometry, known from previous experiments on adsorbates and surface states, we find an anti-symmetric behavior of the

*CDAD*with respect to two bulk mirror planes. A new symmetry condition along the perpendicular momentum

*k*makes

_{z}*CDAD*a valuable tool for an unambiguous identification of high-symmetry planes in direct transitions in the periodic zone scheme. Technically, the method provides a circular polarimeter for soft, tender and hard x-rays.

### Transiently enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, W. Hu, A. Cavalleri, L. Mathey*

Recent pump-probe experiments reported an enhancement of superconducting transport along the c axis of underdoped YBa_{2}Cu_{3}O_{6+δ} (YBCO), induced by a midinfrared optical pump pulse tuned to a specific lattice vibration. To understand this transient nonequilibrium state, we develop a pump-probe formalism for a stack of Josephson junctions, and we consider the tunneling strengths in the presence of modulation with an ultrashort optical pulse. We demonstrate that a transient enhancement of the Josephson coupling can be obtained for pulsed excitation and that this can be even larger than in a continuously driven steady state. Especially interesting is the conclusion that the effect is largest when the material is parametrically driven at a frequency immediately above the plasma frequency, in agreement with what is found experimentally. For bilayer Josephson junctions, an enhancement similar to that experimentally is predicted below the critical temperature *T _{c}*. This model reproduces the essential features of the enhancement measured below

*T*. To reproduce the experimental results above

_{c}*T*, we will explore extensions of this model, such as in-plane and amplitude fluctuations, elsewhere.

_{c}### High-resolution resonant inelastic extreme ultraviolet scattering from orbital and spin excitations in a Heisenberg antiferromagnet

*A. Caretta, M. Dell'Angela, Y. Chuang, A. M. Kalashnikova, R. V. Pisarev, D. Bossini, F. Hieke, W. Wurth, B. Casarin, R. Ciprian, F. Parmigiani, S. Wexler, L. A. Wray, M. Malvestuto*

We report a high-resolution resonant inelastic extreme ultraviolet (EUV) scattering study of the quantum Heisenberg antiferromagnet KCoF_{3}. By tuning the EUV photon energy to the cobalt *M*_{23} edge, a complete set of low-energy 3*d* spin-orbital excitations is revealed. These low-lying electronic excitations are modeled using an extended multiplet-based mean-field calculation to identify the roles of lattice and magnetic degrees of freedom in modifying the resonant inelastic x-ray scattering (RIXS) spectral line shape. We have demonstrated that the temperature dependence of RIXS features upon the antiferromagnetic ordering transition enables us to probe the energetics of short-range spin correlations in this material.

### Extreme ultraviolet resonant inelastic X-ray scattering (RIXS) at a seeded free-electron laser

*M. Dell’Angela, F. Hieke, M. Malvestuto, L. Sturari, S. Bajt, I. V. Kozhevnikov, J. Ratanapreechachai, A. Caretta, B. Casarin, F. Glerean, A. M. Kalashnikova, R. V. Pisarev, Y.-D. Chuang, G. Manzoni, F. Cilento, R. Mincigrucci, A. Simoncig, E. Principi, C. Masciovecchio, L. Raimondi, N. Mahne, C. Svetina, M. Zangrando, R. Passuello, G. Gaio, M. Prica, M. Scarcia, G. Kourousias, R. Borghes, L. Giannessi, W. Wurth and F. Parmigiani*

In the past few years, we have been witnessing an increased interest for studying materials properties under non-equilibrium conditions. Several well established spectroscopies for experiments in the energy domain have been successfully adapted to the time domain with sub-picosecond time resolution. Here we show the realization of high resolution resonant inelastic X-ray scattering (RIXS) with a stable ultrashort X-ray source such as an externally seeded free electron laser (FEL). We have designed and constructed a RIXS experimental endstation that allowed us to successfully measure the d-d excitations in KCoF_{3} single crystals at the cobalt M_{2,3}-edge at FERMI FEL (Elettra-Sincrotrone Trieste, Italy). The FEL-RIXS spectra show an excellent agreement with the ones obtained from the same samples at the MERIXS endstation of the MERLIN beamline at the Advanced Light Source storage ring (Berkeley, USA). We established experimental protocols for performing time resolved RIXS experiments at a FEL source to avoid X ray-induced sample damage, while retaining comparable acquisition time to the synchrotron based measurements. Finally, we measured and modelled the influence of the FEL mixed electromagnetic modes, also present in externally seeded FELs, and the beam transport with ~120 meV experimental resolution achieved in the presented RIXS setup.

### The role of space charge in spin-resolved photoemission experiments

*A. Fognini, G. Salvatella, T.U. Michlmayr, C. Wetli, U. Ramsperger, T. Bähler, F. Sorgenfrei, M. Beye, A. Eschenlohr, N. Pontius, C. Stamm, F. Hieke, M. Dell‘Angela, S. de Jong, R. Kukreja, N. Gerasimova, V. Rybnikov, H. Redlin, J. Raabe, W. Wurth et.*

Spin-resolved photoemission is one of the most direct ways of measuring the magnetization of a ferromagnet. If all valence band electrons contribute, the measured average spin polarization is proportional to the magnetization. This is even the case if electronic excitations are present, and thus is of particular interest for studying the response of the magnetization to a pump laser pulse. Here, we demonstrate the feasibility of ultrafast spin-resolved photoemission using free electron laser (FEL) radiation and investigate the effect of space charge on the detected spin polarization. The sample is exposed to the radiation of the FEL FLASH in Hamburg. Surprisingly, the measured spin polarization depends on the fluence of the FEL radiation: a higher FEL fluence reduces the measured spin polarization. Space-charge simulations can explain this effect. These findings have consequences for future spin-polarized photoemission experiments using pulsed photon sources.

### Ultrafast reduction of the total magnetization in iron

*A. Fognini, T. U. Michlmayr, G. Salvatella, C. Wetli, U. Ramsperger, T. Bähler, F.Sorgenfrei, M. Beye, A. Eschenlohr, N. Pontius, C. Stamm, F. Hieke, M. Dell'Angela, S. de Jong, R. Kukreja, N. Gerasimova, V. Rybnikov, H. Redlin, W. Wurth, et. al*

Surprisingly, if a ferromagnet is exposed to an ultrafast laser pulse, its apparent magnetization is reduced within less than a picosecond. Up to now, the total magnetization, i.e., the average spin polarization of the whole valence band, was not detectable on a sub-picosecond time scale. Here, we present experimental data, confirming the ultrafast reduction of the total magnetization. Soft x-ray pulses from the free electron laser in Hamburg (FLASH) extract polarized cascade photoelectrons from an iron layer excited by a femtosecond laser pulse. The spin polarization of the emitted electrons is detected by a Mott spin polarimeter.

### Speed limit of the insulator metal-transition in magnetite

*S. de Jong, R. Kukreja, C. Trabant, N. Pontius, C.F. Chang, T. Kachel, M. Beye, F. Sorgenfrei, C. H. Back, B. Bräuer, W.F. Schlotter, J.J. Turner, O. Krupin, M. Doehler, D. Zhu, M.A. Hossain, W. Wurth, D. Fausti, F. Novelli, M. Esposito, et. al*

As the oldest known magnetic material, magnetite (Fe3O4) has fascinated mankind for millennia. As the first oxide in which a relationship between electrical conductivity and fluctuating/localized electronic order was shown, magnetite represents a model system for understanding correlated oxides in general. Nevertheless, the exact mechanism of the insulator–metal, or Verwey, transition has long remained inaccessible. Recently, three-Fe-site lattice distortions called trimerons were identified as the characteristic building blocks of the low-temperature insulating electronically ordered phase9. Here we investigate the Verwey transition with pump–probe X-ray diffraction and optical reflectivity techniques, and show how trimerons become mobile across the insulator–metal transition. We find this to be a two-step process. After an initial 300 fs destruction of individual trimerons, phase separation occurs on a 1.5±0.2 ps timescale to yield residual insulating and metallic regions. This work establishes the speed limit for switching in future oxide electronics.

## Project B3

### In-vacuum Helmholtz coils for pulsed magnetic fields studying ultrafast demagnetization

*M. Riepp et al.*

The availability of sub 100 fs short and highly intense free-electron laser (FEL) pulses allows for new insights in laser-induced ultrafast demagnetization (LID) of ferromagnetic thin films on nanometer length scales. We designed a pair of in-vacuum Helmholtz coils, providing pulsed magnetic fields up to* µ*_{0}*H _{z}* = ±45 mT, for time-resolved experiments at FEL sources in transmission geometry. We report on the implementation of the Helmholtz coils in an optical-pump–resonant-magnetic-scattering (tr-XRMS) experiment at the FEL FERMI (Elettra, Trieste) to study LID in different magnetic domain networks. We discuss the limitations for multi-shot measurements, that rely on the full reversibility of the demagnetization process in-between two pump–probe events, and emphasize the importance of reference–pump–probe schemes, especially in tr-XRMS experiments that employ external

*H*fields.

_{z}### Hard X-ray USAXS Fourier Transform Holography

*W. Roseker et al.*

We report on a Fourier transform holography study, employing hard X-ray energies at a 3rd generation storage ring. Nano-structures of various sizes and shapes have been measured in ultra small angle x-ray scattering configuration reaching a resolution in the holographic reconstructions of about 50 nm. Reliable holograms have been obtained with 6.9×10^{6} incident photons. Our results provide an important step forward towards routine split-pulse Fourier transform holography measurements at FEL sources and 4th generation ultralow-emittance sources.

### The beam stop as an intensity monitor

*L. Müller et al.*

Free-electron lasers (FELs) provide unique possibilities in investigating matter down to femtosecond time and nanometer length scales, as well as in the regime of non-linear light-matter interaction. Due to the nature of FEL sources, the produced beam is significantly more unstable than beams produced by 3^{rd} generation synchrotrons. As a result, pulse-resolved normalization of measurement data becomes essential and can be challenging. The intensity monitors permanently installed at a facility might indeed accurately measure the pulse intensities at a certain point of the beamline, but cannot precisely normalize experimental data. For example the impact of pointing instabilities and hence different clipping of the beam downstream on the way to the actual experiment is not reflected in the intensity measurement. Here, we show how the integral intensity of the FEL beam transmitted through the sample can be measured by photodiodes providing a proper normalization of measurement data.

### Modeling of ultrafast X-ray induced magnetization dynamics in magnetic multilayer systems

*Kapcia, K.J., Tkachenko, V., Capotondi, F. et al.*

In this work, we report on modeling results obtained with our recently developed simulation tool enabling nanoscopic description of electronic processes in X-ray irradiated ferromagnetic materials. With this tool, we have studied the response of Co/Pt multilayer system irradiated by an ultrafast extreme ultraviolet pulse at the M-edge of Co (photon energy ~60 eV). It was previously investigated experimentally at the FERMI free-electron-laser facility, using the magnetic small-angle X-ray scattering technique. Our simulations show that the magnetic scattering signal from cobalt decreases on femtosecond timescales due to electronic excitation, relaxation, and transport processes both in the cobalt and in the platinum layers, following the trend observed in the experimental data. The confirmation of the predominant role of electronic processes for X-ray induced demagnetization in the regime below the structural damage threshold is a step toward quantitative control and manipulation of X-ray induced magnetic processes on femtosecond timescales.

### Nanoscale inhomogeneity of charge density waves dynamics in La2−xSrxNiO4

*Gaetano Campi, Antonio Bianconi, Boby Joseph, Shrawan Kr Mishra, Leonard Müller, Alexey Zozulya, Agustinus Agung Nugroho, Sujoy Roy, **Michael Sprung & Alessandro Ricci*

While stripe phases with broken rotational symmetry of charge density are known to emerge in doped strongly correlated perovskites, the dynamics and heterogeneity of spatial ordering remain elusive. Here we shed light on the temperature dependent lattice motion and the spatial nanoscale phase separation of charge density wave order in the archetypal striped phase in La_{2−x}Sr_{x}NiO_{4+y} (LSNO) perovskite using X-ray photon correlation spectroscopy (XPCS) joint with scanning micro X-ray diffraction (SµXRD). While it is known that the CDW in 1/8 doped cuprates shows a remarkable stability we report the CDW motion dynamics by XPCS in nickelates with an anomalous quantum glass regime at low temperature, T < 65 K, and the expected thermal melting at higher temperature 65 < T < 120 K. The nanoscale CDW puddles with a shorter correlation length are more mobile than CDW puddles with a longer correlation length. The direct imaging of nanoscale spatial inhomogeneity of CDW by scanning micro X-ray diffraction (SµXRD) shows a nanoscale landscape of percolating short range dynamic CDW puddles competing with large quasi-static CDW puddles giving rise to a novel form of nanoscale phase separation of the incommensurate stripes order landscape.

### Demonstration of 3D photon correlation spectroscopy in the hard X-ray regime

*Wonhyuk Jo, Rustam Rysov, Fabian Westermeier, Michael Walther, Leonard Müller, André Philippi-Kobs, Matthias Riepp, Simon Marotzke, Irina Lokteva, Michael Sprung, Gerhard Grübel, and Wojciech Roseker*

Three-dimensional photon correlation spectroscopy (3D PCS) is a well-known technique developed to suppress multiple scattering contributions in correlation functions, which are inevitably involved when an optical laser is employed to investigate dynamics in a turbid system. Here, we demonstrate a proof-of-principle study of 3D PCS in the hard X-ray regime. We employ an X-ray optical cross-correlator to measure the dynamics of silica colloidal nanoparticles dispersed in polypropylene glycol. The obtained cross correlation functions show very good agreement with auto-correlation measurements. This demonstration provides the foundation for X-ray speckle-based studies of very densely packed soft matter systems.

### Measurement of Spin Dynamics in a Layered Nickelate Using X-Ray Photon Correlation Spectroscopy: Evidence for Intrinsic Destabilization of Incommensurate Stripes at Low Temperatures

*Alessandro Ricci, Nicola Poccia, Gaetano Campi, Shrawan Mishra, Leonard Müller, Boby Joseph, Bo Shi, Alexey Zozulya, Marcel Buchholz, Christoph Trabant, James C. T. Lee, Jens Viefhaus, Jeroen B. Goedkoop, Agustinus Agung Nugroho, Markus Braden, Sujoy Roy, Michael Sprung, and Christian Schüßler-Langeheine*

We study the temporal stability of stripe-type spin order in a layered nickelate with x-ray photon correlation spectroscopy and observe fluctuations on timescales of tens of minutes over a wide temperature range. These fluctuations show an anomalous temperature dependence: they slow down at intermediate temperatures and speed up on both heating and cooling. This behavior appears to be directly connected with spatial correlations: stripes fluctuate slowly when stripe correlation lengths are large and become faster when spatial correlations decrease. A low-temperature decay of nickelate stripe correlations, reminiscent of what occurs in cuprates as a result of a competition between stripes and superconductivity, hence occurs via loss of both spatial and temporal correlations.

### Nanosecond X-ray photon correlation spectroscopy using pulse time structure of a storage-ring source

*Wonhyuk Jo, Fabian Westermeier, Rustam Rysov, Olaf Leupold, Florian Schulz, Steffen Tober, Verena Markmann, Michael Sprung, Allesandro Ricci, Torsten Laurus, Allahgholi Aschkan, Alexander Klyuev, Ulrich Trunk, Heinz Graafsma, Gerhard Grübel, and Wojciech Roseker*

X-ray photon correlation spectroscopy (XPCS) is a routine technique to study slow dynamics in complex systems at storage-ring sources. Achieving nanosecond time resolution with the conventional XPCS technique is, however, still an experimentally challenging task requiring fast detectors and sufficient photon flux. Here, the result of a nanosecond XPCS study of fast colloidal dynamics is shown by employing an adaptive gain integrating pixel detector (AGIPD) operated at frame rates of the intrinsic pulse structure of the storage ring. Correlation functions from single-pulse speckle patterns with the shortest correlation time of 192 ns have been calculated. These studies provide an important step towards routine fast XPCS studies at storage rings.

### Enabling time-resolved 2D spatial-coherence measurements using the Fourier-analysis method with an integrated curved-grating beam monitor

*Kai Bagschik, Michael Schneider, Jochen Wagner, Ralph Buss, Matthias Riepp, Andre Philippi-Kobs, Leonard Müller, Wojciech Roseker, Florian Trinter, Moritz Hoesch, Jens Viefhaus, Stefan Eisebitt, Gerhard Grübel, Hans Peter Oepen, and Robert Frömter*

Direct 2D spatial-coherence measurements are increasingly gaining importance at synchrotron beamlines, especially due to present and future upgrades of synchrotron facilities to diffraction-limited storage rings. We present a method to determine the 2D spatial coherence of synchrotron radiation in a direct and particularly simple way by using the Fourier-analysis method in conjunction with curved gratings. Direct photon-beam monitoring provided by a curved grating circumvents the otherwise necessary separate determination of the illuminating intensity distribution required for the Fourier-analysis method. Hence, combining these two methods allows for time-resolved spatial-coherence measurements. As a consequence, spatial-coherence degradation effects caused by beamline optics vibrations, which is one of the key issues of state-of-the-art X-ray imaging and scattering beamlines, can be identified and analyzed.

### Observation of compact ferrimagnetic skyrmions in DyCo3 film

*K. Chen, D. Lott, A. Philippi-Kobs, M. Weigand, C. Luo, F. Radu*

Owing to the experimental discovery of magnetic skyrmions stabilized by the Dzyaloshinskii–Moriya and/or dipolar interactions in thin films, there is a recent upsurge of interest in magnetic skyrmions with antiferromagnetic spins in order to overcome the fundamental limitations inherent with skyrmions in ferromagnetic materials. Here, we report on the observation of compact ferrimagnetic skyrmions for the class of amorphous alloys consisting of 4f rare-earth and 3d transition-metal elements with perpendicular magnetic anisotropy, using a DyCo_{3} film, that are identified by combining X-ray magnetic scattering, scanning transmission X-ray microscopy, and Hall transport technique. These skyrmions, with antiparallel aligned Dy and Co magnetic moments and a characteristic core radius of about 40 nm, are formed during the nucleation and annihilation of the magnetic maze-like domain pattern exhibiting a topological Hall effect contribution. Our findings provide a promising route for fundamental research in the field of ferrimagnetic/antiferromagnetic spintronics towards practical applications.

### Double-pulse speckle contrast correlations with near Fourier transform limited free-electron laser light using hard X-ray split-and-delay

*Wojciech Roseker, Sooheyong Lee, Michael Walther, Felix Lehmkühler, Birgit Hankiewicz, Rustam Rysov, Stephan O. Hruszkewycz, G. Brian Stephenson, Mark Sutton, Paul H. Fuoss, Marcin Sikorski, Aymeric Robert, Sanghoon Song & Gerhard Grübel*

The ability to deliver two coherent X-ray pulses with precise time-delays ranging from a few femtoseconds to nanoseconds enables critical capabilities of probing ultra-fast phenomena in condensed matter systems at X-ray free electron laser (FEL) sources. Recent progress made in the hard X-ray split-and-delay optics developments now brings a very promising prospect for resolving atomic-scale motions that were not accessible by previous time-resolved techniques. Here, we report on characterizing the spatial and temporal coherence properties of the hard X-ray FEL beam after propagating through split-and-delay optics. Speckle contrast analysis of small-angle scattering measurements from nanoparticles reveals well-preserved transverse coherence of the beam. Measuring intensity fluctuations from successive X-ray pulses also reveals that only single or double temporal modes remain in the transmitted beam, corresponding to nearly Fourier transform limited pulses.

### Direct 2D spatial-coherence determination using the Fourier-analysis method: multi-parameter characterization of the P04 beamline at PETRA III

*Kai Bagschik, Jochen Wagner, Ralph Buß, Matthias Riepp, André Philippi-Kobs, Leonard Müller, Jens Buck, Florian Trinter, Frank Scholz, Jörn Seltmann, Moritz Hoesch, Jens Viefhaus, Gerhard Grübel, Hans Peter Oepen, and Robert Frömter*

We present a systematic 2D spatial-coherence analysis of the soft-X-ray beamline P04 at PETRA III for various beamline configurations. The influence of two different beam-defining apertures on the spatial coherence properties of the beam is discussed and optimal conditions for coherence-based experiments are found. A significant degradation of the spatial coherence in the vertical direction has been measured and sources of this degradation are identified and discussed. The Fourier-analysis method, which gives fast and simple access to the 2D spatial coherence function of the X-ray beam, is used for the experiment. Here, we exploit the charge scattering of a disordered nanodot sample allowing the use of arbitrary X-ray photon energies with this method.

### Observation of a Chirality-Induced Exchange-Bias Effect

*K. Chen, A. Philippi-Kobs, V. Lauter, A. Vorobiev, E. Dyadkina, V. Yu. Yakovchuk, S. Stolyar, D. Lott*

Chiral magnetism that manifests in the existence of skyrmions or chiral domain walls offers an alternative way for creating anisotropies in magnetic materials that might have large potential for application in future spintronic devices. Here we show experimental evidence for an alternative type of in-plane exchange-bias effect present at room temperature that is created from a chiral 90∘ domain wall at the interface of a ferrimagnetic-ferromagnetic Dy-Co/Ni-Fe bilayer system. The chiral interfacial domain wall forms due to the exchange coupling of Ni-Fe and Dy-Co at the interface and the presence of Dzyaloshinskii-Moriya interaction in the Dy-Co layer. As a consequence of the preferred chirality of the interfacial domain wall, the sign of the exchange-bias effect can be reversed by changing the perpendicular orientation of the Dy-Co magnetization. The chirality-created tunable exchange bias in Dy-Co/Ni-Fe is very robust against high in-plane magnetic fields (μ0H≤6T) and does not show any aging effects. Therefore, it overcomes the limitations of conventional exchange-bias systems.

### Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4

* Gaetano Campi, Nicola Poccia, Boby Joseph, Antonio Bianconi, Shrawan Mishra, James Lee, Sujoy Roy, Agustinus Agung Nugroho, Marcel Buchholz, Markus Braden, Christoph Trabant, Alexey Zozulya, Leonard Müller, Jens Viefhaus, Christian Schüßler-Langeheine 9, Michael Sprung and Alessandro Ricci *

In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below the 120 K onset temperature. We find that the spin-density-wave order shows the formation of nanoscale puddles with large spatial fluctuations. The nano-puddle density changes on the microscopic scale forming a multiscale phase separation extending from nanoscale to micron scale with scale-free distribution. Indeed spin-density-wave striped puddles are disconnected by spatial regions with negligible spin-density-wave order. The present work highlights the complex spatial nanoscale phase separation of spin stripes in nickelate perovskites and opens new perspectives of local spin order control by strain.

### Spatial and temporal pre-alignment of an X-ray split-and-delay unit by laser light interferometry

*Roseker, W. ; Lee, S. ; Walther, M. ; Rysov, R. ; Sprung, M. ; Gruebel, G.*

We present a novel experimental setup for performing a precise pre-alignment of a hard X-ray split-and-delay unit based on low coherence light interferometry and high-precision penta-prisms. A split-and-delay unit is a sophisticated perfect crystal-optics device that splits an incoming X-ray pulse into two sub-pulses and generates a controlled time-delay between them. While the availability of a split-and-delay system will make ultrafast time-correlation and X-ray pump-probe experiments possible at free-electron lasers, its alignment process can be very tedious and time-consuming due to its complex construction. By implementing our experimental setup at beamline P10 of PETRA III, we were able to reduce the time of alignment to less than 3 h. We also propose an alternate method for finding the zero-time delay crossing without the use of X-rays or pulsed laser sources. The successful demonstration of this method brings prospect for operating the split-and-delay systems under alignment-time-critical environments such as X-ray free electron laser facilities.

Review of scientific instruments 90(4), 045106 (2019) [10.1063/1.5089496]

### Towards ultrafast dynamics with split-pulse X-ray photon correlation spectroscopy at free electron laser sources

*Roseker, W. ; Hruszkewycz, S. O. ; Lehmkühler, F. ; Walther, M. ; Schulte-Schrepping, H. ; LEE, S. ; Osaka, T. ; Strüder, L. ;Hartmann, R. ; Sikorski, M. ; Song, S. ; Robert, A. ; Fuoss, P. H. ; Sutton, M. ; Stephenson, G. B. ; Grübel, G.*

One of the important challenges in condensed matter science is to understand ultrafast, atomic-scale fluctuations that dictate dynamic processes in equilibrium and non-equilibrium materials. Here, we report an important step towards reaching that goal by using a state-of-the-art perfect crystal based split-and-delay system, capable of splitting individual X-ray pulses andintroducing femtosecond to nanosecond time delays. We show the results of an ultrafast hard X-ray Photon Correlation Spectroscopy experiment at LCLS where split X-ray pulses were used to measure the dynamics of gold nanoparticles suspended in hexane. We show how reliable speckle contrast values can be extracted even from very low intensity free electron laser(FEL) speckle patterns by applying maximum likelihood fitting, thus demonstrating the potential of a split-and-delay approach for dynamics measurements at FEL sources. This will enable the characterization of equilibrium and, importantly also reversible non-equilibrium processes in atomically disordered materials.

Nature Communications 9(1), 1704 (2018) [10.1038/s41467-018-04178-9]

https://www.nature.com/articles/s41467-018-04178-9.epdf

### Note: Soft X-ray transmission polarizer based on ferromagnetic thin films

*Mueller, L. ; Hartmann, G. ; Schleitzer, S. ; Berntsen, M. H. ; Walther, M. ; Rysov, R. ; Roseker, W. ; Scholz, F. ; Seltmann, J. ;Glaser, L. ; Viefhaus, J. ; Mertens, K. ; Bagschik, K. ; Frömter, R. ; De Fanis, A. ; Shevchuk, I. ; Medjanik, K. ; Öhrwall, G. ;Oepen, H. P. ; Martins, M. ; Meyer, M. ; Grübel, G.*

A transmission polarizer for producing elliptically polarized soft X-ray radiation from linearly polarized light is presented. The setup is intended for use at synchrotron and free-electron laser beamlines that do not directly offer circularly polarized light for, e.g., X-ray magnetic circular dichroism (XMCD) measurements or holographic imaging. Here, we investigate the degree of ellipticity upon transmission of linearly polarized radiation through a cobalt thin film. The experiment was performed at a photon energy resonant to the Co L3-edge, i.e., 778 eV, and the polarization of the transmitted radiation was determined using a polarization analyzer that measures the directional dependence of photo electrons emitted from a gas target. Elliptically polarized radiation can be created at any absorption edge showing the XMCD effect by using the respective magnetic element.

Review of scientific instruments 89(3), 036103 - (2018) [10.1063/1.5018396]

### Employing soft x-ray resonant magnetic scattering to study domain sizes and anisotropy in Co/Pd multilayers

*K. Bagschik, R. Frömter, J. Bach, B. Beyersdorff, L. Müller, S. Schleitzer, M. Hårdensson Berntsen, C. Weier, R. Adam, J. Viefhaus, C. M. Schneider, G. Grübel, H. P. Oepen*

It is demonstrated that the magnetic diffraction pattern of the isotropic disordered maze pattern is well described utilizing a gamma distribution of domain sizes in a one-dimensional model. From the analysis, the mean domain size and the shape parameter of the distribution are obtained. The model reveals an average domain size that is significantly different from the value that is determined from the peak position of the structure factor in reciprocal space. As a proof of principle, a wedge-shaped (CotÅ/Pd10Å)8 multilayer film, that covers the thickness range of the spin-reorientation transition, has been used. By means of soft x-ray resonant magnetic scattering (XRMS) and imaging techniques the thickness-driven evolution of the magnetic properties of the cobalt layers is explored. It is shown that minute changes of the domain pattern concerning domain size and geometry can be investigated and analyzed due to the high sensitivity and lateral resolution of the XRMS technique. The latter allows for the determination of the magnetic anisotropies of the cobalt layers within a thickness range of a few angstroms.

### Spatial coherence determination from the Fourier analysis of a resonant soft X-ray magnetic speckle pattern

*K. Bagschik, R. Frömter, L. Müller, W. Roseker, J. Bach, P. Staeck, C. Thönnißen, S. Schleitzer, M. H. Berntsen, C. Weier, R. Adam, J. Viefhaus, C. M. Schneider, G. Grübel, H. P. Oepen*

We present a method to determine the two-dimensional spatial coherence of synchrotron radiation in the soft X-ray regime by analyzing the Fourier transform of the magnetic speckle pattern from a ferromagnetic film in a multidomain state. To corroborate the results, a Young’s double-pinhole experiment has been performed. The transverse coherence lengths in vertical and horizontal direction of both approaches are in a good agreement. The method presented here is simple and gives a direct access to the coherence properties of synchrotron radiation without nanostructured test objects.

### Indirect excitation of ultrafast demagnetization

*B. Vodungbo, et.al.*

Does the excitation of ultrafast magnetization require direct interaction between the photons of the optical pump pulse and the magnetic layer? Here, we demonstrate unambiguously that this is not the case. For this we have studied the magnetization dynamics of a ferromagnetic cobalt/palladium multilayer capped by an IR-opaque aluminum layer. Upon excitation with an intense femtosecond-short IR laser pulse, the film exhibits the classical ultrafast demagnetization phenomenon although only a negligible number of IR photons penetrate the aluminum layer. In comparison with an uncapped cobalt/palladium reference film, the initial demagnetization of the capped film occurs with a delayed onset and at a slower rate. Both observations are qualitatively in line with energy transport from the aluminum layer into the underlying magnetic film by the excited, hot electrons of the aluminum film. Our data thus confirm recent theoretical predictions.

### Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures

*P. Skopintsev, A. Singer, J. Bach, L. Müller, B. Beyersdorff, S. Schleitzer, O. Gorobtsov, A. Shabalin, R. P. Kurta, D. Dzhigaev, O. M. Yefanov, L. Glaser, A. Sakdinawat, G. Grübel, R. Frömter, H. P. Oepen, J. Viefhaus, I. A. Vartanyants*

A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double-pinhole experiments were conducted and showed good agreement.

### Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation

*C. von Korff Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, S. Eisebitt*

Ultrashort, coherent x-ray pulses of a free-electron laser are used to holographically image the magnetization dynamics within a magnetic domain pattern after creation of a localized excitation via an optical standing wave. We observe a spatially confined reduction of the magnetization within a couple of hundred femtoseconds followed by its slower recovery. Additionally, the experimental results show evidence of a spatial evolution of magnetization, which we attribute to ultrafast transport of nonequilibrium spin-polarized electrons for early times and to a fluence-dependent remagnetization rate for later times.

### Endstation for ultrafast magnetic scattering experiments at the free-electron laser in Hamburg

*L. Müller, C. Gutt, S. Streit-Nierobisch, M. Walther, S. Schaffert, B. Pfau, J. Geilhufe, F. Büttner, S. Flewett, C. M. Günther, S. Eisebitt, A. Kobs, M. Hille, D. Stickler, R. Frömter, H. P. Oepen, J. Lüning, G. Grübel*

An endstation for pump–probe small-angle X-ray scattering (SAXS) experiments at the free-electron laser in Hamburg (FLASH) is presented. The endstation houses a solid-state absorber, optical incoupling for pump–probe experiments, time zero measurement, sample chamber, and detection unit. It can be used at all FLASH beamlines in the whole photon energy range offered by FLASH. The capabilities of the setup are demonstrated by showing the results of resonant magnetic SAXS measurements on cobalt-platinum multilayer samples grown on freestanding Si3N4 membranes and pump-laser-induced grid structures in multilayer samples.

### Invited Article: Coherent imaging using seeded free-electron laser pulses with variable polarization: First results and research opportunities

*F. Capotondi, E. Pedersoli, N. Mahne, R. H. Menk, G. Passos, L. Raimondi, C. Svetina, G. Sandrin, M. Zangrando, M. Kiskinova, S. Bajt, M. Barthelmess, H. Fleckenstein, H. N. Chapman, J. Schulz, S. Schleitzer, L. Müller, C. Gutt, G. Grübel, et. al*

FERMI@Elettra, the first vacuum ultraviolet and soft X-ray free-electron laser (FEL) using by default a “seeded” scheme, became operational in 2011 and has been opened to users since December 2012. The parameters of the seeded FERMI FEL pulses and, in particular, the superior control of emitted radiation in terms of spectral purity and stability meet the stringent requirements for single-shot and resonant coherent diffraction imaging (CDI) experiments. The advantages of the intense seeded FERMI pulses with variable polarization have been demonstrated with the first experiments performed using the multipurpose experimental station operated at the diffraction and projection imaging (DiProI) beamline. The results reported here were obtained with fixed non-periodic targets during the commissioning period in 2012 using 20–32 nm wavelength range. They demonstrate that the performance of the FERMI FEL source and the experimental station meets the requirements of CDI, holography, and resonant magnetic scattering in both multi- and single-shot modes. Moreover, we present the first magnetic scattering experiments employing the fully circularly polarized FERMI pulses. The ongoing developments aim at pushing the lateral resolution by using shorter wavelengths provided by double-stage cascaded FERMI FEL-2 and probing ultrafast dynamic processes using different pump-probe schemes, including jitter-free seed laser pump or FEL-pump/FEL-probe with two color FEL pulses generated by the same electron bunch.

### Breakdown of the X-Ray Resonant Magnetic Scattering Signal during Intense Pulses of Extreme Ultraviolet Free-Electron-Laser Radiation

*L. Müller, C. Gutt, B. Pfau, S. Schaffert, J. Geilhufe, F. Büttner, J. Mohanty, S. Flewett, R. Treusch, S. Düsterer, H. Redlin, A. Al-Shemmary, M. Hille, A. Kobs, R. Frömter, H. P. Oepen, B. Ziaja, N. Medvedev, S.-K. Son, R. Thiele, R. Santra, et. al.*

We present results of single-shot resonant magnetic scattering experiments of Co/Pt multilayer systems using 100 fs long ultraintense pulses from an extreme ultraviolet (XUV) free-electron laser. An x-ray-induced breakdown of the resonant magnetic scattering channel during the pulse duration is observed at fluences of 5 J/cm2. Simultaneously, the speckle contrast of the high-fluence scattering pattern is significantly reduced. We performed simulations of the nonequilibrium evolution of the Co/Pt multilayer system during the XUV pulse duration. We find that the electronic state of the sample is strongly perturbed during the first few femtoseconds of exposure leading to an ultrafast quenching of the resonant magnetic scattering mechanism.

### Nanoscale spin reversal by non-local angular momentum transfer following ultrafast laser excitation in ferrimagnetic GdFeCo

*C. E. Graves, A. H. Reid, T. Wang, B. Wu, S. de Jong, K. Vahaplar, I. Radu, D. P. Bernstein, M. Messerschmidt, L. Müller, R. Coffee, M. Bionta, S. W. Epp, R. Hartmann, N. Kimmel, et. al.*

Ultrafast laser techniques have revealed extraordinary spin dynamics in magnetic materials that equilibrium descriptions of magnetism cannot explain. Particularly important for future applications is understanding non-equilibrium spin dynamics following laser excitation on the nanoscale, yet the limited spatial resolution of optical laser techniques has impeded such nanoscale studies. Here we present ultrafast diffraction experiments with an X-ray laser that probes the nanoscale spin dynamics following optical laser excitation in the ferrimagnetic alloy GdFeCo, which exhibits macroscopic all-optical switching. Our study reveals that GdFeCo displays nanoscale chemical and magnetic inhomogeneities that affect the spin dynamics. In particular, we observe Gd spin reversal in Gd-rich nanoregions within the first picosecond driven by the non-local transfer of angular momentum from larger adjacent Fe-rich nanoregions. These results suggest that a magnetic material’s microstructure can be engineered to control transient laser-excited spins, potentially allowing faster (~ 1 ps) spin reversal than in present technologies.

### Ultrafast optical demagnetization manipulates nanoscale spin structure in domain walls

*B. Pfau, S. Schaffert, L. Müller, C. Gutt, A. Al-Shemmary, F. Büttner, R. Delaunay, S. Düsterer, S. Flewett, R. Frömter, J. Geilhufe, E. Guehrs, C.M. Günther, R. Hawaldar, M. Hille, N. Jaouen, A. Kobs, K. Li, J. Mohanty, H. Redlin et. al*

During ultrafast demagnetization of a magnetically ordered solid, angular momentum has to be transferred between the spins, electrons, and phonons in the system on femto- and picosecond timescales. Although the intrinsic spin-transfer mechanisms are intensely debated, additional extrinsic mechanisms arising due to nanoscale heterogeneity have only recently entered the discussion. Here we use femtosecond X-ray pulses from a free-electron laser to study thin film samples with magnetic domain patterns. We observe an infrared-pump-induced change of the spin structure within the domain walls on the sub-picosecond timescale. This domain-topography-dependent contribution connects the intrinsic demagnetization process in each domain with spin-transport processes across the domain walls, demonstrating the importance of spin-dependent electron transport between differently magnetized regions as an ultrafast demagnetization channel. This pathway exists independent from structural inhomogeneities such as chemical interfaces, and gives rise to an ultrafast spatially varying response to optical pump pulses.

### Femtosecond Single-Shot Imaging of Nanoscale Ferromagnetic Order in Co/Pd Multilayers Using Resonant X-Ray Holography

*Tianhan Wang et al.*

We present the first single-shot images of ferromagnetic, nanoscale spin order taken with femtosecond x-ray pulses. X-ray-induced electron and spin dynamics can be outrun with pulses shorter than 80 fs in the investigated fluence regime, and no permanent aftereffects in the samples are observed below a fluence of 25 mJ/cm2. Employing resonant spatially muliplexed x-ray holography results in a low imaging threshold of 5 mJ/cm2. Our results open new ways to combine ultrafast laser spectroscopy with sequential snapshot imaging on a single sample, generating a movie of excited state dynamics.

## Project B4

### Probing the fluctuations of the optical properties in time-resolved spectroscopy

*F. Randi, M. Esposito, F. Giusti, F. Parmigiani, O. Misochko, D. Fausti, M. Eckstein*

We show that, in optical pump-probe experiments on bulk samples, the statistical distribution of the intensity of ultrashort light pulses after interaction with a nonequilibrium complex material can be used to measure the time-dependent noise of the current in the system. We illustrate the general arguments for a photoexcited Peierls material. The transient noise spectroscopy allows us to measure to what extent electronic degrees of freedom dynamically obey the fluctuation-dissipation theorem, and how well they thermalize during the coherent lattice vibrations. The proposed statistical measurement developed here provides a new general framework to retrieve dynamical information on the excited distributions in nonequilibrium experiments, which could be extended to other degrees of freedom of magnetic or vibrational origin.

### Nonequilibrium GW+EDMFT: Antiscreening and inverted populations from nonlocal correlations

*D. Golez, L. Boehnke, H. Strand, M. Eckstein, P. Werner*

We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the *GW* plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.

### Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

*Y. Murakami, N. Tsuji, M. Eckstein, P. Werner*

We perform a systematic analysis of the influence of phonon driving on the superconducting Holstein model coupled to heat baths by studying both the transient dynamics and the nonequilibrium steady state (NESS) in the weak and strong electron-phonon coupling regimes. Our study is based on the nonequilibrium dynamical mean-field theory, and for the NESS we present a Floquet formulation adapted to electron-phonon systems. The analysis of the phonon propagator suggests that the effective attractive interaction can be strongly enhanced in a parametric resonant regime because of the Floquet side bands of phonons. While this may be expected to enhance the superconductivity (SC), our fully self-consistent calculations, which include the effects of heating and nonthermal distributions, show that the parametric phonon driving generically results in a suppression or complete melting of the SC order. In the strong coupling regime, the NESS always shows a suppression of the SC gap, the SC order parameter, and the superfluid density as a result of the driving, and this tendency is most prominent at the parametric resonance. Using the real-time nonequilibrium DMFT formalism, we also study the dynamics towards the NESS, which shows that the heating effect dominates the transient dynamics, and SC is weakened by the external driving, in particular at the parametric resonance. In the weak coupling regime, we find that the SC fluctuations above the transition temperature are generally weakened under the driving. The strongest suppression occurs again around the parametric resonances because of the efficient energy absorption.

### Slowdown of the Electronic Relaxation Close to the Mott Transition

*Sharareh Sayyad and Martin Eckstein*

We investigate the time-dependent reformation of the quasiparticle peak in a correlated metal near the Mott transition, after the system is quenched into a hot electron state and equilibrates with an environment which is colder than the Fermi-liquid crossover temperature. Close to the transition, we identify a purely electronic bottleneck time scale, which depends on the spectral weight around the Fermi energy in the bad metallic phase in a nonlinear way. This time scale can be orders of magnitude larger than the bare and renormalized electronic hopping time, so that a separation of electronic and lattice time scales may break down. The results are obtained using nonequilibrium dynamical mean-field theory and a slave-rotor representation of the Anderson impurity model.

### Versatile approach to spin dynamics in correlated electron systems

*Malte Behrmann, Alexander I. Lichtenstein, Mikhail I. Katsnelson, and Frank Lechermann*

Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner-Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However, many experimental studies, e.g., of (de)magnetization processes, focus on itinerant local-moment materials, such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows us to treat nonequilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.

### Nonequilibrium itinerant-electron magnetism: a time-dependent mean-field theory

*A. Secchi, A. I. Lichtenstein, and M. I. Katsnelson*

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

### Photo-induced gap closure in an excitonic insulator

*D. Golež, P. Werner, M. Eckstein*

We study the dynamical phase transition out of an excitonic insulator phase after photoexcitation using a time-dependent extension of the self-consistent GW method. We connect the evolution of the photoemission spectra to the dynamics of the excitonic order parameter and identify two dynamical phase transition points marked by a slowdown in the relaxation: one critical point is connected with the trapping in a nonthermal state with reduced exciton density and the second corresponds to the thermal phase transition. The transfer of kinetic energy from the photoexcited carriers to the exciton condensate is shown to be the main mechanism for the gap melting. We analyze the low energy dynamics of screening, which strongly depends on the presence of the excitonic gap, and argue that it is difficult to interpret the static component of the screened interaction as the effective interaction of some low energy model. Instead we propose a phenomenological measure for the effective interaction which indicates that screening has minor effects on the low energy dynamics.

### Nonequilibrium self-energy functional approach to the dynamical Mott transition

*F. Hofmann, M. Eckstein, M. Potthoff*

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are found. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics, and therewith link the dynamical to the equilibrium Mott transition.

### Non-equilibrium variational-cluster approach to real-time dynamics in the Fermi-Hubbard model

*Felix Hofmann, Martin Eckstein, Michael Potthoff*

The non-equilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of non-equilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.

Journal of Physics: Conference Series, Volume 696, conference 1

### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}### Large-amplitude spin oscillations triggered by nonequilibrium strongly correlated t2g electrons

*M. Behrmann, F. Lechermann*

Laser-induced ultrafast (fs) magnetization experiments in antiferromagnets have recently attracted large attention, paving the road for inherently fast spin dynamics in the THz regime without invoking stray fields. The technical importance is emphasized by the rising new research field of antiferromagnetic (AFM) spintronics, where superexchange-dominated strongly correlated compounds provide an interesting materials playground. An intriguing question is whether the Coulomb interaction may be a key to control AFM order on ultrafast time scales. Therefore, we study (de)magnetization processes in a time-dependent multiorbital Hubbard model, focusing on t2g electrons in a wider doping range. Depending on filling, we reveal large-amplitude spin oscillations via interaction quenches from the antiferromagnetic or paramagnetic state. Nonequilibrium ultrafast spin-orientation effects in prominent correlated transition-metal oxides are therefrom predicted.

### Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

*D. Yudin, D. Hirschmeier, H. Hafermann, O. Eriksson, A. I. Lichtenstein, M. I. Katsnelson*

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands (“Fermi condensation”) within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1–0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

### Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium

*M. Behrmann, M. Fabrizio, F. Lechermann*

We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.

### Non-equilibrium magnetic interactions in strongly correlated systems

*A. Secchi, S. Brener, A. I. Lichtenstein, M. I. Katsnelson*

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

### Competing orders in Na_xCoO_2 from strong correlations on a two-particle level

*L. Boehnke, F. Lechermann*

Based on dynamical mean-field theory with a continuous-time quantum Monte-Carlo impurity solver, static as well as dynamic spin and charge susceptibilites for the phase diagram of the sodium cobaltate system Na$_x$CoO$_2$ are discussed. The approach includes important vertex contributions to the q-dependent two-particle response functions by means of a local approximation to the irreducible vertex function in the particle-hole channel. A single-band Hubbard model suffices to reveal several charge- and spin-instability tendencies in accordance with experiment, including the stabilization of an effective kagome sublattice close to x=0.67, without invoking the doping-dependent Na-potential landscape. The in-plane antiferromagnetic-to-ferromagnetic crossover is additionally verified by means of the computed Korringa ratio. Moreover an intricate high-energy mode in the transverse spin susceptiblity is revealed, pointing towards a strong energy dependence of the effective intersite exchange.

Phys. Rev. B 85, 115128 (2012)

http://arxiv.org/abs/1012.5943

## Project B5

### Spin Berry curvature of the Haldane model

*Simon Michel and Michael Potthoff*

The feedback of the geometrical Berry phase, accumulated in an electron system, on the slow dynamics of classical degrees of freedom is governed by the Berry curvature. Here, we study local magnetic moments, modeled as classical spins, which are locally exchange coupled to the (spinful) Haldane model for a Chern insulator. In the emergent equations of motion for the slow classical-spin dynamics there is a an additional anomalous geometrical spin torque, which originates from the corresponding spin Berry curvature. Due to the explicitly broken time-reversal symmetry, this is nonzero but usually small in a condensed-matter system. We develop the general theory and compute the spin Berry curvature, mainly in the limit of weak exchange coupling, in various parameter regimes of the Haldane model, particularly close to a topological phase transition and for spins coupled to sites at the zigzag edge of the model in a ribbon geometry. The spatial structure of the spin Berry curvature tensor, its symmetry properties, the distance dependence of its nonlocal elements, and further properties are discussed in detail. For the case of two classical spins, the effect of the geometrical spin torque leads to an anomalous non-Hamiltonian spin dynamics. It is demonstrated that the magnitude of the spin Berry curvature is decisively controlled by the size of the insulating gap, the system size, and the strength of local exchange coupling.

### Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model

*Robin Quade and Michael Potthoff*

The time-dependent state of a classical spin locally exchange coupled to an edge site of a Kane-Mele model in the topologically nontrivial phase is studied numerically by solving the full set of coupled microscopic equations of motion for the spin and the electron system. Dynamics in the long-time limit is accessible thanks to dissipative boundary conditions, applied to all but the zigzag edge of interest. We study means to control the state of the spin via transport of a spin-polarization cloud through the helical edge states. The cloud is formed at a distant edge site using a local magnetic field to inject an electron spin density and released by suddenly switching off the injection field. This basic process, consisting of spin injection, propagation of the spin-polarization cloud, and scattering of the cloud from the classical spin, can be used to steer the spin state in a controlled way. We find that the effect of a single basic process can be reverted to a high degree with a subsequent process. Furthermore, we show that by concatenating several basic injection-propagation-scattering processes, the spin state can be switched completely and that a full reversal can be achieved.

### Interacting Chern Insulator in Infinite Spatial Dimensions

*David Krüger and Michael Potthoff*

We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension *D* and demonstrate that the model remains well defined and nontrivial in the *D* → ∞ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a *continuum* of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semimetal states, which are unconventional already in the noninteracting case. Topological phases are characterized by a nonquantized Chern *density* replacing the Chern number as *D* → ∞.

### Non-Hamiltonian dynamics of indirectly coupled classical impurity spins

*Simon Michel and Michael Potthoff*

We discuss the emergence of an effective low-energy theory for the real-time dynamics of two classical impurity spins within the framework of a prototypical and purely classical model of indirect magnetic exchange: two classical impurity spins are embedded in a host system which consists of a finite number of classical spins localized on the sites of a lattice and interacting via a nearest-neighbor Heisenberg exchange. An effective low-energy theory for the slow impurity-spin dynamics is derived for the regime, where the local exchange coupling between impurity and host spins is weak. To this end, we apply the recently developed adiabatic spin dynamics (ASD) theory. Besides the Hamiltonian-like classical spin torques, the ASD additionally accounts for a novel topological spin torque that originates as a holonomy effect in the close-to-adiabatic-dynamics regime. It is shown that the effective low-energy precession dynamics cannot be derived from an effective Hamilton function and is characterized by a nonvanishing precession frequency even if the initial state deviates only slightly from a ground state. The effective theory is compared to the fully numerical solution of the equations of motion for the whole system of impurity and host spins to identify the parameter regime where the adiabatic effective theory applies. Effective theories beyond the adiabatic approximation must necessarily include dynamic host degrees of freedom and go beyond the idea of a simple indirect magnetic exchange. We discuss an example of a generalized constrained spin dynamics which does improve the description but also fails for certain geometrical setups.

### Long-time relaxation dynamics of a spin coupled to a Chern insulator

*Michael Elbracht and Michael Potthoff*

The relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model, is studied numerically by solving the full set of equations of motion. A Lindblad coupling of a few sites at the opposite edge to an absorbing bath ensures that convergence with respect to the system size is achieved with only a moderate number of core sites. This allows us to numerically exactly study the long-time limit and to determine the parameter regimes where spin relaxation takes place. Corresponding dynamical phase diagrams for the topologically trivial and the nontrivial cases are constructed. The dynamical phase boundaries, the role of the topological edge state, and its internal Zeeman splitting for the spin-relaxation process, as well as incomplete spin relaxation on long time scales can be explained within the framework of a renormalized linear-response approach when explicitly taking retardation effects and nonequilibrium spin-exchange processes into account.

### Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions

*Michael Elbracht and Michael Potthoff*

The relaxation time of a classical spin interacting with a large conduction-electron system is computed for a weak magnetic field, which initially drives the spin out of equilibrium. We trace the spin and the conduction-electron dynamics on a timescale which exceeds the characteristic electronic scale that is set by the inverse nearest-neighbor hopping by more than five orders of magnitude. This is achieved with a construction of absorbing boundary conditions, which employs a generalized Lindblad master-equation approach to couple the edge sites of the conduction-electron tight-binding model to an external bath. The failure of the standard Lindblad approach to absorbing boundaries is traced back to artificial excitations initially generated due to the coupling to the bath. This can be cured by introducing Lindblad parameter matrices and by fixing those matrices to perfectly suppress initial-state artifacts as well as reflections of physical excitations propagating to the system boundaries. Numerical results are presented and discussed for generic one-dimensional models of the electronic structure.

### Topological spin torque emerging in classical-spin systems with different time scales

*M. Elbracht, S. Michel, M. Potthoff*

In classical spin systems with two largely different inherent timescales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of freedom and demonstrate that this generally includes a topological spin torque. This torque gives rise to anomalous real-time dynamics. It derives from the holonomic constraints defining the fast-spin configuration space and is given in terms of a topological charge density which becomes a quantized homotopy invariant when integrated.

### Magnetic Doublon Bound States in the Kondo Lattice Model

R. Rausch, M. Potthoff, N. Kawakami

We present a novel pairing mechanism for electrons, mediated by magnons. These paired bound states are termed “magnetic doublons.” Applying numerically exact techniques (full diagonalization and the density-matrix renormalization group, DMRG) to the Kondo lattice model at strong exchange coupling * J* for different fillings and magnetic configurations, we demonstrate that magnetic doublon excitations exist as composite objects with very weak dispersion. They are highly stable, support a novel “inverse” colossal magnetoresistance and potentially other effects.

### Pump-probe Auger-electron spectroscopy of Mott insulators

*R. Rausch, M. Potthoff*

In high-resolution core-valence-valence (CVV) Auger electron spectroscopy from the surface of a solid at thermal equilibrium, the main correlation satellite, visible in the case of strong valence-electron correlations, corresponds to a bound state of the two holes in the final state of the CVV Auger process. We discuss the physical significance of this satellite in nonequilibrium pump-probe Auger spectroscopy by numerical analysis of a single-band Hubbard-type model system, including core states and a continuum of high-energy scattering states. It turns out that the spectrum of the photo-doped system, due to the increased double occupancy, shares features with the equilibrium spectrum at higher fillings. The pumping of doublons can be watched when working with overlapping pulses at short ** Δt**. For larger pump-probe delays

**and on the typical femtosecond timescale for electronic relaxation processes, spectra are hardly**

*Δt***dependent, reflecting the high stability of bound two-hole states for strong Hubbard**

*Δt***. We argue that taking into account the spatial expansion of single-particle orbitals when these are doubly occupied, as described by the dynamical Hubbard model, produces an oscillation of the barycenter of the satellite as a function of**

*U***. Pump-probe Auger-electron spectroscopy is thus highly sensitive to dynamical screening of the Coulomb interaction.**

*Δt*### Phase diagram of the Kondo model on the zigzag ladder

*M. Peschke, L.-M. Woelk, M. Potthoff*

The effect of next-nearest-neighbor hopping * t_{2}* on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite

*, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that*

**t**_{2}**at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong**

*t*_{2}**, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker**

*J***, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak**

*J***, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.**

*J*### Non-collinear spin states in bottom-up fabricated atomic chains

*M. Steinbrecher, R. Rausch, Khai Ton That, J. Hermenau, A.A. Khajetoorians, M. Potthoff, R. Wiesendanger, J. Wiebe*

Non-collinear spin states with unique rotational sense, such as chiral spin-spirals, are recently heavily investigated because of advantages for future applications in spintronics and information technology and as potential hosts for Majorana Fermions when coupled to a superconductor. Tuning the properties of such spin states, e.g., the rotational period and sense, is a highly desirable yet difficult task. Here, we experimentally demonstrate the bottom-up assembly of a spin-spiral derived from a chain of iron atoms on a platinum substrate using the magnetic tip of a scanning tunneling microscope as a tool. We show that the spin-spiral is induced by the interplay of the Heisenberg and Dzyaloshinskii-Moriya components of the Ruderman-Kittel-Kasuya-Yosida interaction between the iron atoms. The relative strengths and signs of these two components can be adjusted by the interatomic iron distance, which enables tailoring of the rotational period and sense of the spin-spiral.

### Anomalous spin precession under a geometrical torque

*C. Stahl, M. Potthoff*

Precession and relaxation predominantly characterize the real-time dynamics of a spin driven by a magnetic field and coupled to a large Fermi sea of conduction electrons. We demonstrate an anomalous precession with frequency higher than the Larmor frequency or with inverted orientation in the limit where the electronic motion adiabatically follows the spin dynamics. For a classical spin, the effect is traced back to a geometrical torque resulting from a finite spin Berry curvature.

### Enforcing conservation laws in nonequilibrium cluster perturbation theory

*C. Gramsch, M. Potthoff*

Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.

### Filling-dependent doublon dynamics in the one-dimensional Hubbard model

*R. Rausch and M. Potthoff*

The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction U in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong U, two holes at the same site form a compound object whose decay is impeded by the lack of phase space. Still, a partial decay is possible on an extremely short time scale where phase-space arguments do not yet apply. We argue that the initial decay and the resulting intermediate state are relevant for experiments performed with ultracold atoms loaded into an optical lattice as well as for (time-resolved) CVV Auger-electron spectroscopy. The detailed discussion comprises the mixed ballistic-diffusive real-time propagation of the doublon through the lattice, its partial decay on the short time scale as a function of filling and interaction strength, as well as the analysis of the decay products, which are metastable on the intermediate time scale that is numerically accessible and which show up in the two-hole excitation (Auger) spectrum. The ambivalent role of singly occupied sites is key to understanding the doublon physics; for high fillings, ground-state configurations with single occupancies are recognized to strongly relax the kinematic constraints and to open up decay channels. For fillings close to half-filling, however, their presence actually blocks the doublon decay. Finally, the analysis of the continua in the two-hole spectrum excludes a picture where the doublon decays into unbound electron holes for generic fillings, different from the limiting case of the completely filled band. We demonstrate that the decay products as well as the doublon propagation should rather be understood in terms of Bethe ansatz eigenstates.

### Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

*M. Sayad, R. Rausch, M. Potthoff*

Spin dynamics in the Kondo impurity model, initiated by suddenly switching the direction of a local magnetic field, is studied by means of the time-dependent density-matrix renormalization group. Quantum effects are identified by systematic computations for different spin quantum numbers S and by comparing with tight-binding spin-dynamics theory for the classical-spin Kondo model. We demonstrate that, besides the conventional precessional motion and relaxation, the quantum-spin dynamics shows nutation, similar to a spinning top. Opposed to semiclassical theory, however, the nutation is efficiently damped on an extremely short time scale. The effect is explained in the large-S limit as quantum dephasing of the eigenmodes in an emergent two-spin model that is weakly entangled with the bulk of the system. We argue that, apart from the Kondo effect, the damping of nutational motion is essentially the only characteristics of the quantum nature of the spin. Qualitative agreement between quantum and semiclassical spin dynamics is found down to S=1/2.

### Nonequilibrium self-energy functional approach to the dynamical Mott transition

*F. Hofmann, M. Eckstein, M. Potthoff*

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are found. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics, and therewith link the dynamical to the equilibrium Mott transition.

### One-step theory of two-photon photoemission

*J. Braun, R. Rausch, M. Potthoff, H. Ebert*

A theoretical frame for two-photon photoemission is derived from the general theory of pump-probe photoemission, assuming that not only the probe but also the pump pulse is sufficiently weak. This allows us to use a perturbative approach to compute the lesser Green function within the Keldysh formalism. Two-photon photoemission spectroscopy is a widely used analytical tool to study nonequilibrium phenomena in solid materials. Our theoretical approach aims at a material-specific, realistic, and quantitative description of the time-dependent spectrum based on a picture of effectively independent electrons as described by the local-density approximation in band-structure theory. To this end we follow Pendry's one-step theory of the photoemission process as close as possible and heavily make use of concepts of relativistic multiple-scattering theory, such as the representation of the final state by a time-reversed low-energy electron diffraction state. The formalism allows for a quantitative calculation of the time-dependent photocurrent for moderately correlated systems like simple metals or more complex compounds like topological insulators. An application to the Ag(100) surface is discussed in detail.

### Relaxation of a classical spin coupled to a strongly correlated electron system

*M. Sayad, R. Rausch, M. Potthoff*

A classical spin which is antiferromagnetically coupled to a system of strongly correlated conduction electrons is shown to exhibit unconventional real-time dynamics which cannot be described by Gilbert damping. Depending on the strength of the local Coulomb interaction U, the two main electronic dissipation channels, namely transport of excitations via correlated hopping and via excitations of correlation-induced magnetic moments, become active on largely different time scales. We demonstrate that correlations can lead to a strongly suppressed relaxation which so far has been observed in purely electronic systems only and which is governed here by proximity to the divergent magnetic time scale in the infinite-U limit.

### Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization

*F. Hofmann, M. Potthoff*

The time-dependent Mott transition in a periodic Anderson model with off-site, nearest-neighbor hybridization is studied within the framework of nonequilibrium self-energy functional theory. Using the two-site dynamical-impurity approximation, we compute the real-time dynamics of the optimal variational parameter and of different observables initiated by sudden quenches of the Hubbard-U and identify the critical interaction. The time-dependent transition is orbital selective, i.e., in the final state, reached in the long-time limit after the quench to the critical interaction, the Mott gap opens in the spectral function of the localized orbitals only. We discuss the dependence of the critical interaction and of the final-state effective temperature on the hybridization strength and point out the various similarities between the nonequilibrium and the equilibrium Mott transition. It is shown that these can also be smoothly connected to each other by increasing the duration of a U-ramp from a sudden quench to a quasi-static process. The physics found for the model with off-site hybridization is compared with the dynamical Mott transition in the single-orbital Hubbard model and with the dynamical crossover found for the real-time dynamics of the conventional Anderson lattice with on-site hybridization.

### Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

*R. Rausch, M. Potthoff*

Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon–hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three- and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved four-hole spectrum at n = 2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon–doublon continuum at a critical wave vector. For all fillings with $n\gt 1$, the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the 'hidden' charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices.

### Non-equilibrium variational-cluster approach to real-time dynamics in the Fermi-Hubbard model

*Felix Hofmann, Martin Eckstein, Michael Potthoff*

The non-equilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of non-equilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.

Journal of Physics: Conference Series, Volume 696, conference 1

### Lehmann representation of the nonequilibrium self-energy

*C. Gramsch, M. Potthoff*

It is shown that the nonequilibrium self-energy of an interacting lattice-fermion model has a unique Lehmann representation. Based on the construction of a suitable noninteracting effective medium, we provide an explicit and numerically practicable scheme to construct the Lehmann representation for the self-energy, given the Lehmann representation of the single-particle nonequilibrium Green's function. This is of particular importance for an efficient numerical solution of Dyson's equation in the context of approximations where the self-energy is obtained from a reference system with a small Hilbert space. As compared to conventional techniques to solve Dyson's equation on the Keldysh contour, the effective-medium approach allows us to reach a maximum propagation time, which can be several orders of magnitude longer. This is demonstrated explicitly by choosing the nonequilibrium cluster-perturbation theory as a simple approach to study the long-time dynamics of an inhomogeneous initial state after a quantum quench in the Hubbard model on a 10×10 square lattice. We demonstrate that the violation of conservation laws is moderate for weak Hubbard interaction and that the cluster approach is able to describe prethermalization physics.

### Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation

*M. Sayad, M. Potthoff*

The real-time dynamics of a classical spin in an external magnetic field and local exchange coupled to an extended one-dimensional system of non-interacting conduction electrons is studied numerically. Retardation effects in the coupled electron-spin dynamics are shown to be the source for the relaxation of the spin in the magnetic field. Total energy and spin is conserved in the non-adiabatic process. Approaching the new local ground state is therefore accompanied by the emission of dispersive wave packets of excitations carrying energy and spin and propagating through the lattice with Fermi velocity. While the spin dynamics in the regime of strong exchange coupling J is rather complex and governed by an emergent new time scale, the motion of the spin for weak J is regular and qualitatively well described by the Landau–Lifschitz–Gilbert (LLG) equation. Quantitatively, however, the full quantum–classical hybrid dynamics differs from the LLG approach. This is understood as a breakdown of weak-coupling perturbation theory in J in the course of time. Furthermore, it is shown that the concept of the Gilbert damping parameter is ill-defined for the case of a one-dimensional system.

### Crossover from conventional to inverse indirect magnetic exchange in the depleted Anderson lattice

*M. W. Aulbach, I. Titvinidze, M. Potthoff*

We investigate the finite-temperature properties of an Anderson lattice with regularly depleted impurities. The physics of this model is ruled by two different magnetic exchange mechanisms: conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at weak hybridization strength V and an inverse indirect magnetic exchange (IIME) at strong V, both favoring a ferromagnetic ground state. The stability of ferromagnetic order against thermal fluctuations is systematically studied by static mean-field theory for an effective low-energy spin-only model emerging perturbatively in the strong-coupling limit as well as by dynamical mean-field theory for the full model. The Curie temperature is found at a maximum for a half-filled conduction band and at intermediate hybridization strengths in the crossover regime between RKKY and IIME.

### One-step theory of pump-probe photoemission

*J. Braun, R. Rausch, M. Potthoff, J. Minár, H. Ebert*

A theoretical framework for pump-probe photoemission is presented. The approach is based on a general formulation using the Keldysh formalism for the lesser Green's function to describe the real-time evolution of the electronic degrees of freedom in the initial state after a strong pump pulse that drives the system out of equilibrium. The final state is represented by a time-reversed low-energy electron-diffraction state. Our one-step description is related as close as possible to Pendry's original formulation of the photoemission process. The formalism allows for a quantitative calculation of time-dependent photocurrent for simple metals where a picture of effectively independent electrons is assumed to be reliable. The theory is worked out for valence- and core-electron excitations. It comprises the study of different relativistic effects as a function of the pump-probe delay.

### Cooperation of different exchange mechanisms in confined magnetic systems

*A. Schwabe, M. Hänsel, M. Potthoff*

The diluted Kondo lattice model is investigated at strong antiferromagnetic local exchange couplings J, where almost-local Kondo clouds drastically restrict the motion of conduction electrons, giving rise to the possibility of quantum localization of conduction electrons for certain geometries of impurity spins. This localization may lead to the formation of local magnetic moments in the conduction-electron system, and the inverse indirect magnetic exchange (IIME) provided by virtual excitations of the Kondo singlets couples those local moments to the remaining electrons. Exemplarily, we study the one-dimensional two-impurity Kondo model with impurity spins near the chain ends, which supports the formation of conduction-electron magnetic moments at the edges of the chain for sufficiently strong J. Employing degenerate perturbation theory as well as analyzing spin gaps numerically by means of the density-matrix renormalization group, it is shown that the low-energy physics of the model can be well captured within an effective antiferromagnetic Ruderman–Kittel–Kasuya–Yosida-like two-spin model (“RKKY from IIME”) or within an effective central-spin model, depending on edge-spin distance and system size.

### Nonequilibrium self-energy functional theory

*F. Hofmann, M. Eckstein, E. Arrigoni, M. Potthoff*

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by starting from a reformulation of the original equilibrium theory in terms of double-time Green's functions on the Keldysh-Matsubara contour. With the help of a generalized Luttinger-Ward functional, we construct a functional Ω̂[Σ] which is stationary at the physical (nonequilibrium) self-energy Σ and which yields the grand potential of the initial thermal state Ω at the physical point. Nonperturbative approximations can be defined by specifying a reference system that serves to generate trial self-energies. These self-energies are varied by varying the reference system's one-particle parameters on the Keldysh-Matsubara contour. In the case of thermal equilibrium, this approach reduces to the conventional SFT. Contrary to the equilibrium theory, however, “unphysical” variations, i.e., variations that are different on the upper and the lower branches of the Keldysh contour, must be considered to fix the time dependence of the optimal physical parameters via the variational principle. Functional derivatives in the nonequilibrium SFT Euler equation are carried out analytically to derive conditional equations for the variational parameters that are accessible to a numerical evaluation via a time-propagation scheme. Approximations constructed by means of the nonequilibrium SFT are shown to be inherently causal, internally consistent, and to respect macroscopic conservation laws resulting from gauge symmetries of the Hamiltonian. This comprises the nonequilibrium dynamical mean-field theory but also dynamical-impurity and variational-cluster approximations that are specified by reference systems with a finite number of degrees of freedom. In this way, nonperturbative and consistent approximations can be set up, the numerical evaluation of which is accessible to an exact-diagonalization approach.

### Dynamical symmetry between spin and charge excitations studied by a plaquette mean-field approach in two dimensions

*P. Jurgenowski, M. Potthoff*

The real-time dynamics of local occupation numbers in a Hubbard model on a 6×6 square lattice is studied by means of the nonequilibrium generalization of the cluster-perturbation theory. The cluster approach is adapted to studies of two-dimensional lattice systems by using concepts of multiple-scattering theory and a component decomposition of the nonequilibrium Green's function on the Keldysh-Matsubara contour. We consider “classical” initial states formed as tensor products of states on 2×2 plaquettes and trace the effects of the interplaquette hopping in the final-state dynamics. Two different initially excited states are considered on an individual plaquette, a fully polarized staggered spin state (Néel) and a fully polarized charge-density wave (CDW). The final-state dynamics is constrained by a dynamical symmetry; i.e., the time-evolution operator and certain observables are invariant under an antiunitary transformation composed of time reversal, an asymmetric particle-hole, and a staggered sign transformation. We find an interesting interrelation between this dynamical symmetry and the separation of energy and time scales: In the case of a global excitation with all plaquettes excited, the initial Néel and the initial CDW states are linked by the transformation. This prevents an efficient relaxation of the CDW state on the short time scale governing the dynamics of charge degrees of freedom. Contrarily, the CDW state is found to relax much faster than the Néel state in the case of a local excitation on a single plaquette where the symmetry relation between the two states is broken by the coupling to the environment.

### Inverse indirect magnetic exchange

*A. Schwabe, I. Titvinidze, M. Potthoff*

Magnetic moments strongly coupled to the spins of conduction electrons in a nanostructure can confine the conduction-electron motion due to scattering at almost localized Kondo singlets. We study the resulting local-moment formation in the conduction-electron system and the magnetic exchange coupling mediated by the Kondo singlets. Its distance dependence is oscillatory and induces robust ferro- or antiferromagnetic order in multi-impurity systems.

### Doublon dynamics in the extended Fermi-Hubbard model

*F. Hofmann, M. Potthoff*

### Krylov-space approach to the equilibrium and nonequilibrium single-particle Green's function

*M. Balzer, N. Gdaniec, M.Potthoff*

### Nonequilibrium cluster perturbation theory

*M. Balzer, M. Potthoff*

## Project B6

### Ultrafast momentum imaging of pseudospin-flip excitations in graphene

*S. Aeschlimann, R. Krause, M. Chávez-Cervantes, H. Bromberger, R. Jago, E. Mali, A. Al-Temimy, C. Coletti, A. Cavalleri, I. Gierz*

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photoexcited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy, and in-plane momentum. We first show that the rapidly-established quasithermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photoexcited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photocontrol experiments and optoelectronic device applications.

### Enhanced electron-phonon coupling in graphene with periodically distorted lattice

*E. Pomarico, M. Mitrano, H. Bromberger, M. A. Sentef, A. Al-Temimy, C. Coletti, A. Stohr, S. Link, U. Starke, C. Cacho, R. Chapman, E. Springate, A. Cavalleri, I. Gierz*

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge, and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here, we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically active in-plane bond stretching vibrations with femtosecond midinfrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. First, terahertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Second, the relaxation rate of hot quasiparticles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient threefold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

### Electronic-structural dynamics in graphene

*A. Cavalleri, I. Gierz*

We review our recent time- and angle-resolved photoemission spectroscopy experiments, which measure the transient electronic structure of optically driven graphene. For pump photon energies in the near infrared (ℏω_{pump}=950 meV), we have discovered the formation of a population-inverted state near the Dirac point, which may be of interest for the design of THz lasing devices and optical amplifiers. At lower pump photon energies (ℏω_{pump}<400 meV), for which interband absorption is not possible in doped samples, we find evidence for free carrier absorption. In addition, when mid-infrared pulses are made resonant with an infrared-active in-plane phonon of bilayer graphene (ℏω_{pump}=200 meV), a transient enhancement of the electron-phonon coupling constant is observed, providing interesting perspective for experiments that report light-enhanced superconductivity in doped fullerites in which a similar lattice mode was excited. All the studies reviewed here have important implications for applications of graphene in optoelectronic devices and for the dynamical engineering of electronic properties with light.

Structural Dynamics 3, 051301 (2016)

### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}## Project B7

### Terahertz amplifiers based on gain reflectivity in cuprate superconductors

*Guido Homann, Jayson G. Cosme, and Ludwig Mathey*

We demonstrate that parametric driving of suitable collective modes in cuprate superconductors results in a reflectivity *R*>1 for frequencies in the low terahertz regime. We propose to exploit this effect for the amplification of coherent terahertz radiation in a laserlike fashion. As an example, we consider the optical driving of Josephson plasma oscillations in a monolayer cuprate at a frequency that is blue-detuned from the Higgs frequency. Analogously, terahertz radiation can be amplified in a bilayer cuprate by driving a phonon resonance at a frequency slightly higher than the upper Josephson plasma frequency. We show this by simulating a driven-dissipative* U*(1) lattice gauge theory on a three-dimensional lattice, encoding a bilayer structure in the model parameters. We find a parametric amplification of terahertz radiation at zero and nonzero temperature.

### Terahertz phase slips in striped La2−xBaxCuO4

*D. Fu, D. Nicoletti, M. Fechner, M. Buzzi, G. D. Gu, and A. Cavalleri*

Interlayer transport in high-*T _{C}* cuprates is mediated by superconducting tunneling across the C

_{u}O

_{2}planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value

*I*. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La

_{C}_{2−x}Ba

_{x}C

_{u}O

_{4}(LBCO) also above

*T*for doping values near

_{C}*x*=1/8 and interpreted as an indication of superfluidity in the stripe phase. Here, electric-field-induced second harmonic is used to study the dynamics of time-dependent interlayer voltages when LBCO is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunneling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2π Josephson phase slips, which near x=1/8 are observed both below and above

*T*. These results document a regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.

_{C}### Phase Diagram for Light-Induced Superconductivity in κ−(ET)2−X

*M. Buzzi, D. Nicoletti, S. Fava, G. Jotzu, K. Miyagawa, K. Kanoda, A. Henderson, T. Siegrist, J. A. Schlueter, M.-S. Nam, A. Ardavan, and A. Cavalleri*

Resonant optical excitation of certain molecular vibrations in *κ*−(BEDT−TTF)_{2}Cu[N(CN)_{2}]Br has been shown to induce transient superconductinglike optical properties at temperatures far above equilibrium *T _{c}*. Here, we report experiments across the bandwidth-tuned phase diagram of this class of materials, and study the Mott insulator

*κ*−(BEDT−TTF)

_{2}Cu[N(CN)

_{2}]Cl and the metallic compound

*κ*−(BEDT−TTF)

_{2}Cu(NCS)

_{2}. We find nonequilibrium photoinduced superconductivity only in

*κ*−(BEDT−TTF)

_{2}Cu[N(CN)

_{2}]Br, indicating that the proximity to the Mott insulating phase and possibly the presence of preexisting superconducting fluctuations are prerequisites for this effect.

### Higgs-Mediated Optical Amplification in a Nonequilibrium Superconductor

*Michele Buzzi, Gregor Jotzu, Andrea Cavalleri, J. Ignacio Cirac, Eugene A. Demler, Bertrand I. Halperin, Mikhail D. Lukin, Tao Shi, Yao Wang, and Daniel Podolsky*

We propose a novel nonequilibrium phenomenon, through which a prompt quench from a metal to a transient superconducting state can induce large oscillations of the order parameter amplitude. We argue that this oscillating mode acts as a source of parametric amplification of the incident radiation. We report experimental results on optically driven K_{3}C_{60} that are consistent with these predictions. The effect is found to disappear when the onset of the excitation becomes slower than the Higgs-mode period, consistent with the theory proposed here. These results open new possibilities for the use of collective modes in many-body systems to induce nonlinear optical effects.

### Higgs mode mediated enhancement of interlayer transport in high-Tc cuprate superconductors

*Guido Homann, Jayson G. Cosme, Junichi Okamoto, and Ludwig Mathey*

We put forth a mechanism for enhancing the interlayer transport in cuprate superconductors, by optically driving plasmonic excitations along the c axis with a frequency that is blue-detuned from the Higgs frequency. The plasmonic excitations induce a collective oscillation of the Higgs field which induces a parametric enhancement of the superconducting response, as we demonstrate with a minimal analytical model. Furthermore, we perform simulations of a particle-hole symmetric *U*(1) lattice gauge theory and find good agreement with our analytical prediction. We map out the renormalization of the interlayer coupling as a function of the parameters of the optical field and demonstrate that the Higgs mode mediated enhancement can be larger than 50%.

### Parametric resonance of Josephson plasma waves: A theory for optically amplified interlayer superconductivity in YBa2Cu3O6+x

*Marios H. Michael, Alexander von Hoegen, Michael Fechner, Michael Först, Andrea Cavalleri, and Eugene Demler*

Nonlinear interactions between collective modes play a definitive role in far out of equilibrium dynamics of strongly correlated electron systems. Understanding and utilizing these interactions is crucial to photocontrol of quantum many-body states. One of the most surprising examples of strong mode coupling is the interaction between apical oxygen phonons and Josephson plasmons in bilayer **YBa _{2}Cu_{3}O_{6+x}** superconductors. Experiments by Hu et al. [Nat. Mater. 13, 705 (2014)] and Kaiser et al. [Phys. Rev. B 89, 184516 (2014)] showed that below

**, photoexcitation of phonons leads to enhancement and frequency shifts of Josephson plasmon edges, while above**

_{Tc}*, photoexcited phonons induce plasmon edges even when there are no discernible features in the equilibrium reflectivity spectrum. Recent experiments by von Hoegen et al. (arXiv:1911.08284) also observed parametric generation of Josephson plasmons from photoexcited phonons both below*

**Tc***and in the pseudogap phase. In this paper, we present a theoretical model of three-wave phonon-plasmon interaction arising from changes of the in-plane superfluid stiffness caused by the apical oxygen motion. Analysis of the parametric instability of plasmons based on this model gives frequencies of the most unstable plasmons that are in agreement with experimental observations. We also discuss how strong parametric excitation of Josephson plasmons can explain pump-induced changes in the terahertz reflectivity of*

**Tc****YBa**in the superconducting state, including frequency shifts and sharpening of Josephson plasmon edges, as well as appearance of a new peak around 2 THz. An interesting feature of this model is that overdamped Josephson plasmons do not give any discernible features in reflectivity in equilibrium, but can develop plasmon edges when parametrically excited. We suggest that this mechanism explains photoinduced plasmon edges in the pseudogap phase of

_{2}Cu_{3}O_{6+x}**YBa**.

_{2}Cu_{3}O_{6+x}### Photo-induced electron pairing in a driven cavity

*Hongmin Gao, Frank Schlawin, Michele Buzzi, Andrea Cavalleri, Dieter Jaksch*

We demonstrate how virtual scattering of laser photons inside a cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that laser light that is red (blue) detuned from the cavity yields attractive (repulsive) interactions whose strength is proportional to the laser intensity. Furthermore, we find that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, laser-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results provide a novel route for engineering electron interactions in a wide range of two-dimensional materials including AB-stacked bilayer graphene and the conducting interface between LaAlO** _{3} **and SrTiO

**.**

_{3}### Photomolecular High-Temperature Superconductivity

*M. Buzzi, D. Nicoletti, M. Fechner, N. Tancogne-Dejean, M. A. Sentef, A. Georges, T. Biesner, E. Uykur, M. Dressel, A. Henderson, T. Siegrist, J. A. Schlueter, K. Miyagawa, K. Kanoda, M.-S. Nam, A. Ardavan, J. Coulthard, J. Tindall, F. Schlawin, D. Jaksch, and A. Cavalleri*

The properties of organic conductors are often tuned by the application of chemical or external pressure, which change orbital overlaps and electronic bandwidths while leaving the molecular building blocks virtually unperturbed. Here, we show that, unlike any other method, light can be used to manipulate the local electronic properties at the molecular sites, giving rise to new emergent properties. Targeted molecular excitations in the charge-transfer salt *κ*−(BEDT−TTF)_{2}Cu[N(CN)_{2}]Br induce a colossal increase in carrier mobility and the opening of a superconducting optical gap. Both features track the density of quasiparticles of the equilibrium metal and can be observed up to a characteristic coherence temperature *T*^{∗}≃50 K, far higher than the equilibrium transition temperature *T _{C}*=12.5 K. Notably, the large optical gap achieved by photoexcitation is not observed in the equilibrium superconductor, pointing to a light-induced state that is different from that obtained by cooling. First-principles calculations and model Hamiltonian dynamics predict a transient state with long-range pairing correlations, providing a possible physical scenario for photomolecular superconductivity.

### Higgs time crystal in a high-Tc superconductor

*G. Homann, J. G. Cosme, and L. Mathey*

We propose to induce a time-crystalline state in a high-*T _{c}* superconductor, by optically driving a sum resonance of the Higgs mode and a Josephson plasma mode. The generic cubic process that couples these fundamental excitations converts driving of the sum resonance into simultaneous resonant driving of both modes, resulting in an incommensurate subharmonic motion. We use a numerical implementation of a semiclassical driven-dissipative lattice gauge theory on a three-dimensional layered lattice, which models the geometry of cuprate superconductors, to demonstrate the robustness of this motion against thermal fluctuations. We demonstrate this light-induced time-crystalline phase for mono- and bilayer systems and show that this order can be detected for pulsed driving under realistic technological conditions.

### Electron trimer states in conventional superconductors

*Ali Sanayei, Pascal Naidon, and Ludwig Mathey*

We expand the Cooper problem by including a third electron in an otherwise empty band. We demonstrate the formation of a trimer state of two electrons above the Fermi sea and the third electron, for sufficiently strong interband attractive interaction. We show that the critical interaction strength is the lowest for small Fermi velocities, large masses of the additional electron, and large Debye energy. This trimer state competes with the formation of the two-electron Cooper pair, and can be created transiently via optical pumping.

### Pump Frequency Resonances for Light-Induced Incipient Superconductivity in YBa2Cu3O6.5

*B. Liu, M. Först, M. Fechner, D. Nicoletti, J. Porras, B. Keimer, A. Cavalleri*

Optical excitation in the cuprates has been shown to induce transient superconducting correlations above the thermodynamic transition temperature * T_{C}*, as evidenced by the terahertz-frequency optical properties in the nonequilibrium state. In

**YBa**, this phenomenon has so far been associated with the nonlinear excitation of certain lattice modes and the creation of new crystal structures. In other compounds, like

_{2}Cu_{3}O6_{+x}**La**, similar effects were reported also for excitation at near-infrared frequencies, and were interpreted as a signature of the melting of competing orders. However, to date, it has not been possible to systematically tune the pump frequency widely in any one compound, to comprehensively compare the frequency-dependent photosusceptibility for this phenomenon. Here, we make use of a newly developed nonlinear optical device, which generates widely tunable high-intensity femtosecond pulses, to excite

_{2−x}Ba_{x}CuO_{4}**YBa**throughout the entire optical spectrum (3–750 THz). In the far-infrared region (3–24 THz), signatures of nonequilibrium superconductivity are induced only for excitation of the 16.4- and 19.2-THz vibrational modes that drive c-axis apical oxygen atomic positions. For higher driving frequencies (25–750 THz), a second resonance is observed around the charge transfer band edge at approximately 350 THz. These findings highlight the importance of coupling to the electronic structure of the

_{2}Cu_{3}O_{6.5}**CuO**planes, mediated either by a phonon or by charge transfer.

_{2}### Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition

*Yuto Ashida, Ataç İmamoğlu, Jérôme Faist, Dieter Jaksch, Andrea Cavalleri, and Eugene Demler*

The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum matter by modifying quantum fluctuations of its electromagnetic environment. In contrast to earlier proposals on light-enhanced electron-electron interactions, we consider a dipolar quantum many-body system embedded in a cavity composed of metal mirrors and formulate a theoretical framework to manipulate its equilibrium properties on the basis of quantum light-matter interaction. We analyze hybridization of different types of the fundamental excitations, including dipolar phonons, cavity photons, and plasmons in metal mirrors, arising from the cavity confinement in the regime of strong light-matter interaction. This hybridization qualitatively alters the nature of the collective excitations and can be used to selectively control energy-level structures in a wide range of platforms. Most notably, in quantum paraelectrics, we show that the cavity-induced softening of infrared optical phonons enhances the ferroelectric phase in comparison with the bulk materials. Our findings suggest an intriguing possibility of inducing a superradiant-type transition via the light-matter coupling without external pumping. We also discuss possible applications of the cavity-induced modifications in collective excitations to molecular materials and excitonic devices.

### Floquet dynamics in light-driven solid

*M. Nuske, L. Broers, B. Schulte, G. Jotzu, S. A. Sato, A. Cavalleri, A. Rubio, J. W. McIver, L. Mathey*

We demonstrate how the properties of light-induced electronic Floquet states in solids impact natural physical observables, such as transport properties, by capturing the environmental influence on the electrons. We include the environment as dissipative processes, such as inter-band decay and dephasing, often ignored in Floquet predictions. These dissipative processes determine the Floquet band occupations of the emergent steady state, by balancing out the optical driving force. In order to benchmark and illustrate our framework for Floquet physics in a realistic solid, we consider the light-induced Hall conductivity in graphene recently reported by J.~W.~McIver, et al., Nature Physics (2020). We show that the Hall conductivity is estimated by the Berry flux of the occupied states of the light-induced Floquet bands, in addition to the kinetic contribution given by the average band velocity. Hence, Floquet theory provides an interpretation of this Hall conductivity as a geometric-dissipative effect. We demonstrate this mechanism within a master equation formalism, and obtain good quantitative agreement with the experimentally measured Hall conductivity, underscoring the validity of this approach which establishes a broadly applicable framework for the understanding of ultrafast non-equilibrium dynamics in solids.

### Measuring non-equilibrium dynamics in complex solids with ultrashort X-ray pulses

*Michele Buzzi, Michael Först and Andrea Cavalleri*

Strong interactions between electrons give rise to the complexity of quantum materials, which exhibit exotic functional properties and extreme susceptibility to external perturbations. A growing research trend involves the study of these materials away from equilibrium, especially in cases in which the stimulation with optical pulses can coherently enhance cooperative orders. Time-resolved X-ray probes are integral to this type of research, as they can be used to track atomic and electronic structures as they evolve on ultrafast timescales. Here, we review a series of recent experiments where femtosecond X-ray diffraction was used to measure dynamics of complex solids.

This article is part of the theme issue ‘Measurement of ultrafast electronic and structural dynamics with X-rays’.

### Magnetic-Field Tuning of Light-Induced Superconductivity in Striped La2−xBaxCuO4

Optical excitation of stripe-ordered **La _{2}−_{x}Ba_{x}CuO_{4} **has been shown to transiently enhance superconducting tunneling between the

**CuO**

_{2}planes. This effect was revealed by a blueshift, or by the appearance of a Josephson plasma resonance in the terahertz-frequency optical properties. Here, we show that this photoinduced state can be strengthened by the application of high external magnetic fields oriented along the c axis. For a 7 T field, we observe up to a tenfold enhancement in the transient interlayer phase correlation length, accompanied by a twofold increase in the relaxation time of the photoinduced state. These observations are highly surprising, since static magnetic fields suppress interlayer Josephson tunneling and stabilize stripe order at equilibrium. We interpret our data as an indication that optically enhanced interlayer coupling in

**La**does not originate from a simple optical melting of stripes, as previously hypothesized. Rather, we speculate that the photoinduced state may emerge from activated tunneling between optically excited stripes in adjacent planes.

_{2}−_{x}Ba_{x}CuO_{4}### Pressure tuning of light-induced superconductivity in K3C60

*A. Cantaluppi, M. Buzzi, G. Jotzu, D. Nicoletti, M. Mitrano, D. Pontiroli, M. Riccò, A. Perucchi, P. Di Pietro, A. Cavalleri*

Optical excitation at terahertz frequencies has emerged as an effective means to dynamically manipulate complex materials. In the molecular solid K_{3}C_{60}, short mid-infrared pulses transform the high-temperature metal into a non-equilibrium state with the optical properties of a superconductor. Here we tune this effect with hydrostatic pressure and find that the superconducting-like features gradually disappear at around 0.3 GPa. Reduction with pressure underscores the similarity with the equilibrium superconducting phase of K_{3}C_{60}, in which a larger electronic bandwidth induced by pressure is also detrimental for pairing. Crucially, our observation excludes alternative interpretations based on a high-mobility metallic phase. The pressure dependence also suggests that transient, incipient superconductivity occurs far above the 150 K hypothesized previously, and rather extends all the way to room temperature.

### Probing the Interatomic Potential of Solids with Strong-Field Nonlinear Phononics

*A. von Hoegen, R. Mankowsky, M. Fechner, M. Först, A. Cavalleri*

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities9 at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A_{1} (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

### Probing dynamics in quantum materials with femtosecond X-rays

*M. Buzzi, M. Först, R. Mankowsky, and A. Cavalleri*

Optical pulses are routinely used to drive dynamic changes in the properties of solids. In quantum materials, many new phenomena have been discovered, including ultrafast transitions between electronic phases, switching of ferroic orders and non-equilibrium emergent behaviours, such as photoinduced superconductivity. Understanding the underlying non-equilibrium physics requires detailed measurements of multiple microscopic degrees of freedom at ultrafast time resolution. Femtosecond X-rays are key to this endeavour, as they can probe the dynamics of structural, electronic and magnetic degrees of freedom. Here, we review a series of representative experimental studies in which ultrashort X-ray pulses from free-electron lasers have been used, opening up new horizons for materials research.

### Optical melting of the transverse Josephson plasmon: a comparison between bilayer and trilayer cuprates

*W. Hu, D. Nicoletti, A. V. Boris, B. Keimer and A. Cavalleri*

We report on an investigation of the redistribution of interlayer coherence in the trilayer cuprate **Bi _{2}Sr_{2}Ca_{2}Cu_{3}O_{10}**. The experiment is performed under the same apical-oxygen phonon excitation discussed in the past for the bilayer cuprate

**YBa**. In

_{2}Cu_{3}O_{6.5}**Bi**, we observe a similar spectral weight loss at the transverse plasma mode resonance as that seen in

_{2}Sr_{2}Ca_{2}Cu_{3}O_{10}**YBa**. However, this feature is not accompanied by the light-enhanced interlayer coherence that was found in

_{2}Cu_{3}O_{6.5}**YBa**, for which the transverse plasma mode is observed at equilibrium even in the normal state. These new observations offer an experimental perspective in the context of the physics of light-enhanced interlayer coupling in various cuprates.

_{2}Cu_{3}O_{6+x}### Transiently enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, W. Hu, A. Cavalleri, L. Mathey*

Recent pump-probe experiments reported an enhancement of superconducting transport along the c axis of underdoped YBa_{2}Cu_{3}O_{6+δ} (YBCO), induced by a midinfrared optical pump pulse tuned to a specific lattice vibration. To understand this transient nonequilibrium state, we develop a pump-probe formalism for a stack of Josephson junctions, and we consider the tunneling strengths in the presence of modulation with an ultrashort optical pulse. We demonstrate that a transient enhancement of the Josephson coupling can be obtained for pulsed excitation and that this can be even larger than in a continuously driven steady state. Especially interesting is the conclusion that the effect is largest when the material is parametrically driven at a frequency immediately above the plasma frequency, in agreement with what is found experimentally. For bilayer Josephson junctions, an enhancement similar to that experimentally is predicted below the critical temperature *T _{c}*. This model reproduces the essential features of the enhancement measured below

*T*. To reproduce the experimental results above

_{c}*T*, we will explore extensions of this model, such as in-plane and amplitude fluctuations, elsewhere.

_{c}### Anomalous relaxation kinetics and charge density wave correlations in underdoped BaPb1-xBixO3

*D. Nicoletti, E. Casandruc, D. Fu, P. Giraldo-Gallo, I. Fisher, A. Cavalleri*

We present measurements of transient photoconductivity in BaPb_{1−x}Bi_{x}O_{3} (BPBO)––a poorly understood material belonging to the bismuthate family, which has been coined “the other high-temperature superconductor.” The phase diagram of BPBO encompasses charge-density-wave (CDW) order in BaBiO_{3} (x = 1), through superconductivity for intermediate compositions, to bad metal behavior in BaPbO_{3} (x = 0). We present evidence for the coexistence of CDW order and superconductivity for underdoped compositions of BPBO––something that has been discussed previously, but never definitively established. These results are especially timely given that CDW correlations have recently been found in some underdoped cuprate superconductors, pointing toward a surprising commonality between some aspects of these materials. Our measurements also put energy scales on the associated charge order.

### Ultrafast momentum imaging of pseudospin-flip excitations in graphene

*S. Aeschlimann, R. Krause, M. Chávez-Cervantes, H. Bromberger, R. Jago, E. Mali, A. Al-Temimy, C. Coletti, A. Cavalleri, I. Gierz*

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photoexcited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy, and in-plane momentum. We first show that the rapidly-established quasithermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photoexcited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photocontrol experiments and optoelectronic device applications.

### Enhanced electron-phonon coupling in graphene with periodically distorted lattice

*E. Pomarico, M. Mitrano, H. Bromberger, M. A. Sentef, A. Al-Temimy, C. Coletti, A. Stohr, S. Link, U. Starke, C. Cacho, R. Chapman, E. Springate, A. Cavalleri, I. Gierz*

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge, and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here, we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically active in-plane bond stretching vibrations with femtosecond midinfrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. First, terahertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Second, the relaxation rate of hot quasiparticles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient threefold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

### Parametric amplification of a superconducting plasma wave

*S. Rajasekaran, E. Casandruc, Y. Laplace, D. Nicoletti, G. D. Gu, S. R. Clark, D. Jaksch & A. Cavalleri*

Many applications in photonics require all-optical manipulation of plasma waves, which can concentrate electromagnetic energy on sub-wavelength length scales. This is difficult in metallic plasmas because of their small optical nonlinearities. Some layered superconductors support Josephson plasma waves, involving oscillatory tunnelling of the superfluid between capacitively coupled planes. Josephson plasma waves are also highly nonlinear, and exhibit striking phenomena such as cooperative emission of coherent terahertz radiation, superconductor–metal oscillations and soliton formation. Here, we show that terahertz Josephson plasma waves can be parametrically amplified through the cubic tunnelling nonlinearity in a cuprate superconductor. Parametric amplification is sensitive to the relative phase between pump and seed waves, and may be optimized to achieve squeezing of the order-parameter phase fluctuations or terahertz single-photon devices.

### Nonlinear light–matter interaction at terahertz frequencies

*D. Nicoletti, A. Cavalleri*

Strong optical pulses at mid-infrared and terahertz frequencies have recently emerged as powerful tools to manipulate and control the solid state and especially complex condensed matter systems with strongly correlated electrons. The recent developments in high-power sources in the 0.1–30 THz frequency range, both from table-top laser systems and from free-electron lasers, have provided access to excitations of molecules and solids, which can be stimulated at their resonance frequencies. Amongst these, we discuss free electrons in metals, superconducting gaps and Josephson plasmons in layered superconductors, and vibrational modes of the crystal lattice (phonons), as well as magnetic excitations. This review provides an overview and illustrative examples of how intense terahertz transients can be used to resonantly control matter, with particular focus on strongly correlated electron systems and high-temperature superconductors.

### Dynamical decoherence of the light induced inter layer coupling in YBa2Cu3O6+δ

*C. R. Hunt, D. Nicoletti, S. Kaiser, D. Pröpper, T. Loew, J. Porras, B. Keimer, and A. Cavalleri*

Optical excitation of apical oxygen vibrations in YBa_{2}Cu_{3}O_{6+δ} has been shown to enhance its c axis superconducting-phase rigidity, as evidenced by a transient blueshift of the equilibrium interbilayer Josephson plasma resonance. Surprisingly, a transient c axis plasma mode could also be induced above Tc by the same apical oxygen excitation, suggesting light activated superfluid tunneling throughout the pseudogap phase of YBa_{2}Cu_{3}O_{6+δ}. However, despite the similarities between the transient plasma mode above Tc and the equilibrium Josephson plasmon, alternative explanations involving high-mobility quasiparticle transport should be considered. Here, we report an extensive study of the relaxation of the light induced plasmon into the equilibrium incoherent phase. These new experiments allow for a critical assessment of the nature of this mode. We determine that the transient plasma relaxes through a collapse of its coherence length rather than its carrier (or superfluid) density. These observations are not easily reconciled with quasiparticle interlayer transport and rather support transient superfluid tunneling as the origin of the light induced interlayer coupling in YBa_{2}Cu_{3}O_{6+δ}.

### Possible light-induced superconductivity in K3C60 at high temperature

*M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri*

The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects such as the optical enhancement of superconductivity1. Nonlinear excitation2,3 of certain phonons in bilayer copper oxides was recently shown to induce superconducting-like optical properties at temperatures far greater than the superconducting transition temperature, T*c* (refs 4, 5, 6). This effect was accompanied by the disruption of competing charge-density-wave correlations7,8, which explained some but not all of the experimental results. Here we report a similar phenomenon in a very different compound, K_{3}C_{60}. By exciting metallic K_{3}C_{60} with mid-infrared optical pulses, we induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. These same signatures are observed at equilibrium when cooling metallic K_{3}C_{60} below T*c* (20 kelvin). Although optical techniques alone cannot unequivocally identify non-equilibrium high-temperature superconductivity, we propose this as a possible explanation of our results.

### Theory of Enhanced Interlayer Tunneling in Optically Driven High-Tc Superconductors

*Jun-ichi Okamoto, Andrea Cavalleri, and Ludwig Mathey*

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, nonequilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

### Electronic-structural dynamics in graphene

*A. Cavalleri, I. Gierz*

We review our recent time- and angle-resolved photoemission spectroscopy experiments, which measure the transient electronic structure of optically driven graphene. For pump photon energies in the near infrared (ℏω_{pump}=950 meV), we have discovered the formation of a population-inverted state near the Dirac point, which may be of interest for the design of THz lasing devices and optical amplifiers. At lower pump photon energies (ℏω_{pump}<400 meV), for which interband absorption is not possible in doped samples, we find evidence for free carrier absorption. In addition, when mid-infrared pulses are made resonant with an infrared-active in-plane phonon of bilayer graphene (ℏω_{pump}=200 meV), a transient enhancement of the electron-phonon coupling constant is observed, providing interesting perspective for experiments that report light-enhanced superconductivity in doped fullerites in which a similar lattice mode was excited. All the studies reviewed here have important implications for applications of graphene in optoelectronic devices and for the dynamical engineering of electronic properties with light.

Structural Dynamics 3, 051301 (2016)

### Wavelength-dependent optical enhancement of superconducting interlayer coupling in La1.885Ba0.115CuO4

*E. Casandruc, D. Nicoletti, S. Rajasekaran, Y. Laplace, V. Khanna, G. D. Gu, J. P. Hill, and A. Cavalleri*

We analyze the pump wavelength dependence for the photoinduced enhancement of interlayer coupling in La_{1.88}5Ba_{0.115}CuO_{4}, which is promoted by optical melting of the stripe order. In the equilibrium superconducting state (*T<TC*=13K) in which stripes and superconductivity coexist, time-domain terahertz spectroscopy reveals a photoinduced blueshift of the Josephson plasma resonance after excitation with optical pulses polarized perpendicular to the CuO_{2} planes. In the striped nonsuperconducting state (*T _{C}<T<T_{SO}*≃40K) a transient plasma resonance similar to that seen below

*T*appears from a featureless equilibrium reflectivity. Most strikingly, both these effects become stronger upon tuning of the pump wavelength from the midinfrared to the visible, underscoring an unconventional competition between stripe order and superconductivity, which occurs on energy scales far above the ordering temperature.

_{C}### Redistribution of phase fluctuations in a periodically driven cuprate superconductor

*R. Höppner, B. Zhu, T. Rexin, A. Cavalleri, and L. Mathey*

We study the thermally fluctuating state of a bilayer cuprate superconductor under the periodic action of a staggered field oscillating at optical frequencies. This analysis distills essential elements of the recently discovered phenomenon of light-enhanced coherence in YBa_{2}Cu_{3}O_{6+x}, which was achieved by periodically driving infrared active apical oxygen distortions. The effect of a staggered periodic perturbation is studied using a Langevin and Fokker-Planck description of driven, coupled Josephson junctions, which represent two neighboring pairs of layers and their two plasmons. In a toy model including only two junctions, we demonstrate that the external driving leads to a suppression of phase fluctuations of the low-energy plasmon, an effect which is amplified via the resonance of the high-energy plasmon. When extending the modeling to the full layers, we find that this reduction becomes far more pronounced, with a striking suppression of the low-energy fluctuations, as visible in the power spectrum. We also find that this effect acts on the in-plane fluctuations, which are reduced on long length scales. All these findings provide a physical framework to describe light control in cuprates.

### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}## Project B8

### All-optical generation of antiferromagnetic magnon currents via the magnon circular photogalvanic effect

*Emil Viñas Boström, Tahereh Sadat Parvini, James W. McIver, Angel Rubio, Silvia Viola Kusminskiy, and Michael A. Sentef*

We introduce the magnon circular photogalvanic effect enabled by two-magnon Raman scattering. This provides an all-optical pathway to the generation of directed magnon currents with circularly polarized light in honeycomb antiferromagnetic insulators. The effect is the leading order contribution to magnon photocurrent generation via optical fields. Control of the magnon current by the polarization and angle of incidence of the laser is demonstrated. Experimental detection by sizable inverse spin Hall voltages in platinum contacts is proposed*.*

### Colloquium: Nonthermal pathways to ultrafast control in quantum materials

*Alberto de la Torre, Dante M. Kennes, Martin Claassen, Simon Gerber, James W. McIver, and Michael A. Sentef.*

Recent progress in utilizing ultrafast light-matter interaction to control the macroscopic properties of quantum materials is reviewed. Particular emphasis is placed on photoinduced phenomena that do not result from ultrafast heating effects but rather emerge from microscopic processes that are inherently nonthermal in nature. Many of these processes can be described as transient modifications to the free energy landscape resulting from the redistribution of quasiparticle populations, the dynamical modification of coupling strengths, and the resonant driving of the crystal lattice. Other pathways result from the coherent dressing of a material’s quantum states by the light field. A selection of recently discovered effects leveraging these mechanisms, as well as the technological advances that led to their discovery, is discussed. A road map for how the field can harness these nonthermal pathways to create new functionalities is presented.

### Floquet dynamics in light-driven solid

*M. Nuske, L. Broers, B. Schulte, G. Jotzu, S. A. Sato, A. Cavalleri, A. Rubio, J. W. McIver, L. Mathey*

We demonstrate how the properties of light-induced electronic Floquet states in solids impact natural physical observables, such as transport properties, by capturing the environmental influence on the electrons. We include the environment as dissipative processes, such as inter-band decay and dephasing, often ignored in Floquet predictions. These dissipative processes determine the Floquet band occupations of the emergent steady state, by balancing out the optical driving force. In order to benchmark and illustrate our framework for Floquet physics in a realistic solid, we consider the light-induced Hall conductivity in graphene recently reported by J.~W.~McIver, et al., Nature Physics (2020). We show that the Hall conductivity is estimated by the Berry flux of the occupied states of the light-induced Floquet bands, in addition to the kinetic contribution given by the average band velocity. Hence, Floquet theory provides an interpretation of this Hall conductivity as a geometric-dissipative effect. We demonstrate this mechanism within a master equation formalism, and obtain good quantitative agreement with the experimentally measured Hall conductivity, underscoring the validity of this approach which establishes a broadly applicable framework for the understanding of ultrafast non-equilibrium dynamics in solids.

### Microscopic theory for the light-induced anomalous Hall effect in graphene

*S. A. Sato, J. W. McIver, M. Nuske, P. Tang, G. Jotzu, B. Schulte, H. Hübener, U. De Giovannini, L. Mathey, M. A. Sentef, A. Cavalleri, and A. Rubio*

We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequilibrium steady state that is well described by topologically nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.

## Project B9

### Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

* Lucas Schneider, Philip Beck, Jannis Neuhaus-Steinmetz, Levente Rózsa, Thore Posske, Jens Wiebe & Roland Wiesendanger *

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor—also known as Shiba chains—up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.

### Structural and superconducting properties of ultrathin Ir films on Nb(110)

*Philip Beck, Lucas Schneider, Lydia Bachmann, Jens Wiebe, and Roland Wiesendanger*

The ongoing quest for unambiguous signatures of topological superconductivity and Majorana modes in magnet-superconductor hybrid systems creates a high demand for suitable superconducting substrates. Materials that incorporate *s*-wave superconductivity with a wide energy gap, large spin-orbit coupling, and high surface quality, which enable the atom-by-atom construction of magnetic nanostructures using the tip of a scanning tunneling microscope, are particularly desired. Since single materials rarely fulfill all these requirements, we propose and demonstrate the growth of thin films of a high-Z metal, Ir, on a surface of the elemental superconductor with the largest energy gap, Nb. We find a strained Ir(110)/Nb(110)-oriented superlattice for thin films of one to two atomic layers, which transitions to a compressed Ir(111) surface for thick films of ten atomic layers. Using tunneling spectroscopy, we observe proximity-induced superconductivity in the latter Ir(111) film with a hard gap Δ that is 85.3% of that of bare Nb(110).

### Correlation of Yu–Shiba–Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor

*A. Kamlapure, L. Cornils, R. Zitko, M. Valentyuk, R. Mozara, S. Pradhan, J. Fransson, A.I. Lichtenstein, J. Wiebe, and R. Wiesendanger*

Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu–Shiba–Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle–hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.

### Topological Shiba bands in artificial spin chains on superconductors

*Lucas Schneider, Philip Beck, Thore Posske, Daniel Crawford, Eric Mascot, Stephan Rachel, Roland Wiesendanger & Jens Wiebe*

A major challenge in developing topological superconductors for implementing topological quantum computing is their characterization and control. It has been proposed that a *p*-wave-gapped topological superconductor can be fabricated with single-atom precision by assembling chains of magnetic atoms on *s*-wave superconductors with spin–orbit coupling. Here we analyse Bogoliubov quasiparticle interference in Mn chains, constructed atom by atom on Nb(110), and reveal the formation of multi-orbital Shiba bands using momentum-resolved measurements. We find evidence that one band features a topologically non-trivial *p*-wave gap, as inferred from its shape and particle–hole asymmetric intensity. Our work is an important step towards a distinct experimental determination of topological phases in multi-orbital systems by bulk electron band structure properties only.

### Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

*Beck, P., Schneider, L., Rózsa, L. et al.*

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

### Atomic-scale spin-polarization maps using functionalized superconducting probes

*Schneider, L., Beck, P., Wiebe, J. & Wiesendanger, R.*

A scanning tunneling microscope (STM) with a magnetic tip that has a sufficiently strong spin polarization can be used to map the sample’s spin structure down to the atomic scale but usually lacks the possibility to absolutely determine the value of the sample’s spin polarization. Magnetic impurities in superconducting materials give rise to pairs of perfectly, i.e., 100%, spin-polarized subgap resonances. In this work, we functionalize the apex of a superconducting Nb STM tip with such impurity states by attaching Fe atoms to probe the spin polarization of atom-manipulated Mn nanomagnets on a Nb(110) surface. By comparison with spin-polarized STM measurements of the same nanomagnets using Cr bulk tips, we demonstrate an extraordinary spin sensitivity and the possibility to measure the sample’s spin-polarization values close to the Fermi level quantitatively with our new functionalized probes.

### Temperature and magnetic field dependent behavior of atomic-scale skyrmions in Pd/Fe/Ir(111) nanoislands

*P. Lindner, L. Bargsten, S. Kovarik, J. Friedlein, J. Harm, S. Krause, and R. Wiesendanger*

The thermal stability of atomic-scale skyrmions is of high relevance for potential spintronics applications and validation of theoretical models. We investigated Pd/Fe nanoislands on an Ir(111) substrate as a function of temperature and magnetic field. Utilizing noncollinear magnetoresistance contrast in scanning tunneling microscopy, the thermomagnetic phase space is explored up to 3 T within a temperature range between 1 K to 100 K. Evidence is found for the spin spiral, field-polarized, and fluctuating disordered magnetic phases. Evidence for the presence of atomic-scale skyrmions at up to approximately 80 K is found, irrespective of considerable magnetization dynamics arising from thermal agitation.

### Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors

*Schneider, L., Brinker, S., Steinbrecher, M. et al.*

Chains of magnetic atoms with either strong spin-orbit coupling or spiral magnetic order which are proximity-coupled to superconducting substrates can host topologically non-trivial Majorana bound states. The experimental signature of these states consists of spectral weight at the Fermi energy which is spatially localized near the ends of the chain. However, topologically trivial Yu-Shiba-Rusinov in-gap states localized near the ends of the chain can lead to similar spectra. Here, we explore a protocol to disentangle these contributions by artificially augmenting a candidate Majorana spin chain with orbitally-compatible nonmagnetic atoms. Combining scanning tunneling spectroscopy with ab-initio and tight-binding calculations, we realize a sharp spatial transition between the proximity-coupled spiral magnetic order and the non-magnetic superconducting wire termination, with persistent zero-energy spectral weight localized at either end of the magnetic spiral. Our findings open a new path towards the control of the spatial position of in-gap end states, trivial or Majorana, via different chain terminations, and the realization of designer Majorana chain networks for demonstrating topological quantum computation.

### A radio-frequency spin-polarized scanning tunneling microscope

*J. Friedlein, J. Harm, P. Lindner, L. Bargsten, M. Bazarnik, S. Krause and R. Wiesendanger*

A scanning tunneling microscope for spin-resolved studies of dynamic systems is presented. The cryogenic setup allows the scanning tunneling microscope to achieve a cutoff frequency beyond 26 GHz at the tunnel junction and to be operable at temperatures of 1.1 K–100 K in a magnetic field of up to 3 T. For this purpose, the microscope and its wiring as well as the associated cryostat system were specially designed and manufactured. For sample preparation, an ultrahigh vacuum system was developed, which is equipped with modular preparation platforms. Measurements showing the characteristics of the scanning tunneling microscope in the time and frequency domain are presented. As a proof of concept, experimental data of the Pd/Fe/Ir(111) sample system at 95 K in a magnetic field of 3 T are presented.Rev. Sci. Instrum. 90, 123705 (2019)