**SFB 925**Light induced dynamics and control of correlated quantum systems

# Research Area B

### Project B1

#### Trace phase detection and strain characterization from serial X-rayfree-electron laser crystallography of a Pr0.5 Ca0.5 MnO3 powder

*K. R. Beyerlein, C. Jooss, A. Barty, R. Bean, S. Boutet, S. S. Dhesi, R. Bruce Doak, M. Först, L. Galli, R. A. Kirian, J. Kozak, M. Lang, R. Mankowsky, A. Cavalleri, H. Chapman, et. al*

We report on the analysis of virtual powder-diffraction patterns from serial femtosecond crystallography (SFX) data collected at an X-ray free-electron laser. Different approaches to binning and normalizing these patterns are discussed with respect to the microstructural characteristics which each highlights. Analysis of SFX data from a powder of Pr0.5Ca0.5MnO3 in this way finds evidence of other trace phases in its microstructure which was not detectable in a standard powder-diffraction measurement. Furthermore, a comparison between two virtual powder pattern integration strategies is shown to yield different diffraction peak broadening, indicating sensitivity to different types of microstrain. This paper is a first step in developing new data analysis methods for microstructure characterization from serial crystallography data.

#### Driving Magnetic Order in a Manganite by Ultrafast Lattice Excitation

*M. Foerst, R.I. Tobey, S. Wall, H. Bromberger, V. Khanna, A.L. Cavalieri, Y.D. Chuang, W.S. Lee, R. Moore, W.F. Schlotter, J.J. Turner, O. Krupin, M. Trigo, H. Zheng, J.F. Mitchell, S.S. Dhesi, J.P. Hill, A. Cavalleri*

Femtosecond midinfrared pulses are used to directly excite the lattice of the single-layer manganite La0.5Sr1.5MnO4. Magnetic and orbital orders, as measured by femtosecond resonant soft x-ray diffraction with an x-ray free-electron laser, are reduced within a few picoseconds. This effect is interpreted as a displacive exchange quench, a prompt shift in the equilibrium value of the magnetic- and orbital-order parameters after the lattice has been distorted. Control of magnetism through ultrafast lattice excitation may be of use for high-speed optomagnetism.

#### Polaronic conductivity in the photoinduced phase of 1T-TaS2

*N. Dean, J. C. Petersen, D. Fausti, R. I. Tobey, S. Kaiser, L. V. Gasparov, H. Berger, A. Cavalleri*

The transient optical conductivity of photoexcited 1T-TaS2 is determined over a three-order-of-magnitude frequency range. Prompt collapse and recovery of the Mott gap is observed. However, we find important differences between this transient metallic state and that seen across the thermally driven insulator-metal transition. Suppressed low-frequency conductivity, Fano phonon line shapes, and a midinfrared absorption band point to polaronic transport. This is explained by noting that the photoinduced metallic state of 1T-TaS2 is one in which the Mott gap is melted but the lattice retains its low-temperature symmetry, a regime only accessible by photodoping.

#### Clocking the melting transition of charge and lattice order in 1T-TaS 2 with ultrafast extreme-ultraviolet angle-resolved photoemission spectroscopy

*J.C. Petersen, S. Kaiser, N. Dean, A. Simoncig, H. Y. Liu, A. L. Cavalieri, C. Cacho, I.C.E. Turcu, E. Springate, F. Frassetto, L. Poletto, S. S. Dhesi, H. Berger, A. Cavalleri*

We use time- and angle-resolved photoemission spectroscopy with sub-30-fs extreme-ultraviolet pulses to map the time- and momentum-dependent electronic structure of photoexcited 1T-TaS2. This compound is a two-dimensional Mott insulator with charge-density wave ordering. Charge order, evidenced by splitting between occupied subbands at the Brillouin zone boundary, melts well before the lattice responds. This challenges the view of a charge-density wave caused by electron-phonon coupling and Fermi-surface nesting alone, and suggests that electronic correlations play a key role in driving charge order.

#### Melting of antiferromagnetic order in La0.5Sr1.5MnO4 probed with ultrafast resonant soft X-ray diffraction

*H. Ehrke, R.I. Tobey, S. Wall, S. A. Cavill, M. Först, V. Khanna, Th. Garl, N. Stojanovic, D. Prabhakaran, A.T. Boothroyd, M. Gensch, A. Mirone, P. Reutler, A. Revcolevschi, S. S. Dhesi, A. Cavalleri*

We used ultrafast resonant soft x-ray diffraction to probe the picosecond dynamics of spin and orbital order in La0.5Sr1.5MnO4 after photoexcitation with a femtosecond pulse of 1.5 eV radiation. Complete melting of antiferromagnetic spin order is evidenced by the disappearance of a (1/4,1/4,1/2) diffraction peak. On the other hand, the (1/4,1/4,0) diffraction peak, reflecting orbital order, is only partially reduced. We interpret the results as evidence of destabilization in the short-range exchange pattern with no significant relaxation of the long-range Jahn-Teller distortions. Cluster calculations are used to analyze different possible magnetically ordered states in the long-lived metastable phase. Nonthermal coupling between light and magnetism emerges as a primary aspect of photoinduced phase transitions in manganites.

#### Bidirectional ultrafast electric field gating of interlayer transport in a cuprate superconductor

*A. Dienst, M. Hoffman, J. Petersen, S. Pyon, T. Takayama, H. Takagi, A. Cavalleri*

In cuprate superconductors, tunnelling between planes makes three-dimensional superconductive transport possible. However, the interlayer tunnelling amplitude is reduced when an order-parameter-phase gradient between planes is established. As such, interlayer superconductivity along the c-axis can be weakened if a strong electric field is applied along the c-axis. In this Letter, we use high-field single-cycle terahertz pulses to gate interlayer coupling in La1.84Sr0.16CuO4. We induce ultrafast oscillations between superconducting and resistive states and switch the plasmon response on and off, without reducing the density of Cooper pairs. In-plane superconductivity remains unperturbed, revealing a non-equilibrium state in which the dimensionality of the superconductivity is time-dependent. The gating frequency is determined by the electric field strength. Non-dissipative, bi-directional gating of superconductivity is of interest for device applications in ultrafast nanoelectronics and represents an example of how nonlinear terahertz physics can benefit nanoplasmonics and active metamaterials.

#### Nonlinear phononics as an ultrafast route to lattice control

*M. Foerst, Ch. Manzoni, S. Kaiser, Y. Tokura, Y. Tomioka, R. Merlin, A. Cavalleri*

Two types of coupling between electromagnetic radiation and a crystal lattice have so far been identified experimentally. The first is the direct coupling of light to infrared-active vibrations carrying an electric dipole. The second is indirect, involving electron–phonon coupling and occurring through excitation of the electronic system; stimulated Raman scattering1, 2, 3 is one example. A third path, ionic Raman scattering (IRS; refs 4, 5), was proposed 40 years ago. It was posited that excitation of an infrared-active phonon could serve as the intermediate state for Raman scattering, a process that relies on lattice anharmonicities rather than electron–phonon interactions6. Here, we report an experimental demonstration of IRS using femtosecond excitation and coherent detection of the lattice response. We show how this mechanism is relevant to ultrafast optical control in solids: a rectified phonon field can exert a directional force onto the crystal, inducing an abrupt displacement of the atoms from their equilibrium positions. IRS opens up a new direction for the optical control of solids in their electronic ground state7, 8, 9, different from carrier excitation.

#### Moving the Frontier of Quantum Control into the Soft X-Ray Spectrum

*A. Aquila, M. Drescher, T. Laarmann, M. Barthelmeß, H. N. Chapman, S. Bajt*

International Journal of Optics Volume 2011 (2011), Article ID 417075

### Project B2

#### 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

#### 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.*

### Project B4

#### 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

#### 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*

#### 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

#### 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.

#### 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

*13.09.2016 00:00 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.

#### 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*

#### 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*