Subpicosecond metamagnetic phase transition driven by non-equilibrium electron dynamics
Federico Pressacco, Davide Sangalli, Vojt?ch Uhlí?, Dmytro Kutnyakhov, Jon Ander Arregi, Steinn Ymir Agustsson, Günter Brenner, Harald Redlin, Michael Heber, Dmitry Vasilyev, Jure Demsar, Gerd Schönhense, Matteo Gatti, Andrea Marini, Wilfried Wurth, Fausto Sirotti
SSubpicosecond metamagnetic phase transitiondriven by non-equilibrium electron dynamics
Federico Pressacco , Davide Sangalli , Vojt ˇech Uhl´ıˇr , Dmytro Kutnyakhov , Jon Ander Arregi ,Steinn Ymir Agustsson , G ¨unter Brenner , Harald Redlin , Michael Heber , Dmitry Vasilyev , Jure Demsar ,Gerd Sch ¨onhense , Matteo Gatti , Andrea Marini , Wilfried Wurth , and Fausto Sirotti The Hamburg Centre for Ultrafast Imaging, Hamburg University, Luruper Chaussee 149, 22761, Hamburg, Germany DESY Photon Science, Hamburg Germany Istituto di Struttura della Materia—Consiglio Nazionale delle Ricerche (CNR-ISM), Division of Ultrafast Processes in Materials(FLASHit), Via Salaria Km 29.5, CP 10, I-00016 Monterotondo Stazione, Italy European Theoretical Spectroscopy Facility (ETSF) CEITEC BUT, Brno University of Technology, Purkyˇnova 123, 612 00 Brno, Czech Republic Institute of Physical Engineering, Brno University of Technology, Technick´a 2, 616 69 Brno, Czech Republic Johannes Gutenberg-Universit¨at, Institute of Physics, Staudingerweg 7, 55128 Mainz, Germany Laboratoire des Solides Irradi´es, ´Ecole Polytechnique, CNRS, CEA/DRF/IRAMIS, Institut Polytechnique de Paris, F-91128
Palaiseau, France Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette, France Physique de la Mati´ere Condens´ee, CNRS and ´Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France * e-mail: [email protected] ABSTRACT
Femtosecond light-induced phase transitions between different macroscopic orders provide the possibility to tunethe functional properties of condensed matter on ultrafast timescales. In first-order phase transitions, transientnon-equilibrium phases and inherent phase coexistence often preclude non-ambiguous detection of transitionprecursors and their temporal onset. Here, we present a study combining time-resolved photoelectron spec-troscopy and ab-initio electron dynamics calculations elucidating the transient subpicosecond processes governingthe photoinduced generation of ferromagnetic order in antiferromagnetic FeRh. The transient photoemissionspectra are accounted for by assuming that not only the occupation of electronic states is modified during thephotoexcitation process. Instead, the photo-generated non-thermal distribution of electrons modifies the electronicband structure. The ferromagnetic phase of FeRh, characterized by a minority band near the Fermi energy, isestablished ± fs after the laser excitation. Ab-initio calculations indicate that the phase transition is initiatedby a photoinduced Rh-to-Fe charge transfer. Introduction
Emergence of long-range ordered states in condensed matter is typically a consequence of a fine interplay between thecoupled spin, charge, orbital, and lattice degrees of freedom . The mechanisms vary between different correlatedoxides and metallic systems leading to specific dynamical behavior. Excitation with ultrashort electromagnetic pulsesoffers the most efficient means to control the physical properties of condensed matter systems on a femtosecond timescale . Materials featuring first-order phase transitions (FOPTs) with abrupt changes in their order parameters areespecially appealing for ultrafast devices based on a functionality switch. In this regard, prominent examples are theinsulator-metal transition in VO
28, 9 or 1T–TaS .In order to obtain a good understanding of the relevant mechanisms triggering the transition, it is necessary toexplore the fundamental timescale of FOPTs. However, this is often challenging with multiple coupled degrees offreedom displaying complex dynamics upon laser-induced excitation. Moreover, macroscopic phase coexistence atthe FOPT, specifically, the processes of nucleation and domain growth, complicate the disentanglement of dynamicchanges in order parameters. The fundamental question, whether the modification of electronic structure drivesthe transition, is extensively debated in the literature, giving key arguments on the role of photoexcited states indouble-exchange interactions , electronic precursors closing the insulating gap , or the existence of intermediatetransient phases
2, 9, 14, 15 . a r X i v : . [ c ond - m a t . s t r- e l ] F e b n the case of ferromagnetic materials, magnetization dynamics triggered by a laser pulse leads to ultrafastdemagnetization , associated with changes in the spin polarization , which is impacted by the spin-dependentmobility of electrons . In contrast, disentangling the ultrafast response of coupled order parameters of magneticFOPTs has been far less investigated. Ultrafast generation of ferromagnetic (FM) order has been observed so farin a relatively small group of materials such as manganites
1, 24 or CuB O . Understanding the subpicosecondgeneration of FM order across a FOPT is still a major challenge in femtomagnetism . Figure 1. Electronic properties of FeRh across the metamagnetic phase transition . (a) Sketch of the isostruc-tural metamagnetic phase transition in FeRh. At room temperature (top) the system is AFM showing atomic magneticmoments only at the Fe atom sites ( m Fe = ± . µ B ). Above 360 K (bottom) the system has ferromagneticallycoupled magnetic moments at the Fe ( m Fe = µ B ) and Rh ( m Rh = µ B ) sites. The whole unit cell expandsisotropically by about 1% in volume . (b) Schematic representation of the two possible paths in the AFM toFM phase transition: direct thermally-driven transition to the FM phase (green arrow), and two-step transitiongoing through a transient electronic state reached during photoexcitation (red arrow) followed by relaxation to theequilibrium FM state (blue and black arrows). (c)
Calculated spin-resolved electronic density of states in the AFMand FM phases. The filled areas represent the electronic occupation at thermal equilibrium, with the green areahighlighting the position of the Fe minority band (see manuscript text). (d)
Measured x-ray photoelectron spectra ofFeRh in the AFM (black dots) and FM (red dots) phase. The solid curve at the bottom of the graph is the differencebetween the two spectra, which allows to appreciate the relative electron density change across the transition. Thedata correspond to quasi-static thermal cycling experiments prior to the time-resolved measurements.In this work we focus on FeRh, a metallic material that undergoes a metamagnetic FOPT from antiferromagnetic(AFM) to FM order at T M ∼
360 K and exhibits coupled structural, magnetic and electronic order parameters
28, 29 (see Fig. 1a). The thermally induced, quasi-static phase transition in FeRh (depicted in Fig. 1b by the greenarrow) has been extensively studied by following the sample magnetization, lattice parameter or resistivity .Moreover, numerous works have studied the AFM-FM phase transition by means of time-resolved techniques,where photoexcitation above a threshold intensity results in a nonzero net magnetization. Seminal pump-probemagneto-optical studies of FeRh films suggested subpicosecond generation of FM order
34, 35 . These results werediscarded by subsequent works, which implied a much slower transition on the order of several picoseconds .Time-resolved x-ray diffraction indicated that the speed of the transition might be set by the time scale of thestructural changes and thus limited by the speed of sound ( ∼ . The establishment of long range magnetic order is naturally slower, since it is mediated byphase boundary expansion, domain coalescence, and magnetic moment alignment. Thus, detection of FM phase viatechniques susceptible to the magnetization direction results in a perceived delay in the emergence of FM order . owever, FM order can also be traced by directly exploiting the specifics of the electronic structure, naturallymanifested in terms of spin unbalance and the appearance of majority and minority spin bands . This is indepen-dent of spin alignment along a particular direction, and thus allows inspecting FM order via x-ray photoelectronspectroscopy (XPS) . Similar to the electronic signature of the insulator-metal transition
8, 10 , it was demonstratedthat the modification of electronic bands might prove equally useful to investigate laser-induced generation of FMorder across the magnetic FOPT in FeRh .Here, utilizing time-resolved photoelectron momentum microscopy and supported by first principle calculations,we demonstrate that it is the light-induced modification of the electronic band structure that triggers the phasetransition in FeRh. In particular, we show that ultrafast laser excitation induces a charge transfer between the Rh andFe atoms, serving as a non-equilibrium precursor for the formation of the FM band structure on the subpicosecondtimescale. Results
The establishment of the FM phase in FeRh is accompanied by the appearance of a narrow peak located about150 meV below the Fermi energy E F due to the occupation of a spin-polarized Fe band (see green highlighted areain Fig. 1c). The photoelectron spectroscopy data shown in Fig. 1d are the momentum integrated energy distributioncurves measured at room temperature for the AFM phase (black dots) and at 420 K for the FM phase (red dots). Weuse this spectral feature to follow the emergence of the FM phase after laser excitation. Pump-probe experimentswere performed at the FLASH Free Electron Laser (FEL) in Hamburg using near-infrared (800 nm, 1 .
55 eV) pulsesof 90 fs coupled with 130 fs soft x-ray pulses with a photon energy of (cid:125) ω = . . , which is above the threshold value to induce the FOPT .Fig. 2a presents the time-resolved, k -integrated photoelectron spectra measured as a function of the delaybetween the optical pump and x-ray probe pulses, focusing on a 4 ps window around time zero t . One can clearlyidentify distinct regions in the time-dependent spectra: the temporal overlap between the optical and x-ray pulses(about 100 fs around t ), the relaxation of electrons towards the Fermi energy on the 100 fs timescale, and thesubsequent changes in the density of states near the Fermi level, associated with the formation of the Fe minorityband. Differential energy-dependent profiles, reported in Fig. 2b, provide a clearer picture. These are retrieved byaveraging the measured photoelectron spectra within a ±
50 fs temporal region for each of the indicated time delays,and subtracting the average photoelectron spectra at negative time delays.The photoexcited electrons relax via electron-electron and electron-phonon scattering, leading to the onset ofa Fermi-like distribution (see the red shaded areas for E − E F > t (blue shaded areas for E − E F < . E F (see also the inset in Fig. 3). Note that the electrondensity above 1.5 eV is almost two orders of magnitude lower. The changes in the population above the Fermi levelcan be explained by one- and two-photon absorption processes, such that laser excitation ( (cid:125) ω p = .
55 eV) promoteselectrons into states within the energy range [ E F , E F + (cid:125) ω p ]. Then, electrons start to relax towards the Fermi leveland accumulate in an energy region of a few hundred meV above E F . On the other hand, the transient depletion ofelectronic density below the Fermi level is concentrated between − . − .
55 eV [ E F − (cid:125) ω p , E F − (cid:125) ω p ].Assuming the photo-induced depletion, one would expect to observe measurable changes in the photoelectron yieldonly for energies 1 .
55 eV below the E F (two photon contribution should be negligible). This suggests that the laserinduced changes in the electronic distribution close to the Fermi level cause severe modifications of the deeper lyingbands. This implies that the in-fieri FOPT involves changes in the overall electronic structure of the system.To elucidate the electronic dynamics near the zero time delay, we compare the experimental results with time-dependent density functional theory (TD-DFT) calculations of the electronic structure performed on FeRh (seeFig. 3). Here, we select a laser fluence which gives a good quantitative agreement with the measured photoelectronspectra. The calculated one- and two-photon absorption intensity above the Fermi level presented in the inset ofFig. 3 corresponds to an excitation of 0 .
25 electrons per FM unit cell of FeRh (see Fig. 1a), i.e. ∼ cm − . Thisis close to the experimental estimate of 0 .
15 electrons per unit cell for a 5 . fluence. In Fig. 3, the calculatedXPS spectrum and its time evolution are obtained considering (i) the time evolution of the electronic distribution igure 2. Time-resolved x-ray photoelectron spectroscopy at room temperature . (a) Energy- and delay-dependent matrix of the measured spectra. The vertical dashed line marks the position of the Fermi level E F , whilethe horizontal solid line designates the time zero, t . The appearance of electronic density in the unoccupied states isa fingerprint of the laser excitation. We used this spectral feature to identify the temporal overlap between the opticalpump and the x-ray probe pulses. (b) Differential photoelectron spectra at selected delays. To enhance the signalto noise ratio, we average the unpumped spectra (between − − . −
500 fs) as well asaccentuating the temporal evolution of the photoelectron spectra. Red and blue shaded areas indicate an increase anda reduction of the electron density with respect to the spectra at negative delays, respectively.function f n k ( t ) , and (ii) the time evolution of the electronic band structure ε n k ( t ) (see Methods). The changes in f n k ( t ) give rise to a significant signal only in the red and green shaded regions between − .
55 eV and + .
55 eV,while the effect of changes in ε n k ( t ) is most prominent well below the Fermi level. Thus, the signal below − . ε n k ( t ) . The fact that it is negative implies a reduction in the density of states (see therelative height difference of the red and blue solid curves in Fig. 3).On the other hand, the changes in the region between − .
55 eV and 0 eV result from two effects which sumto a negligible signal: f n k ( t ) gives a negative contribution due to the promotion of electrons into the originally igure 3. Comparison of experimental and computed photoelectron spectra of FeRh . Spectra at equilibrium( t = − . t = ε n k ( t ) must result in an increase of the DOS. The region above the Fermi levelseams to be mainly governed by f n k ( t ) . The overall agreement between theory and experiment is very good. Theobserved slight differences may be due to relaxation processes in the experiment already active during the pumpingphase, making the electron distribution more peaked towards the Fermi level.The relaxation of excited electrons proceeds with the formation of a peak above the Fermi level between 100fs and 300 fs (see Fig. 2b). At a time delay of around 400 fs, the peak crosses the Fermi level and after 500 fs, itsposition stabilizes at the energy value which is characteristic for the Fe minority band of the FM phase in FeRh .Further insights into the FOPT dynamics are obtained from the complete differential matrix, presented in Fig. 4a,monitoring the modification of the electronic density. We selected three energy ranges marked by the red, blue, andblack bars placed on the right hand side of Fig. 4a. The first (red) accounts for the electronic density above 200 meVand identifies the total number of electrons injected into the unoccupied states upon photoexcitation. The second(blue) goes from −
240 meV to 0 meV and is used to monitor the formation of the Fe minority peak across the phasetransition. The third (black) includes the region from − . − . t D and subsequent rise time τ of the transition areobtained by fitting the integrated electron density at the Fe minority peak region with an error function (see Methods)and yields values of t D = ±
30 fs and τ = ±
110 fs. In addition, the data represented by black diamonds inFig. 4b, which indicate the time-dependent population of bands in a region below E F , nearly mirror the populationof the unoccupied levels up to 300 fs, with a fast depletion and recovery. The curve stabilizes thereafter at a finitevalue, implying permanent modifications of the deeper bands already after 300 fs, during which the Fe minority igure 4. Subpicosecond generation of the electronic FM order in FeRh . (a) Energy- and delay-dependentdifferential matrix of the measured photoelectron spectra. We subtracted the average of unpumped spectra (between − − . (b) Temporal evolution of the electronic density in the three characteristic energy regions marked in (a) . The populationof states above the Fermi level shows a fast rise and a consecutive decay around t (empty red circles). The deeperbands (empty black diamonds) show a corresponding depletion and recovery which reflects the dynamics of theunoccupied states. However, their occupation level stabilizes 300 fs after t and remains constant thereafter. Theelectronic density slightly below E F (filled blue circles) shows a moderate increase during the laser excitation up to300 fs delay, followed by a pronounced increase due to the shift of Fe minority band below E F at a delay t D of 350fs. This value was extracted by fitting the error function to the experimental results (black solid line). Subsequently,the minority Fe band peak intensity remains constant throughout the investigated delay range.peak is still shifting towards its final position at 150 meV below E F . Similar differences in the behaviour of theelectronic density at and below the Fermi level have been observed during ultrafast demagnetization process in Fe igure 5. Computed photoinduced changes in charge and spin density in FeRh . ( a , b ) Changes in the chargedensity n ( r , t f ) − n eq ( r ) and ( c ) spin density S z ( r , t f ) − S eqz ( r ) at the end of the laser pulse ( t = t f ) with respect tothe equilibrium configuration. Densities are represented in atomic units on two different FeRh{111}-planes: theplane just below the Fe ( ↑ ) atoms (panel a ) and the plane containing the Rh atoms (panels b , c ). Fe and Rh atompositions are indicated by red and grey segments of the lattice, respectively. Charge is transferred from the occupied(bonding) orbitals of Rh atoms (panel b ), to the unoccupied (anti-bonding) orbitals of Rh and Fe (panel a ). Sincethe Fe anti-bonding levels are filled in this process, the local Fe spin density is reduced. As a result, there is aredistribution of spin density around the Rh atoms and a reduction of the local spin moment at the Fe atoms (panel c ).The movies in the Supplementary Information show the simulated time evolution of the charge density variationsat the Fe and Rh sites as represented in panels ( a ) and ( b ) at the beginning and the end of the laser pulse.and Co . In the present case, this behavior shows that the FOPT in FeRh is mediated by a transient electronic phasein which the electronic structure is different from both the AFM and FM phases. The transient phase exists in adelay range from up to 500 fs after laser excitation. Discussion
The unexpected reduction of the photoelectron yield below the one-photon absorption range ( ∼ .
55 eV), an energyregion where the electronic populations f n k ( t ) cannot be strongly affected by the laser excitation, is explainedby theoretical calculations. The effect can only be accounted for by considering the photoinduced change in theelectronic band structure (i.e. density of states). Time-resolved XPS spectra are usually described and interpreted interms of changes in the population f n k ( t ) only. This is clearly insufficient for the ultrafast dynamics in FeRh, sincechanges in ε n k ( t ) must be considered on the same level even before the phase transition is complete.The changes in ε n k ( t ) during and after photoexcitation provide insights into why FeRh would relax towards theFM phase. The photoexcitation process in the AFM state depletes the valence states, which are characterised byhybridized Fe-Rh bonding states, and fills the unoccupied states, where empty Fe “local minority-spin” anti-bondingstates are mainly available. As a result two processes occur: a charge (and spin) transfer from Rh to Fe ( Rh → Fe ),and a symmetric spin transfer from Fe “local majority” → Fe “local minority” ( Fe ( ↑ ) ↔ Fe ( ↓ ) ). Simulated chargeand spin density changes upon photoexcitation clearly show this, Fig. 5. Here, the blue regions around the Rh atomsindicate a charge depletion, which can only partially be explained by a local redistribution. Most of the charge istransferred to the Fe atoms (see Fig. 5a), while there is a strong charge depletion around Rh atoms (see Fig. 5b).The Rh → Fe process also increases the spin density around the Rh atoms (see Fig. 5c). On the other hand, the Fe ( ↑ ) ↔ Fe ( ↓ ) is a pure spin transfer process, with a strong reduction ( ∼
3, 42, 47 . Thephotoexcitation alters this delicate balance. As shown for the magnetic disorder associated with the temperatureincrease, the decrease of the Fe-Fe first-neighbor AFM couplings favors the FM order of the Fe subsystem, whileinducing magnetic fluctuations on the Rh sites . In turn, the induced Rh magnetic moments stabilize the FM over theAFM state
3, 34, 48, 49 . Our simulations therefore suggest that the change of Fe-Rh hybridization ( Rh → Fe process) lays a critical role in the photoinduced transition. The Fe ( ↑ ) ↔ Fe ( ↓ ) process corresponds to the intersite spintransfer which has been recently proposed, on the basis of TD-DFT simulations, as a key mechanism also in othermulticomponent magnetic materials . Here, it causes to weaken the AFM ordering but is not sufficient to triggerthe magnetic transition alone (just after the photoexcitation, the system is still in the AFM phase).The theoretical simulation, not including dissipating effects, cannot describe the dynamics after the photoexcita-tion when electron-electron, electron-phonon and electron-magnon interactions are at play, and the actual phasetransition takes place. Taking into account dissipating effects, one would expect further dynamics of both f n k ( t ) and ε n k ( t ) : the formation of a Fermi distribution and its subsequent cooling (for f n k ( t ) ), and the formation of the FMband structure (for ε n k ( t ) ). Instead, our experimental time resolution is fast enough to allow the identification of abottleneck time in this process, i.e., the metamagnetic transformation exhibiting a 350 fs delay. It is associated witha change in the band structure, with the spin-minority Fe band slightly pushed below the Fermi level and gettingfilled by the electrons that progressively cool down. This transformation occurs on a subpicosecond timescale that isfaster than what was determined by previous experiments on FeRh with a lower time resolution . Most importantly,our results set a new timescale that is faster than the lattice expansion and the establishment of the macroscopic,long-range magnetic order .The process is schematically depicted in Fig. 1b. Immediately after the action of the pulse, a significant numberof electrons is excited to unoccupied states, with a non-thermal distribution of electrons f n k ( t ) (red arrow in Fig. 1b)decaying towards the Fermi level on a time scale of about 200 fs. This is accompanied by the slower dynamics ofthe band structure ε n k with the formation of the peak of the Fe minority band. The peak crosses the Fermi level atabout 350 fs delay, and stabilizes at −
150 meV binding energy after 400 fs. During this step, the system undergoesa purely electronic transition through a transient phase, where the electronic band configuration evolves from ε n k ( t ) to an intermediate electronic FM phase ε e − FMn k (blue arrow in Fig. 1b). Once the electronic distribution reaches theconfiguration of the FM phase (after 400 fs), the relaxation of the lattice parameter towards the equilibrium value ofthe FM phase then follows on a longer time scale (black arrow in Fig. 1b). Conclusion
In conclusion, we determine the existence of a transient electronic phase needed to induce the AFM to FMphase transition of FeRh using pump-probe photoelectron spectroscopy at the FLASH FEL facility. The resultsare supported by electronic structure calculations, which explain the details of the dynamics following the laserexcitation. The time-resolved photoemission experiment at a laser fluence of 5 . is well reproduced assumingthe excitation of 0 .
25 electrons per unit cell of FeRh. At these fluences, the photon absorption cannot be describedsimply as promotion of electrons from filled to empty states of the calculated band structure, but the modifiedelectron population induces a modification of the band structure as well, which is confirmed by the good agreementbetween theory and experiments. The laser excitation results in the transfer of electrons from the occupied d orbitalsbelow the Fermi level to the unoccupied d orbitals above the Fermi level, with a partial transfer of electrons from theRh to the Fe sites. The transient electronic phase exists up to 500 fs after the laser excitation. The emergence ofthe FM phase can be followed by the appearance and position of the Fe minority band near the Fermi level withcharacteristic time of τ = ± could lead to ultrafast devices based on magnetic order-order phase transitions at room temperature. ethods Sample and surface preparation . The sample consists of an epitaxial 80-nm-thick FeRh(001) film grown onto aMgO(001) substrate by dc magnetron sputtering using an equiatomic target. The films were grown at 725 K andpost-annealed in situ at 1070 K for 45 minutes in order to achieve CsCl-type chemical ordering. Upon coolingdown the samples in the ultra high vacuum chamber, single-layer graphene is formed on top of the FeRh surface bysegregating the carbon from the film . This provides oxidation protection in air and avoids the need for furthercapping layers of the FeRh layer to be transported to the FEL facility without degradation. The good quality of thecrystallographic texture and the existence of the magnetic phase transition were confirmed using x-ray diffractionand vibrating sample magnetometry, respectively . The sample surface was prepared via annealing only, in orderto preserve the graphene layer, and tested with XPS prior to the time-resolved experiments as described in earlierworks
42, 46 . Examination with low-energy electron diffraction revealed the expected reconstruction pattern of theFeRh(001) surface.
Experiment . The experiments are performed at the plane grating monochromator beamline
55, 56 at FLASH
57, 58 ,using the HEXTOF end-station . The pump-probe scheme is established by a near-infrared pulse of 90 fs coupledwith a FEL pulse of about 130 fs (both values are the full width half maximum, FWHM), which provide an estimatedsystem response function , i.e., the effective pump-probe correlation, of ∼
150 fs FWHM. The optical pumpand x-ray probe energies were set to 1 .
55 eV and 123 . ∼
150 meV isextracted from the Fermi level fit.Photoexcited electrons near normal emission were detected using a momentum microscope, which has anacceptance angle of 2 π above the sample surface and can image the full Brillouin zone (BZ) with up to 7 Å − diameter
59, 60 . We used a negative extractor voltage ( ∼
40 V with respect to the sample potential). This retardingfield between the sample and extractor effectively removes the slow secondary electrons originating from the x-rayphotons and pump-laser-induced slow electrons. All background electrons with energies less than ∼ µ m above the sample surface. This removal of space charge comes at the expenses of k -resolution and causes a reduction of the k -field-of-view to 1 . − . Integrating over this k -field represents theintegral of 60% of the BZ of FeRh, which was sufficient to well identify the peak associated with the FM phase.We characterize the sample surface by measuring the spectra of the system in the AFM and FM phases at fixedtemperatures, and obtained line-shapes equivalent to those reported in ref. 46 (see Fig. 1d). The presence of the peakat about ∼
150 meV below the Fermi level is the signature of the Fe minority band characteristic of the FM phase.To fit the experimental data in Fig. 4b, we used an error function of the following form: f ( t ) = y + A (cid:20) + erf (cid:18) t − t D τ (cid:19)(cid:21) where y is a vertical offset, A is the amplitude, t D is the temporal onset of the transition (with respect to t ), and τ isthe characteristic rise time. Theory . We calculate from first principles the equilibrium and non–equilibrium properties of FeRh using the pw.x and yambo codes within Density Functional Theory (DFT) and its Time Dependent (TD–DFT) extension.At equilibrium both the FM and AFM phases are computed within the local density approximation (LDA) fullyincluding spin–orbit coupling (SOC). An energy cut-off of 65 Ry is used for the wave–functions with a 5 × × s more easily handled in the non equilibrium TD–DFT simulations with SOC. Finally we verified that the AFMstructure displays a phonon instability as reported in the literature .Subsequently, a non self–consistent calculation (NSCF) on a 8 × × for a probe of 125 eV(in practice the signal is dictated by Fe(3d) orbitals). Moreover, we use energy dependent lifetimes of the form γ n k = A + B d ( ε n k ) + C ( ε F − ε n k ) , where the first constant contribution A =
60 meV mimics the experimentalresolution, the second term B , proportional to the electronic DOS d ( ε ) , mimics the electron–phonon lifetimes and,finally, the term which grows quadratically away from the Fermi level mimics the elecron–electron lifetimes. Finally,the effect of temperature is included in the Fermi distribution used for the electronic occupations. The resultingspectrum is shown in Fig. 1c.The TD–DFT simulations, as implemented in the yambo code , are then performed propagating the Kohn–Sham density matrix in the basis–set of the equilibrium wave–functions under the action of the same pump pulse usedin the experiment. The NSCF DFT calculation is used as a starting point for TD–DFT. The laser pulse parametersare equivalent to the experimental conditions. In particular, the fluence is chosen considering: (i) the experimentalfluence, (ii) the fact that part of the pulse is reflected by the sample, and (iii) the fact that the external field isrenormalized by the induced field. The effect of both (ii) and (iii) is estimated taking into account the dielectricfunction of bulk FeRh. In particular, point (iii) needs to be considered since we adopt the so called transverse gauge,where the macroscopic (or G =
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J. Phys.: Condens. Matter , 325902 (2019). URL https://doi.org/10.1088%2F1361-648x%2Fab15d0 . cknowledgements This work is dedicated to Wilfried Wurth, who passed away on May 8, 2019. We acknowledge support by thescientific and technical staff of FLASH, as well as Holger Meyer and Sven Gieschen form University of Hamburg.This work was supported by the excellence cluster “The Hamburg Centre for Ultrafast Imaging - Structure, Dynamicsand Control of Matter at the Atomic Scale” of the Deutsche Forschungsgemeinschaft (DFG EXC 1074) and throughthe SFB 925 "Lichtinduzierte Dynamik und Kontrolle korrelierter Quantensysteme" (project B2). It received fundingfrom the EU-H2020 research and innovation program under European Union projects “MaX” Materials design at theeXascale H2020-EINFRA-2015-1 (Grant Agreement No. 824143) and “NFFA” Nanoscience Foundries and FineAnalysis-Europe H2020-INFRAIA-2014-2015 (Grant Agreement No. 654360) having benefited from the accessprovided by the ISM node (CNR, Italy). We acknowlege the Deutsche Forschungsgemeinschaft (DFG, GermanResearch Foundation) – TRR 173 – 268565370 (projects A02 and A05). Access to the CEITEC Nano ResearchInfrastructure was supported by the Ministry of Education, Youth and Sports (MEYS) of the Czech Republicunder the projects CEITEC 2020 (LQ1601) and CzechNanoLab (LM2018110). We acknowledge funding from theItalian project MIUR PRIN Grant No. 20173B72NB. This work has received funding from the European Union’sHorizon 2020 research and innovation program under the Marie Skłodowska-Curie and it is co-financed by theSouth Moravian Region under grant agreement No. 665860.
Author contributions
F.P., V.U., J.A.A., M.G., D.S. and F.S. designed the project. F.P., D.K., M.H., S.Y.A., G.B., H.R., D.V., V.U., J.A.A.and F.S. performed the time-resolved XPS experiments and analyzed the data. M.G., D.S. and A.M. designed thetheoretical approach to the problem. J.A.A. and V.U. prepared and characterized the samples. All authors discussedthe results. F.P., V.U., J.A.A., D.S., M.G. and F.S. wrote the paper with contributions from all authors and criticalrevision from J.D., G.S. and W.W.
Competing financial interests
The authors declare no competing interests.
Supplementary Information
We provide four animations showing the simulated dynamics of charge density variations n ( r , t ) − n eq ( r ) asrepresented in panels a and b of Fig.5 during two time-windows. The first time window ( −
65 fs < t < −
55 fs)corresponds to the beginning of the photoexcitation process and shows the laser-induced charge oscillationsfor about four periods of the main laser frequency (for λ =
800 nm, T = .
67 fs). During this time window, n ( r , t ) − n eq ( r ) ∼ − a.u. (see Supplementary Videos 1 & ). The second time window (135 fs < t < . n ( r , t ) − n eq ( r ) ∼ − a.u. (see Supplementary Videos 3 & .).)