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Probing dynamics in quantum materials with femtosecond x-rays

Optical pulses are routinely used to drive dynamical 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 nonequilibrium emergent behaviors such as photo-induced 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 endeavor, as they can access the dynamics of structural, electronic and magnetic degrees of freedom. Here, we cover 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.

The equilibrium functional properties of solids are determined by the interplay between many microscopic degrees of freedom. These include the crystallographic structure, the arrangement of charges, spins, and orbitals as well as their dynamical fluctuations.
The strong interactions between these many degrees of freedom create complex energy surfaces and make the ground state highly dependent on subtle differences in microscopic parameters, and on fine-tuning of external conditions. Understanding the origin of these "emergent" phenomena is, even at equilibrium, a formidable task that requires monitoring several degrees of freedom in the material at once. In the past two decades, equilibrium x-ray 1,2 and photoemission techniques 3,4 have provided an enormous amount of information and have contributed to understanding of equilibrium emergent states.
The present paper covers a new experimental direction in the physics of complex correlated electron systems, in which electromagnetic fields are used to control emergent properties away from thermodynamic equilibrium. Indeed, ultrashort laser pulses have been shown to be especially effective tools to manipulate magnetism 5,6 or ferroelectricity 7,8 , to induce phase transitions at an ultrafast speed 9,10 and to trigger new emergent phenomena [10][11][12][13] . The underlying physics proceeds on femtosecond and picosecond timescales. Although these timescales have long been accessible with optical laser pulses since the 1970's, changes in the optical constants at visible and near infrared frequencies provide very limited information, only indirectly related to the microscopic degrees of freedom of interest.
Hence, complementary techniques that directly interrogate charge, spin and lattice degrees of freedom in the material are often applied to gain a deeper insight into the underlying physics. Time-resolved x-ray and electron diffraction, for example, directly track the photo-induced evolution of the crystal lattice (see Box 1), with some limitations in time resolution for electron diffraction experiments. 14  The development of ultrafast x-ray probes dates back at least two decades, made possible by the development of high intensity 15,16 amplified optical pulses 17,18 . Already in the 1990's, x-ray fluorescence from plasmas 19,20 spurred activity in this area. Despite the low flux and limited tunability of these first femtosecond x-ray sources, many rudimentary structural dynamics experiments were already reported at that stage, including studies of laser-induced disordering of organic films 21 , photo-induced melting of semiconductors [22][23][24] , detection of coherent acoustic 25,26 and optical 27 phonons, and photo-induced solid-solid phase transitions 28 .
Other techniques combined the same high peak power femtosecond lasers with relativistic electron beams, first by exploiting 90-degrees Thomson scattering [29][30][31] and later by using lasers as energy modulators in electron storage rings [32][33][34][35] . These sources were tunable, and opened up femtosecond x-ray spectroscopies like ultrafast near edge x-ray absorption spectroscopy 36 or x-ray magnetic circular dichroism 37 . Accelerator based sources brought to the fore multiple-order-of-magnitude improvements in the x-ray flux 38,39 , and culminated in the demonstration of x-ray from free electron laser (FEL) operation 40 .
The present review covers the evolution of ultrafast materials research after x-ray FELs became available, focusing on how ultrafast x-ray diffraction and spectroscopy were used. We present a few representative experiments, especially those on ultrafast rearrangement of ferroic orders, of coupled charge, spin and orbital dynamics in complex oxides and in other strongly correlated materials. The notable case of photoinduced superconductivity will also be discussed, especially with respect to the contributions made by x-ray FEL experiments.

Ultrafast Switching in Ferroelectric Materials
Ferroelectric materials are of great scientific and technological interest, as they exhibit bi-stable, structurally distorted states of oppositely phased electrical polarization. For this reason, digital information can be stored in in ferroelectrics, making them interesting candidates for non-volatile memories. Typically, switching of the ferroelectric polarization is achieved by the application of pulsed electric fields.
However, this reversal is based on incoherent dynamics and on the propagation of domain boundaries, which limits switching times to hundreds of picoseconds [41][42][43] .
Several attempts to achieve ultrafast ferroelectric switching have been made, by driving the ferroelectric soft mode coherently with light pulses, either with impulsive Raman scattering 34,[44][45][46] or direct excitation 8,47 .
The properties of ferroelectrics can for example be controlled by the photoexcitation of charge carriers across the bandgap or by excitation of impurity levels. Such schemes have been used to facilitate polarization switching, control the domain nucleation and induce self-organized domain patterns 48-51 . The light-induced structural dynamics of ferroelectric PbTiO 3 thin films were shown to involve a distortion of the unit cell along the c-axis 52 . The response of the lattice constant along this direction was extracted from changes in the time-resolved x-ray scattering angle of an out-of-plane diffraction peak. A fast contraction of the film within the first 5 ps preceded a long-lived expansion, which was explained by dynamical charge screening of the depolarization field that in thin film ferroelectrics acts against the ferroelectric polarization 53 .
More directly, the structural response of ferroelectric Sn 2 P 2 S 6 to the direct excitation of its soft mode was also measured with x-ray probes. 54 Following excitation with THz pulses of 120-kV/cm electric fields, coherent oscillations of the atoms along the soft mode coordinate were measured, through the corresponding modulation of the intensity of selected Bragg peaks. The amplitude of these motions corresponded only to a change of the ferroelectric polarization by 8%. The authors extrapolated that switching may become possible if the THz electric field was increased to 1 MV/cm.
In this context the development of mode-selective lattice control, so called "nonlinear phononics", has opened up new opportunities in ferroelectrics 55 . Transient reversal of the ferroelectric polarization 7 was observed using nonlinear optical probes, an important achievement that will likely motivate structural studies using ultrafast x-ray scattering of the involved atomic motions.

Ultrafast magnetism in metallic systems
It has long been known that ferromagnetism can be destabilized by light, although the use of optical pumping was shown to be able to drive the same phenomenon along a highly non-equilibrium path, and hence far faster than expected 6,56-58 . Time-resolved xray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) were used to provide new insight into this class of processes, rejuvenating the field.  Figure 1a shows the chemical inhomogeneities in GdFeCo on a 10-nm length scale that divide the material into Gd-and Fe-rich regions. The magnetic scattering signal S q at low scattering momenta (q < 0.2nm -1 ) allows for retrieving the average sample magnetization of the Gd and Fe spin sublattices, which are oppositely aligned at equilibrium. Figure 1b  Lastly, magnetic scattering allows for imaging magnetization dynamics using x-ray holography 69   The area of femtosecond magnetism has hence made extensive use of ultrafast x-ray sources. In addition, these experiments have been effective in developing a whole set of new techniques, which will impact this and other areas of non-equilibrium dynamics as FEL sources improve in quality and grow in number.

Charge, orbital, spin and lattice dynamics in complex oxides
Many transition-metal oxides with fractionally filled d-shells exhibit interesting collective phenomena that descend from strong electronic correlations. Especially, new phases emerge that are not captured by the familiar concepts of band theory and classical magnetism. These phases are also delicate, in that they can be easily switched by external stimulation, for example with static magnetic or electric fields and hydrostatic pressure. Excitation with light can also tip the balance between stable phases, sometimes switching the electronic properties on ultrafast time scales. As discussed above in the magnetism section, femtosecond resonant soft x-ray scattering (RSXS) is a natural tool to study the evolution of these electronic or magnetic degrees of freedom. In combination with time-resolved hard x-ray scattering, which tracks atomic structural rearrangements, or terahertz spectroscopy that measures the optical conductivity, time resolved RSXS determines directly how the electronic ordering is affected and through which stages the phase transition occurs. Time-resolved RSXS studies at the Ni L-edge revealed that charge and spin order melt also in this material when excited by near-infrared electronic 89,90 , as well as midinfrared lattice excitation 91 .
In multiferroic materials (anti-)ferromagnetic order and ferroelectricity coexist and interact by magnetoelectric coupling [92][93][94] 99 where the application of an external magnetic field to the conical phase creates a skyrmion phase.
The skyrmions are topologically protected spin configurations that have recently attracted attention for their robustness to external perturbations and for their potential in data storage applications 100 . Interestingly, the work showed that the skyrmion phase is more robust to optical excitation than the conical phase, possibly due to different spin scattering processes involved in the two phases.

Heterostructures
Complex oxide heterostructures have attracted significant interest over the past years, since interfacial coupling allows one to manipulate the static electronic and magnetic material properties and to create new functionalities at equilibrium 101   This dynamical interplay of competing orders was also observed in YBa 2 Cu 3 O 6.6 above the equilibrium critical temperature. The resonant optical excitation of the apical oxygen vibrational mode, which induces out-of-plane interlayer coherence as discussed above, partially melts the in-plane charge-density wave order as identified in a timeresolved RSXS experiment at the 932 eV Cu L 3 -edge 131 .
For the first time, x-ray scattering measurements succeeded to capture the crystallographic and the electronic properties of a transient room temperature superconductor. These findings may illustrate new pathways towards the design of novel materials exhibiting equilibrium room temperature superconductivity.

Electron phonon coupling in high-T C superconductors
As demonstrated in many cases above, combining direct measurements of the lattice phonon mode in bismuth 147 . In this experiment, they also obtained, for the first time, a quantitative measurement of the anharmonic force constants between the A 1g mode and the anharmonically-coupled longitudinal acoustic modes.

Perspectives and Conclusions
All the experiments discussed above show how the advent of short x-ray pulses has enabled a far deeper understanding of non-equilibrium phenomena in complex solids.
In most cases, free-electron laser operation is based on self-amplified spontaneous emission (SASE), producing pulses with a large bandwidth and strong shot-to-shot fluctuations in most of their key parameters, such as intensity, duration, and spectrum 40 . While one can often account for these fluctuations using single-shot diagnostics, [148][149][150] the large bandwidth of the x-ray pulses severely limits the energy resolution achieved during experiments. This problem is typically mitigated by the use of monochromators, with the caveat that they cause a severe reduction (up to two orders of magnitude) in the available x-ray intensity.
To overcome this limitation, a key aspect in the design of advanced FEL sources is the adoption of seeding schemes with the ultimate aim of reaching Fourier transformlimited x-ray pulses. [151][152][153] Compared to SASE operation, seeded FEL operation produces pulses with narrower bandwidth and significantly improved energy and intensity stability. Another important benefit of newly developed FEL sources is the increase in pulse repetition rate that will allow collecting data at reduced experimental time. In combination, we expect that seeded FEL sources with high repetition rates will foster a number of flux hungry techniques, such as time-resolved resonant x-ray diffraction or resonant inelastic x-ray scattering, with even higher time and spectral resolution.
Finally, these new sources promise the complete control of the x-ray pulse parameters, aiming to reach sub-fs duration with arbitrary pulse shape. With more precise synchronization between the x-ray pulses and the optical excitation fields, for example in the case of THz and mid-infrared pulses, 154 it is already becoming possible to make the x-ray pulses stable with respect to the absolute phase of the pump pulses. We envision that this advancement will open up entirely new areas of research investigating coherence effects. For example, it will be possible to follow changes in the material structure and electronic properties as they are induced by the excitation electric field, promising further insight into the origin of nonlinear couplings between different excitations in condensed matter.

Box 1 -Time Resolved X-ray Techniques
Pump-probe x-ray techniques constitute a valuable tool to reconstruct material dynamics by capturing directly the transient light-induced changes in the microscopic degrees of freedom. A typical x-ray time-resolved experiment is illustrated in the figure below. The sample under study is excited with a strong laser pulse, identified as pump, that triggers dynamics in the material. A time-delayed x-ray pulse probes the pump-induced changes by interaction with the material and subsequent collection of the scattered (or transmitted) beam on a detector. Depending on the choice of the photon energy in the hard and soft x-ray regimes, information about the atomic or electronic structure of the material can be retrieved using techniques such as x-ray diffraction, x-ray absorption spectroscopy and resonant x-ray diffraction. Discovered by Max von Laue in 1912, x-ray diffraction is arguably one of the most useful tools in material characterization. X-ray waves scattered by the periodically ordered atoms in a crystal interfere constructively or destructively along specific directions. The analysis of the measured interference patterns allows for determining the average position of each atom in the crystal with sub-picometer spatial resolution. For example, by monitoring the position and relative intensities of a purposely chosen set of Bragg peaks as a function of time, one can trace lattice dynamics triggered by the excitation of a coherent phonon [25][26][27] . With the symmetry of the material determining the measured diffraction pattern, one can also follow through which stages an ultrafast light-induced phase transition occurs 28 . As a last example, in analogy to the case of thermal diffuse scattering, the time-dependence of the scattered intensity in-between Bragg peaks reveals information about the dispersion of phonons without the need of ab-initio modeling of force constants 145 . X-ray absorption spectra contain fingerprints of materials' electronic and magnetic structures.
As the x-ray energy is tuned to resonance with an atomic transition, the absorption increases dramatically and electronic and magnetic states can be reconstructed in an element-specific manner. By analyzing how the absorption spectrum of a substance changes upon photoexcitation, it is possible, for example, to gain insight into transient changes in the oxidation states and bond lengths of a compound 124,155 . Also, changes in the magnetic moment of a specific atom can be disclosed by measuring x-ray magnetic circular dichroism under resonance condition 156 .
Such absorption spectroscopy captures sample properties without the possibility of spatial reconstruction, making it difficult to observe complex long-range ordering of charges, spins, and orbitals. Resonant x-ray diffraction combines the contrast mechanisms given by absorption spectroscopy with the spatial resolution given by diffraction. By performing diffraction experiments with incoming photons tuned in resonance with appropriate atomic transitions it is possible to study directly phenomena such as charge stripe order in cuprates 128,129 or orbital and spin order in manganites 75,77 . In recent years, also this technique has been brought into the time domain and has become a standard experiment for materials research at x-ray FELs. Fig. 1| Ultrafast angular momentum transfer in a ferromagnetic film. Non-local, ultrafast transfer of angular momentum in GdFeCo was revealed by time resolved magnetic small angle X-ray scattering 5 . a| Local chemical nanoscale variations for Gd, Fe and Co in Gd 24 Fe 66.5 Co 9.5 as measured with energy dispersive X-ray spectroscopy. Darker coloured areas indicate elemental enrichment, whereas white areas indicate below average concentrations. b| Temporal evolution of the magnetic diffraction, S q , for Gd 4f (red) and Fe 3d (blue) spins. The time delay (Δt) is defined as the time interval between the arrival of the pump pulse and the x-ray probe pulse. The measurement of S q at low-scattering momenta (q) (top part) probes the average sample magnetization, whereas the high-q S q (bottom part) measures the evolution of the magnetization at the nanoscale, showing the transfer of angular momentum to the Gdrich regions. c| Time evolution of the angular momentum transfer to the Gd-rich regions as extracted from the analysis of the high-q S q scattering data. The ultrafast transfer of angular momentum takes 1 ps and is followed by a slow recovery through spin dissipation within the Gd regions. Adapted with permission from Graves et al. 5 , Nature Publishing Group.

Fig. 2|
Ultrafast interfacial strain engineering. In a LaAlO 3 /NdNiO 3 heterostructure, the dynamics of multiple magnetic, electronic and structural degrees of freedom in the NdNiO 3 thin film can be observed when an insulator-metal transition is driven by resonant excitation of a high-frequency vibrational mode in the underlying LaAlO 3 substrate. a| Transient momentum-resolved intensity of the (¼ ¼ ¼) diffraction peak measured at the 852 eV Ni L 3 -edge, which is sensitive to antiferromagnetic ordering. b| Transient peak intensity of the NdNiO 3 (2½ 2½ 2½) reflection measured at X-ray energies resonant (8.346 keV, blue) and off-resonant (8.329 keV, red) with the Ni Kedge. The measured resonant diffraction intensity includes a charge order contribution (grey shaded region), which disappears on a time scale shorter than that of the offresonant intensity and is sensitive only to structural dynamics. c| Spatiotemporal evolution of the NdNiO 3 lattice, magnetic and insulator-metal dynamics along the thin film out-of-plane direction, extracted from the time-resolved diffraction experiments. Individual phase fronts of insulator-metal, antiferromagnetic-paramagnetic and structural transitions propagate at different speeds from the LaAlO 3 /NdNiO 3 heterointerface into the nickelate film. d| Illustration of these dynamics induced by the substrate phonon excitation. Panel (a) adapted with permission from Först et al., 103 Nature Publishing Group. Panels (b), (c) adapted with permission from Först et al. 104   The orbital-resolved electron-phonon deformation potential in an FeSe superconducting thin film was determined using time resolved X-ray diffraction and time-resolved angular-resolved photoemission spectroscopy (tr-ARPES). a| Displacement of the Se atom, δZ Se , extracted from the evolution of the intensity of the (004) Bragg peak. b, c| Momentum-averaged energy shifts <E> of the d xz/yz and d z 2 bands extracted from tr-ARPES measurements. All measurements are shown for different photoexcitation levels, ranging from 0.12 to 1.83 mJ cm -2 . Adapted with permission from Gerber et al. 136 , AAAS.