Introduction

Since the advent of lasers capable of producing pulses on subpicosecond timescales, the study of materials on these time scales has become a significant field of research. The interaction of intense and short light pulses with solid-state matter can produce transient non-equilibrium states that differ nontrivially from known equilibrium states. Such states are of interest from multiple perspectives. On a fundamental level, understanding the properties of strongly non-equilibrium states poses a challenge for existing theoretical and computational models that typically assume only small deviations from thermodynamic equilibrium. These states also provide a useful way to quantify the coupling among electronic, magnetic, and structural degrees of freedom in a non-perturbative regime. This can be a particularly powerful idea in cases where the excitation that drives the system out of equilibrium is tailored to selectively drive one degree of freedom1. Beyond using such experiments to better understand the couplings that underlie the physics of complex materials, they also offer new approaches for driving phase transitions and domain switching, with possible applications in faster and more efficient solid-state data processing and storage2,3 and the transient manipulation of superconducting transport4,5.

Initially, experiments studying ultrafast dynamics in materials made use of ultrafast lasers operating in the visible and infrared wavelength range. As the availability of other wavelengths and pulsed radiation sources (e.g., electrons) expanded so did also the range of capabilities of such experiments. The focus of this perspective is a discussion of the new opportunities that arise from recent developments in combining phase-stable and narrow-band pulsed light sources in the THz and mid-infrared with new instrumentation at X-ray free electron lasers. Tailored long-wavelength pulses offer unique opportunities to controllably and selectively drive coherent dynamics in a variety of materials, which can be powerfully combined with X-ray spectroscopy performed at modern free-electron laser facilities to directly and quantitatively characterize changes of spins, orbital, and lattice order. We first give a brief overview of the current state of such efforts, then discuss recent progress in both the generation of long-wavelength radiation and new X-ray techniques, and then we give an outlook on how we view possible future opportunities.

Short laser pulses with near-visible wavelengths can efficiently generate coherent dynamics of the lattice (coherent phonons) or spin (coherent magnons). Typically such processes are modeled in a semiclassical framework where the interaction of the light with the material is considered to generate an effective force on an oscillator (see Fig. 1)6,7,8. For femtosecond-duration pulses where the pulse duration is small compared to the inverse frequency of the excitation, there are two mathematical limits for this effective force: the “impulsive” limit, where the effective force relaxes back to zero on a time scale fast compared to the inverse oscillator frequency, and the “displacive” limit, where the effective force relaxes very slowly in comparison to the inverse of the oscillator frequency. The latter case tends to occur when the driving laser pulse is in resonance with a long-lived electronic transition for oscillators with coordinates that preserve preexisting structural (or magnetic) symmetries8. Time-resolved X-ray diffraction has been used to track dynamics in both limiting cases for coherent phonons9,10,11,12 and for coherent magnons in the displacive limit13. Typically coherent excitations driven in the displacive limit are larger in amplitude but are limited in scaling by strong local heating effects that arise from large densities of resonant electronic transitions.

Fig. 1: Excitation schemes.
figure 1

Classical view of the coherent excitation of an oscillator in different mathematical limits in the absence of damping, showing the time domain effective force (top row), the corresponding Fourier transform of the force (middle row) and the classical response of the expectation value of the oscillator coordinate \(\left\langle y\right\rangle\). The columns show the different limiting cases: (a) impulsive excitation, where the effective force on the oscillator exists for only a short time in comparison to the natural period of the oscillator, (b) displacive excitation, where the effective force follows a step-like behavior, and (c) resonant excitation, where the excitation frequency is set to match the natural frequency of the oscillator (vertical dashed lines).

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In the last couple of decades significant progress in methods for generating short, very broad bandwidth pulses in the mid- and far-infrared have made it possible to drive similar dynamics using long-wavelength light14,15. As with short-wavelength optical drives, sufficiently broadband long wavelength radiation can drive dynamics impulsively or displacively, depending on the interaction of the light and the relaxation dynamics of the material. For example, the transient magnetic field of nearly half-cycle THz pulses can drive a coherent magnon response in NiO in the impulsive limit16. In some metallic systems a type of displacive excitation has also been observed in response to few-cycle THz excitation17. The low cycle frequency of such light offers also a straightforward possibility for a third option: that of resonant excitation (see Fig. 1c). For cases where the effective force on the oscillator is driven by the field of the light pulse (e.g., for electric- or magnetic-dipole active degrees of freedom) one can in principle tailor the spectrum of the light pulse to match that of the resonance associated with the excitation of interest, offering a more efficient pathway to large amplitude coherent responses. Considerable work has been done using such sources in combination with optical and THz frequency probes to quantify the response of the material, using such excitations to manipulate properties such as conductivity18, magnetic order19,20,21, and superconductivity5,22,23,24.

The use of X-ray probes in combination with resonant phonon excitation by mid-IR pulses has been explored since high intensity femtosecond X-ray pulses have become available from X-ray free electron lasers, starting with the LCLS at SLAC. One such early work was concerned with the melting of the antiferromagnet and orbital order in a half doped manganites by using mid-IR excitation to drive the Mn-O stretching vibration25. In the meantime, more work using resonant mid-IR pumping combined with X-ray probes have been performed. Examples include studying the structural dynamics associated with transient changes in superconducting transport26, characterizing the nature of an insulator- metal transition in manganites27 and looking at the influence of resonantly excited phonon modes in a substrate on the structural28 and magnetic order in epitaxial NdNiO3 films29. To date such studies have involved the use of mid-IR pulses with an uncontrolled phase, which made it impossible to resolve dynamics within the period of the oscillations of the electromagnetic field of the driving light.

The situation in this respect is a bit different for longer wavelength pump pulses in the THz range, where typical pulse generation methods such as optical rectification naturally create pulses with a stable carrier-envelope phase (CEP). These kinds of few-cycle THz excitations have been used to study the properties of electromagnons in multiferroic TbMnO3 using resonant soft X-ray diffraction to measure coherent spin dynamics driven resonantly by the electric field of the THz pulse (see Fig. 2)30. More recently, a combination of soft- and hard-X-ray diffraction in another system has demonstrated the ability to separately measure the vibrational and spin components of a resonantly-driven electromagnon31. Phase-stable THz excitations were also used to study the structural response of the metal-insulator transition in VO232, though in this case no coherent response was observed. Extensive work has been performed on SrTiO333,34,35 where it could be shown that a strong resonant driving of a low-frequency soft mode could lead to phonon upconversion (see Fig. 3). All these hard X-ray studies used X-ray diffraction as a probe. THz driving has most recently been extended to use diffuse X-ray scattering to obtain coherent phonon response that is dispersive (q dependent)36. Hard X-ray diffraction in resonance with an orbital transition was very recently used to observe coherent entanglement between orbital states when driving an orbital excitation in a f-level system (Tb2Ti2O7)37.

Fig. 2: Spin dynamics.
figure 2

Time-dependent magnetic X-ray diffraction intensity I of the (0q0) peak of TbMnO3 at different temperatures, compared with the electric field E of the THz of the pump trace (red solid line). The intensity oscillations can be directly related to transient rotations of spins due to an electromagnon excited by the THz pulse. Reproduced from the data of Kubacka et al., Science 343, 1333 (2014)30.

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Fig. 3: X-ray diffraction.
figure 3

Time-dependent X-ray diffraction intensities of the (2−23) reflection of a SrTiO3 epitaxial film driven by phase stable THz excitation for various peak electric field strengths. Higher peak field strengths show evidence of additional frequencies caused by phonon upconversion. Reproduced from M. Kozina et al., Nature Phys. 15, 390 (2019)35.

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The studies described so far have focused on the direct excitation of the lattice or the magnetic subsystems as it covers the 1–25 THz regime. In insulators, it is also possible to excite resonantly d-d excitations at much higher energies. This has been used to obtain all optical switching in Co:YIG crystals by an ultrafast change of the magnetic anisotropy3, and X-rays have been used to investigate the initial behavior of the magnetization dynamics after such an excitation38.

Generating intense THz and mid-infrared light

To better understand the potential for the study of materials using long-wavelength light in combination with novel X-ray spectroscopies at XFELs, we briefly review the main techniques that are most suitable for such studies.

We begin with a discussion of methods to create phase-stable THz-frequency pulses, the lower frequency range of the spectrum. Most modern XFEL sources are coupled with conventional amplified femtosecond laser systems that output near-optical wavelength pulses that are synchronized to the X-ray output to within a few femtoseconds. These ultrashort near-optical pulses can then be converted to very broadband pulses of THz radiation via a process known as “optical rectification”39. In short, a pulse with a duration of 40–500 fs is sent into a crystal with a large second-order nonlinear susceptibility. Because of this nonlinearity, the polarization density P inside the material has a component that is proportional to the square of the electric field E of the oscillating near-optical pulse. The far-field radiation of the nonlinear response thus results in a quasi-single-cycle pulse with a duration on the order of 1 ps, which contains a large continuum of frequencies in the THz spectral range. The efficiency and relative spectral content of this pulse depends strongly on the material used. It is in particular highly sensitive to deviations from the phase-matching condition, which for a collinear beam geometry is a matching of the group velocity of the near-optical input pulse with the phase velocity of the generated THz. Recently considerable effort has gone into identifying organic crystals that are optimized for collinear THz generation. Efficient THz generation (with peak fields on the order of 1 MV/cm) in a conventional collinear geometry has been reported for 800 nm input wavelengths in the organic crystal BNA40,41 and at wavelengths near 1300 nm for DAST42, DSTMS43, OH144 and PNPA45. Each of these generation crystals have somewhat different output spectra that peak in the range of 1–2.5 THz due to differences in the frequencies of IR-active vibrational resonances in the THz range. These organic crystals are also known to degrade after some time in response to long-term exposure to intense driving fields. As a more robust inorganic alternative, LiNbO3 is often used to generate broadband THz near 1 THz46. Since the collinear phase matching conditions are not satisfied in LiNbO3 for any practical driving wavelengths, LiNbO3 is typically used to generate THz radiation in a noncollinear geometry using driving pulses that are tilted by imaging the first order reflection from a grating47. Peak fields as high as 4 MV/cm have been reported for optical rectification in LiNbO348.

Another method that can convert amplified femtosecond near-optical pulses to broadband THz pulses is so-called “air-plasma” generation, where an intense femtosecond pulse is partially frequency-doubled and then tightly focused into air at intensities sufficient to create a plasma49. The breaking of inversion symmetry caused by the superposition of the two driving frequencies can lead to a transient current in the plasma that has a component that roughly corresponds to the time-envelope of the original pulses. Although the physical mechanisms leading to THz generation are complex50, air-plasma generation can create extremely broadband pulses, typically with lower pulse energies that is possible with optimized optical rectification setups with similar input fields. The efficiency of generation improves dramatically by using longer wavelength drivers, with in excess of 100 MV/cm peak fields reported for a 3.9 μm driver51.

Recently, the use of spintronic emitters has emerged as an alternative to optical rectification and air-plasma generation for converting amplified femtosecond near-optical light to broadband THz pulses. Spintronic emitters are solid-state devices that consist of a film heterostructure with at least one ferromagnetic metal and a non-magnetic metal with strong spin-orbit coupling. Femtosecond laser excitation of the ferromagnetic layer causes a spin-polarized current to move into the non-magnetic layer, where the spin-hall effect causes the spin current to transform into a transversal charge current52. For femtosecond input pulses this gives rise to the emission of broadband pulses in the THz range. Since materials for the emitter can be selected such that there are no strong infrared-active vibrations in the THz range, the frequency content is very broadband, similar to that created by air-plasma sources. Spintronic emitters have been used to generate peak fields as high as 1.5 MV/cm when driven by appropriately intense near-optical lasers53.

While sufficiently broadband THz pulses provide a nearly impulsive force to magnetic or vibrational excitations with resonant frequencies below 5–10 THz, for some applications it is more appropriate to use narrow-band pulses to drive particular resonances more selectively and efficiently. This is of particular relevance for vibrational resonances with frequencies above about 10 THz, where linewidths become relatively narrow. Creating pulses at these higher frequencies is most often accomplished using difference-frequency generation (DFG), where two intense pulses at a much higher frequency (the pump and signal) are superimposed on a material with a large second-order susceptibility to create a pulse with a center frequency corresponding to the difference between the two (the idler). If Fourier-transform-limited pulses are used for the pump and signal pulses, the idler frequency can be tuned by changing the center frequency of one or both of the signal and pump pulses. This is often accomplished by using the output of one or two collinear optical parametric amplifiers (OPAs). Alternatively, the pump and signal can be chirped via dispersion or a grating stretcher before the mixing, which allows the idler frequency to be tuned by varying the delay between the pump and signal14. The latter scheme can also be used to create highly narrowband pulses, since the instantaneous difference frequency between the pump and signal contains a smaller range of frequencies than is possible with two Fourier-transform limited pulses with the same bandwidth.

One important consideration of THz generation for some applications is whether the phase of the waveform is stable with respect to the intensity maximum of the original driving pulse(s), which is typically synchronized and cross-correlated with the arrival time of the X-rays. Since the timing of the intensity maximum of the driving pulse (or pulses) typically also determines the timing of the intensity maximum of the THz pulse, this is usually equivalent to imposing a requirement on the carrier-envelope phase (CEP) of the generated THz pulse. Using a source with a perfectly stable CEP in combination with a synchronized X-ray pulse allows for a characterization of the dynamics of materials in response to the electric field of the THz pulse. In such cases the time-resolution of the experiment is not determined by the pulse duration of the THz pulse, but rather by the degree of CEP stability–in addition to the probe pulse duration, synchronization uncertainty and other experiment-specific factors. The methods of broadband THz pulse duration discussed above naturally produce CEP-stable pulses; for the DFG-based methods of narrowband generation the CEP stability depends on the method. If the pump and signal pulses do not have a stable relative phase, the generated DFG will also not be CEP stable. One way to achieve such stability in DFG is to mix the signal outputs of two OPAs that are seeded by a common white light source54.

Recent interest in the physics of chiral excitations in materials has stimulated efforts to generate THz pulses with elliptical and circular polarizations55,56. One method to achieve this is to generate two CEP stable pulses and to recombine them with a variable relative delay57,58. Another method is to use a quarter-waveplate to convert linearly polarized THz pulses into pulses with elliptical or circular polarization by inducing a relative phase delay between orthogonally polarized components59. For broad and moderate THz bandwidths the polarization state is less well defined as is typical for optical frequencies, due to the general inability of both methods to achieve a phase shift of exactly one quarter wavelength throughout the entire bandwidth.

Driving THz coherences in materials

Now that we have reviewed methods of THz and mid-IR pulse generation, we now turn to the question of how these can be used to drive excitations in materials. We focus primarily on systems where there is an electronic band gap Eg for transitions involving delocalized electronic states such that Eg ≫ hν, where ν is a frequency contained within the THz pulse. We also assume a negligible free carrier density due to doping. If the peak THz field is also not sufficient to induce Zener tunneling60 or multiphoton excitation across the gap, we can then ignore the interaction of the THz pulse with delocalized carriers. We instead consider the interaction of the THz pulse with low-frequency excitations such as vibrations, spin waves and localized electronic excitations.

For excitations that are electrically or magnetically dipole-active, the conceptually simplest mechanism for driving such excitations is via linear interaction with the field of the frequency components of the THz pulse close to the resonant frequency of the excitation. For infrared-active vibrational excitations this interaction is often treated classically, since the classical Lorentz oscillator model is usually an excellent approximation for the interaction. If such excitations have a large oscillator strength the interaction is very strongly frequency dependent, resulting in sometimes dramatic changes in the penetration depth of the THz pulse for different frequency components within its bandwidth. Spin-wave resonances are also possible to drive, typically with the magnetic field component of the pulse and with a much smaller interaction strength16. Orbital excitations, particularly for 4f and 5d systems, can also be excited directly by THz light. Note that since the interaction is (at least to leading order) linear in the field, in reality for all these excitations the THz light propagation in the material actually hybridizes with the excitation itself, forming so-called polaritons of various flavors. This is important for determining the wavevectors involved in the excitation, which is typically extremely low in magnitude relative to the Brillouin zone dimensions due to the high speed of light relative to other excitations in most materials.

Besides this direct, linear excitation of dipole-active excitations, it is also possible to use nonlinear channels to drive excitations with THz light. Raman-active excitations, for example, can be driven using frequency components of the intensity of the THz pulse. In some cases this interaction can be dramatically enhanced via anharmonic coupling between two or more vibrational modes, particularly when one mode is linearly driven in resonance with the pulse. This case is often referred to as “nonlinear phononics” and has been employed in many systems, typically using the direct linear driving of one high frequency vibrational mode to drive a lower frequency Raman-active mode25. Anharmonic coupling is, however, not strictly necessary to see significant nonlinear driving; for example, sum-frequency excitation of a vibration using purely electronic effects has been reported61.

X-ray probing schemes

The increasing availability of intense, femtosecond X-rays over a wide range of wavelengths has offered new ways to understand the effects of strong-field THz and mid-IR light on materials. Broadly speaking, the advantages of X-rays over other kinds of ultrafast probes rest on either the short wavelength of X-rays or on the high energy of X-ray photons.

The range of wavelengths covered by X-rays includes typical interatomic distances in solids. This makes it possible to use X-ray diffraction to measure interferometrically the structure of materials with atomic resolution. This relies on the elastic scattering of X-ray photons, which far from core level transitions is predominantly sensitive to the spatial distribution of electrons. Since most electrons for typical materials are localized to the vicinity of nuclei, the scattering is often well-approximated as a measure of the ionic lattice structure. Many ultrafast X-ray diffraction measurements focus on the measurement of intensity changes of Bragg peaks, which are to first order sensitive to dynamics of coherent optical phonons near the Γ point of the Brillouin zone9,10,11,12. These changes can be related to atomic displacements with minimal input from theory, making X-ray diffraction a uniquely quantitative tool for characterizing the amplitude of coherent vibrations induced by a pump excitation. This technique can be extended to include excitations elsewhere in the Brillouin zone by measuring changes to the weak diffuse scattering between Bragg reflections62, offering the possibility to study in detail the ways in which light can couple to off-Γ point modes36 and how the phonon subsystem equilibrates via phonon-phonon scattering63.

Bragg diffraction can also be performed using wavelengths near an X-ray absorption edge, which can cause a strong enhancement of contributions from orbital or magnetic order. This is called resonant Bragg diffraction (more generally resonant X-ray scattering), and can be applied in both the soft and in the hard X-ray regimes. This method is sensitive to orbital and spin orderings with arbitary length scales, and is related to core-level spectroscopies such as X-ray absorption near edge spectroscopy (XANES) and X-ray magnetic circular dichroism (XMCD). As mentioned in the introduction, resonant Bragg diffraction with femtosecond time resolution at XFEL facilities has been successfully applied to the study of coherent magnetic30 and orbital37 excitations in materials. These studies have operated in the mode where they infer dynamic response by measuring changes to intensity of Bragg reflections, and thus they have been applied so far only to the study of Γ-point coherent excitations. Using resonant diffuse scattering to measure off-Γ-point coherent dynamics of magnetic or orbital order is a fascinating potential extension of this idea that has so far not been reported.

A method with strong connections to resonant diffuse scattering is resonant inelastic X-ray scattering (RIXS), where scattered photons near a resonance are measured as a function of both momentum transfer and energy change64. In equilibrium RIXS is a powerful technique to measure the dispersion of excitations. Some pioneering experiments have explored the question of how RIXS can be extended to the study of transient material states driven by strong optical and near-infrared excitation65,66,67. These experiments so far are typically studying material states that are driven very far from equilibrium by very strong redistributions of electronic states. When combined with phase-stable THz or mid-IR pumps tuned to a vibrational or magnetic resonance, RIXS has the interesting potential to selectively probe how particular excitations couple to this resonance. Such experiments will likely require measurements with exceptionally high statistics relative to the current state of the art, which may be forthcoming with the upcoming availability of RIXS instrumentation at high-repetition rate XFELs68,69.

X-ray absorption spectroscopy is another potentially important tool for studying transient changes to electronic states and local structure70. Here in particular we would highlight the potential utility of X-ray magnetic circular and linear dichroism, which have been used extensively in studies of magnetic order in response to strong excitation at near optical wavelengths71,72,73. The element and edge specificity of X-ray magnetic dichroism offers the ability to study how different magnetic species interact and also how magnetism is shared between spin and orbital reservoirs74. Combining this with resonant pumping of particular vibrations or magnetic excitations can offer new and exciting opportunities to study detailed aspects of the interaction between structural and magnetic degrees of freedom.

Current efforts at XFEL sources to achieve seeded operation at shorter wavelengths may offer advantages in terms of better time resolution, reduced intensity fluctuations as well as a reduction of angular and spatial jitter. An interesting potential future development is combining coherent driving with ultrafast X-ray imaging, made possible by the transverse coherence of the X-ray pulses from XFELs. Spatial resolution on the nanometer length scale could potentially offer a direct view of dynamics of skyrmions or domain walls of various types.

Summary and Outlook

The ability of long-wavelength light to selectively drive large amplitude coherence in materials coupled with the ability of X-ray probes to selectively interrogate the response of these same materials is a powerful combination that will become more powerful as the capabilities and availability of XFEL facilities increase. This offers unique opportunities to directly measure the mode-selective strength of couplings, which is vital input for understanding the mechanisms for material manipulation by ultrafast pulses. As time resolution and repetition rates at facilities improve it will be possible to more completely cover the full energy and momentum scale of relevance for materials. Less incrementally, experiments involving multiple pump pulses that excite two or more degrees of freedom simultaneously could open the door to a form of multidimensional nonlinear spectroscopy with the advantages of X-ray selectivity. Another perspective is the possibility to use circular drives to break time reversal symmetry and use X-ray techniques to investigate the magnetization or the chirality of a charge density wave. Progress in both driving and probing schemes might also help discover new schemes for switching for polarization and/or magnetization with minimal dissipation, with strong impact on energy efficient computation and storage.