X-ray nanodiffraction imaging reveals distinct nanoscopic dynamics of an ultrafast phase transition

Significance

Phase transitions, the changes between states of matter with distinct electronic, magnetic, or structural properties, are at the center of condensed matter physics and underlie valuable technologies. First-order phase transitions are intrinsically heterogeneous. When driven by ultrashort excitation, nanoscale phase regions evolve rapidly, which has posed a significant experimental challenge to characterize. The newly developed laser-pumped X-ray nanodiffraction imaging technique reported here has simultaneous 100-ps temporal and 25-nm spatial resolutions. This approach reveals pathways of the nanoscale structural rearrangement upon ultrafast optical excitation, different from those transitions under slowly varying parameters. The spatiotemporally resolved structural characterization provides crucial nanoscopic insights into ultrafast phase transitions and opens opportunities for controlling nanoscale phases on ultrafast time scales.

Abstract

Ultrafast first-order phase transitions exhibit distinct transition pathways and dynamical properties that are not accessible during quasi-equilibrium transitions. Phenomena arising at the ultrafast timescale are important for understanding the transition mechanisms and in applications using the fast switching of electronic properties or magnetism. These transitions are accompanied by nanoscale structural dynamics that have been challenging to explore by optical or electronic transport probes. Here, X-ray nanodiffraction imaging shows that the nanoscale structural dynamics arising in ultrafast phase transitions differ dramatically from the transitions under slowly varying parameters. The solid-solid phase transitions in a FeRh thin film involve concurrent structural and magnetic changes and can be sensitively probed by monitoring their diffraction signatures following femtosecond optical excitation. Time-dependent nanodiffraction maps with 100-ps temporal and 25-nm spatial resolutions reveal that the preexisting nanoscale variation in phase composition results in spatially inhomogeneous changes of phase fraction after ultrafast optical excitation. The spatial inhomogeneity leads to nanoscale temperature variations and subsequent in-plane heat transport, which are responsible for spatially distinct relaxation pathways on nanometer length scales. The spatial gradients of the phase composition and elastic strain increase upon excitation rather than exhibiting the decrease previously reported in quasi-equilibrium transformations. Long-range elastic interactions thus do not play significant roles in the ultrafast phase transition. These microscopic insights into first-order phase transitions provide routes to manipulate nanoscopic phases in functional materials on ultrafast time scales by engineering initial nanoscale phase distributions.

First-order phase transitions are characterized by an abrupt change of an order parameter that parametrizes the degree of ordering in structural, electronic, or spin degrees of freedom. Ultrafast optical excitation of first-order phase transitions has the potential to allow high-speed manipulation of material properties for future technologies (1–5). A hallmark of first-order phase transitions is the coexistence of multiple phases (6–10), with phase heterogeneity at length scales as small as nanometers (10, 11). Although an extensive series of pump-probe studies have aimed to understand relevant ultrafast processes, the microscopic processes involved in ultrafast first-order phase transformations have just begun to be explored. Ultrafast nanoscopic imaging of phase transitions can reveal the dynamical evolution of the heterogeneity during the phase transition and the microscopic mechanism through which the ultrafast transitions occur.

Ultrafast nanoscale characterization methods based on optical (2, 12–15), electron (16, 17), and X-ray (18–23) microscopies have been recently developed and have revealed new physical phenomena. Hard X-ray microscopy is particularly advantageous in the study of phase transformations involving structural changes because X-ray diffraction is highly sensitive to structural heterogeneity, due to its high reciprocal-space resolution (24, 25). X-ray diffraction microscopy also preserves the spatially heterogenous stress state in complex structures such as quantum devices (25–27) because experiments do not require the preparation of the free-standing thin specimens typically required for transmission electron microscopy. Here, X-ray nanodiffraction microscopy combined with ultrafast optical excitation reveals that the nanoscale processes of the optically driven first-order phase transition in FeRh thin films are distinct from those occurring in a quasi-equilibrium transformation with slowly varying external parameters.

The intermetallic compound FeRh exhibits a first-order phase transition from a low-temperature antiferromagnetic (AFM) phase to a high-temperature ferromagnetic (FM) phase (28). Thin films of FeRh serve as an important platform to test concepts for applications in magnetic data storage (29–31). The AFM-FM phase transition in FeRh and related materials has been intensively studied on the ultrafast time scale (3, 32–36) and the nanometer length scale (37–42), separately. Early optical pump-probe studies (3, 32) initially suggested that the onset of magnetic phase transitions occurs at subpicosecond time scales through the rapid nucleation of the FM phase. Recent time-resolved X-ray studies (33–36), however, show that simultaneous structural and magnetic transformation occurs on tens to hundreds of picosecond time scales. Static X-ray imaging studies of FeRh (37, 38, 40) show that phase heterogeneity is evident on nanometer scales and changes as a function of temperature. The separate use of spatially and temporally resolved probes, however, has not revealed the dynamics of nanoscale phase transformations in FeRh.

We have developed a laser-pumped synchrotron hard X-ray diffraction nanoprobe with spatiotemporal resolutions of 25 nm and 100 ps. This instrument integrated an ultrafast laser system into a hard X-ray nanoprobe beamline for pump-probe experiments. Spatiotemporal X-ray nanodiffraction maps revealed several key nanoscale processes of the first-order phase transition in FeRh. First, the optically induced transformation is highly influenced by the preexisting spatial distribution of the FM phase, resulting in a spatially heterogeneous phase transition. The relationship between the preexisting FM phase and the optically induced FM phase suggests a mechanism in which the growth of the preexisting FM domains contributes to the phase transition over the first 100 ps. Second, the relaxation dynamics are consistent with in-plane nanoscale heat transport. This in-plane heat transport is a consequence of the spatial variation of the temperature rise due to the preexisting FM phase. Third, the spatial gradients of both the nanoscale strain and the phase composition increase upon optical excitation, suggesting that the transient structural state after optical excitation has higher elastic energy than the initial state, in contrast to structural transformations as the temperature slowly varies.

Results

Characterization of FeRh Thin Films and Laser-Pumped Synchrotron Hard X-Ray Nanodiffraction.

FeRh has the CsCl crystal structure and exhibits AFM ordering with magnetic moments of ±3 μ_B on the Fe atoms and zero magnetic moment on the Rh atoms below the AFM-FM transition temperature T_AFM-FM (28), as illustrated in Fig. 1A. At high temperatures, FeRh is in the FM phase with a magnetic moment of 1 μ_B on the Rh atoms, which are ferromagnetically coupled to nearest Fe neighbors (43). Our temperature-dependent X-ray diffraction measurements show that the epitaxial FeRh films exhibit a phase transition starting at 360 K with an out-of-plane lattice expansion (Fig. 1B) (see Materials and Methods). Fig. 1C displays a diffraction profile along the detector angle 2θ at 370 K. The profile shows a broadening of the X-ray reflection as a result of the coexistence of structurally distinct AFM and FM phases (SI Appendix, Fig. S1). The FM phase fraction within the probed volume can be obtained by using the two-peak fitting method (34) with the FM phase volume fraction given by f_FM = I_FM/(I_FM + I_AFM) where I_FM and I_AFM are the integrated diffraction intensities from FM phase and AFM phase, respectively. The investigated FeRh thin film shows a spatially homogeneous AFM phase at room temperature (SI Appendix, Fig. S2).

Fig. 1.

Ultrafast X-ray nanoimaging of a first-order phase transition. (A) Illustration of the unit cells of AFM and FM phases in FeRh. The AFM-FM magnetic phase transition occurs at the transition temperature T_AFM-FM accompanied by a lattice expansion visualized exaggeratedly. Blue arrows indicate the directions of the magnetic moments of Fe and Rh atoms. (B) Out-of-plane lattice parameter as a function of temperature during heating. The shaded region indicates the temperature range in which AFM/FM phases coexist. (C) Diffraction profile of the 002 FeRh reflection along the detector angle 2θ at 370 K measured by a 50 µm X-ray beam. (D) Schematic of the optical pump, hard X-ray probe experiment at the 26-ID beamline of the Advanced Photon Source. Detector images are measured at each X-ray probe location by raster-scanning the X-ray beam across the sample. 1 × 1 μm² maps of lattice parameter at different t are extracted from the 2θ value of the 002 Bragg peak.

Laser-pumped synchrotron hard X-ray diffraction nanoprobe measurements were developed and conducted at the hard X-ray nanoprobe beamline of the Advanced Photon Source, as illustrated in Fig. 1D. X-ray pulses with a photon energy of 11 keV and 100 ps pulse duration were focused to a full-width-at-half-maximum (FWHM) spot size of 25 nm employing high-numerical-aperture X-ray focusing optics consisting of a Fresnel zone plate and an order-sorting aperture. The detector images from nanoscale regions were obtained by raster-scanning focused X-ray probe beams across a FeRh sample (see Materials and Methods). Laser pulses with a central wavelength of 515 nm and a pulse duration of 400 fs were electronically synchronized to the synchrotron X-ray pulses. A laser incident fluence of 0.12 mJ cm⁻² was used to excite the FeRh film. The absorbed fluence is calculated to be 0.07 mJ cm⁻² using optical parameters of FeRh and experiment geometry (SI Appendix, section I). The phase composition and structural parameters were determined by analyzing diffraction patterns of the 002 FeRh reflection in detector images along 2θ at each scanned position. The experiments yielded nanoscale maps of structural variations with out-of-plane lattice parameters as a function of time (gray color maps in Fig. 1D). Further details of experimental methods are provided in Materials and Methods.

Nanoscale Variation of the Dynamics of the Optically Driven AFM-FM Phase Transition.

Fig. 2 presents maps of the FM phase fraction f_FM for three different delay times: t = −0.1 ns, 0.1 ns, and 1.5 ns. Positive values of t correspond to the laser pump pulse preceding the X-ray probe pulse. The values of f_FM are obtained from the diffraction patterns following the method described above. The map at −0.1 ns shows that f_FM varies spatially from 0.25 to 1, which is a signature of the AFM/FM phase coexistence as expected at 370 K (SI Appendix, section II). The spatial variation of f_FM is continuous rather than discrete because the size of individual AFM and FM phase domains is on the order of ∼50 nm (41), smaller than that of the effective X-ray probe size of 136 × 25 nm² under the experimental condition (see Materials and Methods). The spatial variation of f_FM at this temperature partially originates from location-dependent transition temperatures, which have been attributed to local structural variations (37, 40, 44, 45). Upon optical excitation, f_FM generally exhibits an increase at t = 0.1 ns. The magnitude of optically driven change in f_FM varies at different locations. Nearly half of the probed regions exhibit a saturation of f_FM at 1 while the other areas have f_FM less than 1. This partial AFM-FM phase transition at t = 0.1 ns is consistent with the expectation that results from an absorbed fluence that is less than the latent heat per unit area of 0.14 mJ cm⁻² (46) for a 27 nm-thick FeRh thin film. Since the nucleation and growth in FeRh complete at ∼0.1 ns (34), the spatial measurement of f_FM at t = 0.1 ns reveals the spatially dependent ultrafast phase transition as a result of nucleation and growth. The regions with f_FM <1 at t = 0.1 ns undergo either no change or their f_FM values continue to increase, as evident in the X-ray diffraction map measured at t = 1.5 ns. Whereas the regions with f_FM = 1 at t = 0.1 ns exhibit a relaxation in f_FM at t = 1.5 ns. The results clearly show that both the phase transition as monitored at 0.1 ns and subsequent relaxation dynamics are spatially inhomogeneous, although the dynamics faster than the temporal resolution of 0.1 ns, such as the onset of phase transition, cannot be resolved in our experiments.

Fig. 2.

X-ray nanodiffraction maps of the FM phase fraction f_FM at three delay times: t = −0.1 ns, 0.1 ns, and 1.5 ns. The image at t = −0.1 ns corresponds to the state at a steady-state temperature of 370 K.

To explore the nanoscale variations of the phase transition and its dynamics, the local changes in f_FM and the associated phase transition dynamics up to 15 ns after optical excitation were measured by scanning the X-ray probe along the y axis at X = 0 nm in Fig. 2. The position-time map in Fig. 3A exhibits spatial variations of f_FM both before and after optical excitation. The subsequent change in f_FM following optical excitation also shows spatially dependent relaxation dynamics. The spatial dependence of the phase transition is examined by plotting the variation of the FM phase fraction f_FM(0.1 ns) after optical excitation as a function of the preexisting FM phase fraction f_FM(−0.1 ns), as shown in Fig. 3B. A key feature of spatially dependent phase transitions is evident in the relationship between f_FM(0.1 ns) and f_FM(−0.1 ns), exhibiting two distinct regimes of the AFM-FM phase transition: (i) for values of f_FM(−0.1 ns) less than 0.55, there is a monotonic increase in f_FM(0.1 ns) as a function of f_FM(−0.1 ns); and (ii) for values of f_FM(−0.1 ns) between 0.55 and 1, f_FM(0.1 ns) saturates at 1.

Fig. 3.

Nanoscopic dynamics of phase composition. (A) Space- and time-resolved FM phase fraction f_FM measured along the y axis at X = 0 nm in Fig. 2. (B) FM phase fraction f_FM(0.1 ns) as a function of the initial FM phase fraction f_FM(−0.1 ns) obtained from the data shown in (A). Blue curve is a fit based on the Avrami equation (see text). (C and D) Changes (dots) in f_FM as a function of t measured at Y = 360 nm and Y = 210 nm at which the initial FM phase fraction is larger and less than 0.55, respectively. Solid and dashed curves are the fits by the phenomenological thermal-transport models described in the main text.

The monotonic trend as a function of f_FM(−0.1 ns) in regime (i) can be described by Avrami kinetics (47). The FM phase fraction at 0.1 ns is given by f_FM(0.1 ns) = f_FM(−0.1 ns) + Δf_FM, where Δf_FM is a transformed fraction of FM phase at t = 0.1 ns. Assuming a spatially random distribution of FM phase regions, the transformed FM fraction is $\mathrm{\Delta }{f}_{\text{FM}}\left(t\right)=1-e^{-K{t}^n}$, where K is the growth rate and n is the Avrami exponent. The phase transitions in thin films generally exhibit n = 2, indicating quasi-instantaneous heterogeneous nucleation followed by two-dimensional domain growth (48, 49). The growth rate K is defined as K = πρv² for the phase transition with n = 2 where ρ is the density of FM nucleation per unit area and v is the growth velocity (47). The spatially dependent density of FM nucleation is defined by ρ = ρ_ave f_FM(−0.1 ns) where ρ_ave is the average nucleation density in the mapped area. Based on Fig. 2, we estimate the nucleation density ρ_ave to be 2 × 10¹³ m⁻² by counting the number of domains per unit area, which sets the lower bound of the nucleation density because each domain can grow from at least one nucleation. Using v as the only fitting parameter, the best fitting result (the blue curve in Fig. 3B) shows v = 1.3 × 10³ m s⁻¹. This value represents the upper bound of the growth speed of FM domains in the probed region. The obtained value of the growth velocity is smaller than the longitudinal sound speed of 5.1 × 10³ m s⁻¹ in FeRh, which is consistent with the slower phase front propagation speed of the laser-induced phase transition than the speed of sound (19, 34). The dependence of the transformation on the number of preexisting FM nucleation provides an evidence that the growth contributes to the AFM-FM phase transition within 100 ps upon excitation, a process that was not captured by the previous ensemble-averaged experiments (34).

In regime (ii), the AFM phase is completely converted to the FM phase by optical excitation, as indicated by the saturation of f_FM(0.1 ns) at 1, because the absorbed energy is larger than the latent heat required to complete the phase transition. The excess energy, the difference between the absorbed energy and latent heat, further raises the temperature in these regions. Because the excess energy is larger in higher f_FM(−0.1 ns) regions, the temperature rises spatially vary, contributing to subsequent heat transport processes as discussed in detail below.

We next examine the nanoscale variation of the relaxation dynamics of Δf_FM. Fig. 3 C and D show Δf_FM as a function of delay time at two positions with coordinates Y = 360 nm and 210 nm, at which the values of f_FM(−0.1 ns) are larger and smaller than 0.55, respectively. The relaxation time scales at these two positions differ significantly, in particular, in the range from 0.1 ns to 3 ns. A phenomenological model can be used to quantify the time dependence of f_FM (SI Appendix, section III and Fig. S3). As shown in Fig. 3C, the relaxation of Δf_FM in the high f_FM(−0.1 ns) region exhibits a good agreement with a time-dependent phase fraction change $\text{Δ}{f}_{FM}\sim \left[f_{\mathit{rise}}\left(t, t_1,{\xi }_1\right)e^{-\frac{t-t_1}{{\tau }_0}}\right]$. Here $f_{\mathit{rise}}(t, t_i,{\xi }_i)=\left(1+\text{erf}\left(\frac{2\sqrt{2}\left(t-t_i\right)}{{\xi }_i}\right)\right)$ describes the increase in f_FM, modeled by an error-function with the rising edge at a time t_i and a time constant ξ_i. The factor $e^{-\frac{t-t_i}{{\tau }_0}}$ represents an exponential decay of the transformed fraction with a time constant τ₀ starting at t_i. This relaxation of the FM phase fraction is consistent with the cooling of the film through the heat transport from the film to the substrate, which can be approximated by an exponential decay within the relatively narrow time window of Fig. 3C. In Fig. 3D, Δf_FM shows a transient plateau from 0.1 ns to 3 ns, in poor agreement with the exponential decay model, which indicates that additional processes occur at this location. To model these previously unknown processes, we have modified the model by adding a second term to the model for Δf_FM in regions of low f_FM(−0.1 ns): $\text{Δ}{f}_{FM}\sim \left[f_{\mathit{rise}}\left(t, t_1,{\xi }_1\right)e^{-\frac{t-t_1}{{\tau }_0}}\right]+\left[f_{\mathit{rise}}\left(t, t_2,{\xi }_2\right)e^{-\frac{t-t_2}{{\tau }_0}}\right]$. The first term in the decay model describes a fast rise within 0.1 ns and the subsequent relaxation on the nanosecond time scale, shown by the blue dashed line in Fig. 3D, similar to the observation at Y = 360 nm. The second term describes a process that leads to an additional slow increase of the phase fraction up to 3.5 ns and relaxes on the same time scale (red dashed line in Fig. 3D). The combined result of the first and second terms in the model provides an excellent fit to the data. The contribution of the second term to the relaxation dynamics is consistently observed in regions with f_FM(−0.1 ns) < 0.55.

The spatial variations of the relaxation timescale are attributed to distinct heat-transport processes resulting from the nanoscale temperature variations upon optical excitation. In regions where f_FM(−0.1 ns) < 0.55, most of the absorbed optical energy is devoted to supplying the latent heat for the phase transition so that the sample temperature does not change significantly. In regions where f_FM(−0.1 ns) > 0.55, however, only a portion of the absorbed energy is used for the phase transition. The remaining energy leads to further temperature increases of the FM phase. The expected temperature rise due to the absorbed fluence is calculated by the equation ΔT = F_abs/(C_FeRh × D) where F_abs is the absorbed fluence, C_FeRh is a specific heat of FeRh (33), and D is the thickness of the thin film. The absorbed fluence of 0.07 mJ cm⁻² can lead to a maximum temperature change of the FM phase by 5.6 K. Thus, the in-plane temperature gradient from high f_FM(−0.1 ns) to low f_FM(−0.1 ns) regions emerges upon optical excitation. As a result, the in-plane heat diffusion leads to a slow secondary increase in the FM phase fraction in the low f_FM(−0.1 ns) region, which is well described by the second component in the phenomenological model. The slow rate of the phase transition in low-f_FM(−0.1 ns) regions is apparent in the map collected at t = 1.5 ns (Fig. 2). The characteristic in-plane heat diffusion time is ξ_char ∼ L²/α, where L is a distance between two probed regions and α is the thermal diffusivity. With α = 0.9 × 10⁻⁵ m²/s (50, 51) and L = 150 nm, we obtain ξ_char ∼ 2.5 ns, which agrees with the observed characteristic time scale of ξ₂ = 3.2 ± 1.6 ns (SI Appendix, section III).

Nanoscale Phase Composition and Microstructure during the Phase Transition.

The spatial variation of the FM phase composition and the structural distortion during the phase transition can be extracted by measuring the magnitude of the spatial gradient of f_FM and out-of-plane strain ε₃₃, termed $\mid \nabla f_{\text{FM}}\mid$ and $\mid \nabla {\text{ε}}_{33}\mid$, respectively. Fig. 4A displays line profiles of $\mid \nabla f_{\text{FM}}\mid$ and $\mid \nabla {\text{ε}}_{33}\mid$ at t = −0.1 ns from Y = 112.5 nm to 312.5 nm in Fig. 3A. Local maxima in both $\mid \nabla f_{\text{FM}}\mid$ and $\mid \nabla {\text{ε}}_{33}\mid$ are observed at Y = 160 nm and 260 nm, indicating the significant spatial variation of both phase composition and strain at these locations. The observed strain gradient of 10⁴ m⁻¹ is consistent with the strain gradient sustainable in thin films (52). Upon optical excitation, $\mid \nabla f_{\text{FM}}\mid$ and $\mid \nabla {\text{ε}}_{33}\mid$ increase while the locations of the maxima of $\mid \nabla f_{\text{FM}}\mid$ and $\mid \nabla {\text{ε}}_{33}\mid$ do not shift within the experimental uncertainty of ±10 nm as shown in Fig. 4B.

Fig. 4.

Time-dependent phase composition gradient $\mid \nabla f_{\text{FM}}\mid$ and strain gradient $\mid \nabla {\text{ε}}_{33}\mid$. (A and B) Line profiles of $\mid \nabla f_{\text{FM}}\mid$ (circles) and $\mid \nabla {\text{ε}}_{33}\mid$ (squares) at t = −0.1 ns and 0.1 ns. The data are obtained from Y = 112.5 nm to 312.5 nm in Fig. 3A. Error bar indicates the experimental uncertainty of ±10 nm. (C) Time-dependent $\mid \nabla f_{\text{FM}}\mid$ along the y axis in the region identical to Fig. 3A. (D) Spatial variation of $\mid \nabla f_{\text{FM}}\mid$ at t = −0.1 (blue) and 0.1 ns (orange). The red and gray stripe patterns highlight the regions where the $\mid \nabla f_{\text{FM}}\mid$ peaks disappear and appear, respectively, after excitation.

The observations above are distinct from what was found when the phase transition is driven by slowly varying the temperature (37). In that case, nanoscale strain fields and the accompanying distribution of phases gradually shift and disappear during the structural phase transition. The spatial variations of the phase composition and strain are the consequences of the competing short- and long-range interactions (10, 11, 53). When the temperature slowly varies, long-range elastic interactions minimize the free energy through the reduction of the elastic strain energy (53). However, the observation of larger gradients of both f_FM and ε₃₃ indicates that the elastic energy increases upon excitation, in contrast to the elastic energy relaxation observed when the order parameters slowly vary. These results suggest that the long-range elastic interaction does not significantly contribute to the free energy landscape during the ultrafast phase transition in this system, consistent with the sharpening of domain walls observed during an ultrafast structural phase transition in a 1T-TaS₂ crystal (17).

Fig. 4C shows a position-time map of $\mid \nabla f_{\text{FM}}\mid$ spanning 0.9 μm in length. Comparing with Fig. 4 A and B, this wider range shows various characteristic responses that are present across the sample. Most locations generally undergo increases in $\mid \nabla f_{\text{FM}}\mid$ upon excitation as discussed in Fig. 4 A and B, while the changes in $\mid \nabla f_{\text{FM}}\mid$ relax fully within 15 ns. The positions of most $\mid \nabla f_{\text{FM}}\mid$ maxima do not exhibit a transient shift within the probed delay time. Fig. 4D compares the phase composition gradient $\mid \nabla f_{\text{FM}}\mid$ in the same wide range before and after the excitation at t = 0.1 ns. The regions from Y = −300 nm to −450 nm, indicated by the red striped pattern, display a reduction of $\mid \nabla f_{\text{FM}}\mid$, distinct from the general change in $\mid \nabla f_{\text{FM}}\mid$. This decrease in $\mid \nabla f_{\text{FM}}\mid$ results from the reduced phase heterogeneity followed by the completion of the AFM-FM phase transition, i.e., f_FM(0.1 ns) = 1, at the positions where f_FM(−0.1 ns) is larger than 0.55 as presented in Fig. 3A. In rare cases (e.g., around Y = −50 nm shaded by gray-striped pattern), we also note that a new maximum of $\mid \nabla f_{\text{FM}}\mid$ appears upon photoexcitation, which may be caused by intrinsic structural defects that alter the photoinduced structural changes locally.

Discussion

The behavior of FeRh at the AFM-FM transition temperature is relevant to the operating conditions of heat-assisted magnetic recording (29). The phase-transition dynamics as observed close to the transition temperature provide several important perspectives for the potential applications. First, the strong dependence of the phase transition on the FM phase fraction implies a possible strategy to control the magnitude and dynamics of the nanoscale phase transition by varying preexisting FM phase composition. Second, a narrow region with phase gradient between heterogeneous phases can be realized on ultrafast time scales, rather than broadened phase gradient which typically forms through long-range elastic interactions under quasi-equilibrium conditions (53). This observation indicates that nanometer magnetic domains with sharper boundaries can be achieved by ultrafast excitation. Third, the structural nanoscale phase transition processes are reversible at subnanosecond timescale as presented in this study because the same pathway occurs over thousands of pump-probe cycles during the measurements. This phenomenon may originate in a structural pinning effect that has also been observed during the slow thermal cycling (37). This reversible rather than irreversible process is particularly important for manipulating phases in a predictable manner for magnetic recording accompanied by structural phase transitions on the ultrafast timescale. We note that the irreversible process may present during ultrafast phase transition, but the pump-probe technique used in this study is not sensitive to them.

In conclusion, the laser-pumped synchrotron hard X-ray nanodiffraction technique enables the nanoscale visualization of physical phenomena during the optically driven first-order structural phase transitions. Our observations reveal a strong dependence of the AFM-FM phase transition of FeRh on preexisting FM domains after optical excitation. The spatially inhomogeneous relaxation dynamics is a consequence of spatially varying phase transformation leading to an additional in-plane thermal transport. We further find that the phase transition driven by ultrafast energy deposition results in an increase in the strain gradient, distinct from the case under slowly varying temperature conditions. It suggests that the effect of the long-range elastic interaction in the structural phase transition can be different depending on the rate of energy deposition, providing a nanoscopic perspective of phase transition dynamics. Besides studying nanoscale phase transitions, the spatiotemporally resolved X-ray diffraction demonstrated here can be applied to a wide range of functional materials and devices for studying nanoscale dynamical phenomena that are previously inaccessible.

Materials and Methods

Sample Preparation.

An epitaxial FeRh thin film with a thickness of 27 nm was deposited on a (001)-oriented MgO substrate by the comagnetron sputtering method. Due to the lattice mismatch between the film and the substrate, the in-plane compressive strain was applied to the FeRh thin film, resulting in tetragonally distorted FeRh film. The transition temperature of FeRh film is T_AFM-FM = 360 K, above which AFM phases start to transform into FM phase spanning a temperature range of ∼20 K. The magnetic phase transition is accompanied by a structural distortion along the out-of-plane direction.

Laser-Pumped Synchrotron Hard X-Ray Diffraction Nanoprobe Technique.

The laser-pumped synchrotron hard X-ray diffraction nanoprobe technique was implemented at the 26-ID-C beamline of the Advanced Photon Source (APS) at Argonne National Laboratory. Laser pulses with a central wavelength of 515 nm were provided by the second harmonic generation from the fundamental wavelength of 1,030 nm from a high-repetition-rate laser (Satsuma, Amplitude Laser). The laser repetition rate was tuned to 271 kHz to match the repetition rate of the singlet X-ray pulse in the hybrid fill operation mode of the APS. The sample, X-ray optics, and optomechanical nanopositioning system were housed in a vacuum chamber. The laser pulse, with a maximum energy of 3.5 μJ, was focused by a pair of concave and convex lenses. The distance between the two lenses was adjusted to vary the laser spot size. The focused beam entered the vacuum chamber through a viewport and propagated about 70 cm to the sample surface. The smallest spot size at the sample surface (full-width-at-half-maximum) was 0.4 mm. The laser incident angle was 25° with respect to the sample surface. The maximum incident fluence was 0.12 mJ cm⁻². X-ray pulses with a photon energy of 11 keV and 100 ps pulse duration were focused on the sample surface with an incident angle of 22.16° with respect to the sample surface, satisfying the Bragg condition of the 002 FeRh reflection. Due to the X-ray footprint, the X-ray spot size was elongated along the horizontal direction. The spot size on the sample surfaces was 25 nm (vertical) × 70 nm (horizontal) while the smallest resolvable feature size, in consideration of the sample thickness and diffraction geometry, is 136 nm (SI Appendix, Fig. S4). Thus, the effective spot size is 136 × 25 nm². A two-dimensional pixel array detector was positioned at 23.9 cm from the focused X-ray spot on the sample and gated to capture the X-ray diffraction pattern at a given delay time. Location-dependent X-ray diffraction patterns were measured by scanning the X-ray beam via X-ray focusing optics across the sample in the transverse plane with respect to the X-ray propagation direction with a step size ranging from 10 nm to 30 nm. The scales of the X-axis in the resultant real-space maps have been corrected by considering the crossing angle of 67.84° between the X-ray scanning axis and the sample X-axis shown in Fig. 2.

The lattice parameters of FeRh were measured without scanning the X-ray incident angle in our experiment. A Fresnel zone plate was used to focus the X-ray pulse with an angular divergence of Δθ = 0.48° at a photon energy of 11 keV. Due to the large divergence of the focused X-ray beam, the geometry at a fixed incident angle satisfied the Bragg condition in a range of Δθ. Based on the diffraction geometry, this angular range corresponded to 2% of lattice parameter changes in FeRh. This change was larger than the expected change in the lattice parameter (0.6%) during the structural phase transition in FeRh. It was thus sufficient to obtain the 2θ value of the peak using the centroid of the diffraction patterns at the fixed incident angle on the pixel array detector during the phase transition.

Temperature-Dependent X-Ray Diffraction.

X-ray diffraction measurements at a series of temperatures were conducted at station 7-ID-C of the APS. The photon energy and the spot size of the X-ray beam were 11 keV and 50 μm, respectively. The FeRh film on the MgO substrate was placed on a heating stage mounted on a six-circle Huber diffractometer. The temperature of the heating stage was electronically controlled (Lakeshore model 340). Diffracted X-rays were measured by a two-dimensional pixel array detector (Pilatus 100 K) placed 99.5 cm from the FeRh sample. The 002 FeRh reflection was measured as a function of temperature ranging from 300 K to 390 K with a step size of 10 K. The lattice parameters along the out-of-plane direction were obtained by measuring the θ-2θ curve of 002 FeRh reflection.

Data Availability

Some study data are available. (The raw data files are too large to be deposited in a persistent repository. The data will be provided upon request by the corresponding author.)