Laser-induced transient magnons in Sr₃Ir₂O₇ throughout the Brillouin zone

Fig. 1B shows the time evolution of the ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ magnetic Bragg peak intensity up to 7 ps after the arrival of the 2-$\mathrm{\mu }$m (620-meV) laser pump that excites carriers across the band gap (18). This was measured using Ir $L_3$-ege tr-REXS at $T\approx 110$ K $\ll T_N$ = 285 K using the (−3.5, 1.5, 18) magnetic Bragg peak (Materials and Methods). Immediately after the pump, magnetism is reduced by 50 to 75% for laser fluences between 5.2 and 32.2 mJ/${\mathrm{c}\mathrm{m}}^2$. This occurs faster than our time resolution of 0.15 ps, which is substantially quicker than in other materials including ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (19). It is noted that even for strong fluences some remnant magnetic fraction is observed immediately after the laser pump, suggesting some experimental mismatch between pumped laser and probed X-ray volumes (c.f. SI Appendix). However, the transient signal shows signs of saturation, suggesting the pumped volume is completely demagnetized. We refer to further details on the recovery of the magnetic long-range order in SI Appendix. The tr-REXS results in Fig. 1B clearly show that a 2-$\mathrm{\mu }$m laser pump results in an appreciable quenching of magnetic long-range order that survives on a picosecond timescale. However, the experiment does not reveal the microscopic spin configuration of the transient state. As illustrated in Fig. 1A, a transiently suppressed magnetic order parameter can arise from several very different microscopic configurations that give the same REXS response. We thus studied the RIXS response of the transient state to gain insight into the Q dependence of the magnetic correlations.

Fig. 2 A and B display energy-loss spectra of ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ measured at ($\pi ,\pi$) and $\left(\pi ,0\right)$, corresponding to the magnetic Brillouin zone center and zone boundary. The blue data points correspond to RIXS spectra in the equilibrium state, showing four features: an elastic line, a collective magnon, a magnon continuum, and an orbital excitation (20–23). The collective magnon features a moderate dispersion, shifting in energy from 100 meV at ($\pi ,\pi$) to 150 meV at $\left(\pi ,0\right)$, while the magnon continuum (250 meV) and orbital excitation (680 meV) reveal negligible dispersion. It is believed that the magnetic excitations in equilibrium arise predominantly from the combination of Heisenberg-like interactions within the iridium layers and an anisotropic exchange perpendicular to the tetragonal plane (see also SI Appendix) (20, 24, 25). The orbital excitation, on the other hand, can be understood considering the electronic configuration of ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$. It is defined by the five iridium valence electrons, residing in a crystal-field-derived $t_{2g}$ orbital manifold. The ground state is further split by strong spin–orbit coupling and moderate Coulomb interactions, establishing a filled $J_{\text{eff}}$ = 3/2 and half-filled $J_{\text{eff}}$ = 1/2 Mott state (20, 24–26). Thus, the excitation epitomizes a transition between these two manifolds (20, 22, 23).

We have overplotted the energy-loss spectra in equilibrium (blue) with transient state data (orange). These have been prepared with a 20 mJ/${\mathrm{c}\mathrm{m}}^2$ laser pulse, for which a substantial suppression of magnetic order has been found (see Fig. 2B). Because small drifts in the X-ray source position can result in shifts of the measured RIXS spectrum, static and pumped spectra were measured with alternate shots of the free electron laser for each delay. The time resolution of the setup equaled $\sim$400 fs (see Materials and Methods for details). At both reciprocal lattice positions we observe significant changes in the electronic correlations at $t>0$. This is seen most clearly in the difference spectra shown in Fig. 2 C and D, evincing that the magnon and orbital excitations are altered upon photodoping at both ($\pi ,\pi$), and $\left(\pi ,0\right)$.

Further insight into the transient short-range correlations is gained from a quantitative analysis of the excitation spectra. A sum of four Gaussian-shaped peaks was used to represent the energy-loss data in Fig. 2 A and B (see dotted lines in the figure and Materials and Methods for further information). The fit shows that the magnon and orbital amplitudes are suppressed in the transient state and that their width is enlarged (see Fig. 3 A and B). Notably, at the magnetic wavevector the fitting parameters are most strongly modified at 0.5 ps and recover only partially within 5 ps, which is in line with the incomplete recovery of magnetic long-range order (see Fig. 1B).

The cross-section of the orbital excitation around 680 meV is dependent on the respective charge occupations of the $J_{\text{eff}}$ = 3/2 and $J_{\text{eff}}$ = 1/2 state. The intensity would, for instance, decrease if fewer than four electrons per Ir side reside in the $J_{\text{eff}}$ = 3/2 ground state and increase if the $J_{\text{eff}}$ = 1/2 state was empty. The transient depletion of the excitation thus provides direct evidence that not only $J_{\text{eff}}$ = 1/2 but also 3/2 electrons are pumped over the insulating band gap, and that some of the $J_{\text{eff}}$ = 3/2 carriers do not decay into their orbital ground state within 5 ps. This supports a picture in which the electronic subsystem remains in a transient state for appreciable time delays.

Having established the dynamics of the orbital excitation, we now turn to the transient behavior of the collective (pseudo-)spins. In equilibrium, magnetic long-range order ensures the existence of well-defined spin-waves. Upon photoexcitation, broader peaks are observed while the magnetic exchange couplings are unaffected. This can be conceptualized as a redistribution of magnons out of the modes populated in equilibrium into a range of transient magnons around the original mode. Our data allow us to directly investigate how magnons are modified at different delays after photoexcitation and to examine how they change across the Brillouin zone using ($\pi ,\pi$) and $\left(\pi ,0\right)$ as representative points.

The substantial anisotropy perpendicular to the tetragonal plane leads to collinear magnetic long-range order, revealing a large magnon gap that is minimal at ($\pi ,\pi$) and maximal at $\left(\pi ,0\right)$ (cf. Fig. 4B for details) (20–24). Thus, the results in Fig. 3A show that magnons are modified over an extended area in reciprocal space and that these changes persist for several picoseconds. This experimental result is strikingly different from the behavior in materials hosting a gapless excitation spectrum. In isotropic Heisenberg-like ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (see Fig. 4A), for instance, the only observable changes in the magnon occurred at the magnetic Brillouin zone center of $\left(\pi ,\pi \right)$ (2). In the following discussion, we aim to assess these differences.

The transient state created here features suppressed magnetic long- and short-range correlations throughout the Brillouin zone and it, therefore, has some similarities to a thermal state at elevated temperature. This state, however, appears to form effectively instantaneously, within our time resolution of either 150 or 400 fs depending on whether one considers the REXS or RIXS signatures. These timescales are much faster than typical thermalization processes in magnetic insulators, ranging from several to hundreds of picoseconds (27–30). We thus consider the physical mechanisms at play, beyond a simple effective temperature model.

The photo-excitation process promoting charge carriers across the insulating gap leaves behind local spin vacancies that create nonthermal magnons spread across the entire Brillouin zone. These high-energy magnons can decay into lower-energy multiple-particle excitations via magnon–magnon scattering processes following the dispersion relation—which, in lowest approximation, is similar to the one of the unperturbed state. A full thermalization of the system, however, requires coupling to other subsystems, which becomes unavoidable for the dissipation of transient magnons around the minimum of the dispersion relation.

In gapless antiferromagnets, such as ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (25, 31), a steep magnon dispersion from high to effectively zero energy establishes a well-defined decay channel (see Fig. 4A). Thus, spin waves at high energy face multiple possibilities to disintegrate, but the options become increasingly limited around the minimum of the Goldstone-like mode. This gives a natural explanation of why ultrafast magnons were observed only at ($\pi ,\pi$) but not at $\left(\pi ,0\right)$ for ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (2). Furthermore, the small spin-wave gap enables an efficient energy transfer into the lattice subsystem via low-energy phonons, restoring the equilibrium configuration.

We note that Néel order in ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ is unstable if one considers only a single Ir layer but stabilized by a very small interlayer c-axis coupling amplified by a divergence in the in-plane magnetic correlation length within the Ir layers (see SI Appendix). This is in strong contrast to bilayer materials such as ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ which order magnetically without necessarily invoking coupling between different bilayers. Although the bilayer system features far stronger anisotropy and intrabilayer coupling, this is offset by the spin gap impeding the growth of the in-plane magnetic correlation proceeding the transition. Empirically, ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ and ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ feature comparable Néel temperatures (285 and 240 K, respectively) despite the spin-wave gap of the former material being roughly 150 times larger (see Fig. 4) (20, 25, 31). Thus, no pronounced decay channel is present in ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$, which inherently limits the thermalization of transient magnons along a particular wavevector. Furthermore, phonon-assisted energy transfer processes are strongly reduced by the large spin gap, leading to long-lived magnons that are trapped over a large reciprocal space area.

Following this argument, the partial recovery of magnetic long-range order at a picosecond timescale may arise from two mechanisms. The magnetic time constant is close to the charge timescale that has been reported previously via ultrafast reflectivity measurements (32). This may attest to a link between charge and magnetic degrees of freedom, which is also supported by the wavevector-independent suppression of the orbital excitation below 2 ps (see Fig. 3B). In Mott materials the (pseudo-)spin configuration is directly related to the charge distribution on the atomic sites, whose recovery reinstates the original one spin/site population. Thus, it is conceivable to attribute the partial recovery of magnetic order in ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ to its Mott nature. Alternatively, the partial recovery of magnetic long-range order may originate from a redistribution of transient magnons within the Brillouin zone, pointing toward a scenario in which the laser pump generates an excess of magnons at the magnetic wavevector. In fact, the results shown in Fig. 3A suggest a suppression of spin waves at ($\pi ,\pi$), which is absent at $\left(\pi ,0\right)$.

In summary, we report a near-instantaneous creation of transient magnons in the gapped antiferromagnet ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ after a laser excitation of 2 $\mathrm{\mu }$m. The ultrafast transverse short-range correlations occur at both extremes of the magnetic dispersion in momentum space, showing the existence of trapped spin waves that are likely present throughout the entire Brillouin zone. This demonstrates an incoherent response of transient magnetism, which is fundamentally different from in gapless antiferromagnets such as in Heisenberg-like ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (2). The results are interpreted in the context of a spin-bottleneck effect. In ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ a steep dispersion exists from high energy magnons at the magnetic zone boundary into low-energy magnons at $\left(\pi ,\pi \right)$, which allows for a highly efficient magnon decay. In contrast, the large magnon gap and moderate dispersion of ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ leads to transient spin waves that are trapped in the entire Brillouin zone. Thus, our results emphasize the need to include contributions like anisotropic magnetic exchange interactions alongside electron–phonon couplings in theoretical approaches that model transient magnetic states. Finally, we remind the reader that neither a collinear antiferromagnetic spin alignment nor magnons are exact eigenstates of an $S=1/2$ quantum magnet. Thus, it may be natural to expect strong magnon–magnon scattering occurs in some transient states. Further experimental and theoretical efforts along these lines will be vital to progress in the understanding of the ultrafast dynamics in quantum materials, including cases where complex competitions of macroscopic quantum phases appear via photodoping.

Sample Preparation and Characterization.

All measurements were performed on ${\mathrm{S}\mathrm{r}}_3{\mathrm{I}\mathrm{r}}_2{\mathrm{O}}_7$ single crystals that were grown with a flux method as described in ref. 33 and references therein. The high quality of the crystals was confirmed via Laue and single-crystal diffraction. Here, we denote reciprocal space using a pseudo-tetragonal unit cell with $a$ = 3.896 Å and $c$ = 20.88 Å at room temperature.

All experiments were conducted on the same sample with crystal orientations $\left[\mathrm{1,0,0}\right]$ and $\left[\mathrm{0,0,1}\right]$ or $\left[\mathrm{1,1,0}\right]$ and $\left[\mathrm{0,0,1}\right]$ in the scattering plane for tr-REXS or tr-RIXS experiments, respectively. In both cases, a horizontal scattering geometry was used and the sample was cooled to $T\approx$ 110 K via nitrogen cryostreams.

Optical Laser Pump.

One hundred-femtosecond-long pump pulses of 620 meV (2 $\mathrm{\mu }$m) were generated by an optical parametric amplifier similar to previous ultrafast experiments on ${\mathrm{S}\mathrm{r}}_2{\mathrm{I}\mathrm{r}\mathrm{O}}_4$ (2). The angle between the incident X-ray and infrared pulses was ${\mathrm{20}}^{○}$. This leads to an estimated laser penetration depth of $\sim 82$ nm for grazing incident X-rays (see SI Appendix).

tr-REXS.

The ultrafast recovery of magnetic long-range order was studied at beamline 3 of the SPring-8 Angstrom Compact free-electron LAser (SACLA) featuring a repetition rate of 30 Hz (34, 35). The X-ray energy was tuned to the Ir $L_3$-edge at 11.215 keV and refined via a resonant energy scan of the $\left(-3.5,1.5,18\right)$ magnetic Bragg peak. The reflection was detected at 2$\theta$ = 92.${\mathrm{2}}^{○}$ using a multiport charged coupled device area detector (0.0086 r.l.u. per pixel) (36). The Bragg condition was established by rotating the sample surface normal $\mathrm{\Delta }\chi$ = 21.${\mathrm{2}}^{○}$ out of the scattering plane. The X-rays were focused to a spot size of 20-$\mathrm{\mu }$m FWHM and hit the sample at a grazing angle of $\sim 1.{\mathrm{6}}^{○}$. The X-ray penetration depth was estimated to 162 nm (see SI Appendix). The laser spot size was $\sim$230-$\mathrm{\mu }$m FWHM at normal incidence. The detector was read out shot-by-shot and thresholded to reduce background arising from X-ray fluoresence and electrical noise. Two-dimensional detector images were integrated around the position where the Bragg peak was observed. Each data point contains statistics from 300 to 600 shots. The 300-fs jitter of the free electron laser was corrected with a GaAs timing tool for delays $t\hspace{0.17em}<$ 7 ps, yielding an effective time resolution of 150 fs at FWHM (37).

Fig. 1B reports the magnetic Bragg peak ratio $I_{\text{on}}$/$I_{\text{off}}$, where $I_{\text{on}}$ denotes the intensity after laser excitation and $I_{\text{off}}$ when the laser was switched off. It is noted that even for strong fluences some remnant magnetic signal is observed for $t\hspace{0.17em}>$ 0, suggesting some experimental mismatch between pumped laser and probed X-ray volumes Further information on the time evolution of the magnetic order parameter is given in SI Appendix.

tr-RIXS.

The ultrafast recovery of magnetic short-range correlations was studied at the X-ray Pump Probe instrument of the Linac Coherent Light Source (LCLS) running at a repetition rate of 120 Hz (38). The data at ($\pi ,\pi$) and $\left(\pi ,0\right)$ correspond to measurements at $\left(-3.5,0.5,20\right)$ and $\left(-3.5,\mathrm{0,19.6}\right)$ with $2\theta =93.7$ and $91.8^{○}$. The X-rays were focused to a spot size of 50-$\mathrm{\mu }$m FWHM. We used a grazing incident geometry of 3.7 and 2.${\mathrm{1}}^{○}$ for the two reciprocal lattice positions, yielding an X-ray penetration depth of 378 and 214 nm, respectively (see SI Appendix). The laser spot size equaled 845-$\mathrm{\mu }$m FWHM at normal incidence and the fluence was fixed to 20 mJ/${\mathrm{c}\mathrm{m}}^2$. The same RIXS spectrometer as in ref. 2 was used, delivering an energy resolution of $\sim 70$ meV with an angular acceptance of $6^{○}$ (0.28 Å${}^{-1}$) on the analyzer. The ePix100a area detector was read out every shot (39). The time resolution of the experiment arising from a combined jitter and beam drift effect was limited to $\sim$0.4 ps. It is noted that it proved impractical to use the timing tool, as it was insufficiently sensitive on the aggressively monochromatized incident beam. RIXS spectra were collected in a stationary mode of 144,000 shots each. Two to six acquisitions were taken for each time delay. The data presented in Fig. 2 A and B were normalized to an incident beam intensity monitor and calibrated to the energy of the orbital excitation at 680 meV (20–23). The center of the elastic line and its width were fixed in the analysis to 0 meV and the experimental resolution, respectively. Robust fits were obtained by further constraining the energy of the magnon continuum to 260 meV and its amplitude to the mean values of 2.02 and 1.44 for ($\pi ,\pi$) and $\left(\pi ,0\right)$, respectively. All other parameters were varied freely and are shown in SI Appendix, Fig. S2.

We thank Chris Homes for discussions. The design, execution of the experiments, and the data analysis are supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division, under Contracts DE-SC0012704(BNL) and DE-AC02-06CH11357(ANL). D.G.M. acknowledges funding from the Swiss National Science Foundation, Fellowship P2EZP2_175092. C.D.D. was supported by the Engineering and Physical Sciences Research Council (EPSRC) Centre for Doctoral Training in the Advanced Characterization of Materials under Grant EP/L015277/1. X.L. and J. Lin were supported by the ShanghaiTech University startup fund MOST of China under Grant 2016YFA0401000, National Natural Science Foundation of China under Grant 11934017, and the Chinese Academy of Sciences under Grant 112111KYSB20170059. Work at University College London was supported by the EPSRC under Grants EP/N027671/1 and EP/N034872/1. The work at the Institute of Photonic Sciences received financial support from the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” program for Centers of Excellence in R&D (SEV-2015-0522), from Fundació Privada Cellex, from Fundació Mir-Puig, and from Generalitat de Catalunya through the CERCA program and from the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant Agreement 758461). J. Liu. acknowledges support from the NSF under Grant DMR-1848269. The magnetic Bragg peak measurements were performed at BL3 of SACLA with the approval of the Japan Synchrotron Radiation Research Institute (Proposals 2017A8077, 2018A8032, and 2019A8087). This research made use of the LCLS, SLAC National Accelerator Laboratory, which is a DOE Office of Science User Facility, under Contract DE-AC02-76SF00515.