Abstract
Understanding how microscopic spin configuration gives rise to exotic properties at the macroscopic length scale has long been pursued in magnetic materials1,2,3,4,5. One seminal example is the Einstein–de Haas effect in ferromagnets1,6,7, in which angular momentum of spins can be converted into mechanical rotation of an entire object. However, for antiferromagnets without net magnetic moment, how spin ordering couples to macroscopic movement remains elusive. Here we observed a seesaw-like rotation of reciprocal lattice peaks of an antiferromagnetic nanolayer film, whose gigahertz structural resonance exhibits more than an order-of-magnitude amplification after cooling below the Néel temperature. Using a suite of ultrafast diffraction and microscopy techniques, we directly visualize this spin-driven rotation in reciprocal space at the nanoscale. This motion corresponds to interlayer shear in real space, in which individual micro-patches of the film behave as coherent oscillators that are phase-locked and shear along the same in-plane axis. Using time-resolved optical polarimetry, we further show that the enhanced mechanical response strongly correlates with ultrafast demagnetization, which releases elastic energy stored in local strain gradients to drive the oscillators. Our work not only offers the first microscopic view of spin-mediated mechanical motion of an antiferromagnet but it also identifies a new route towards realizing high-frequency resonators8,9 up to the millimetre band, so the capability of controlling magnetic states on the ultrafast timescale10,11,12,13 can be readily transferred to engineering the mechanical properties of nanodevices.
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Source data for the main figures are provided with this paper. Further datasets collected for this study are available from the corresponding authors on request.
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Acknowledgements
We thank Xirui Wang and P. Jarillo-Herrero for helping with sample characterization and C. Settens for the support in preparing the powder X-ray diffraction sample. We thank B. Freelon, T. Rohwer and A. Kogar for the instrumentation work of the keV ultrafast electron diffraction (UED) setup at MIT and R. Li and S. Weathersby for their support of the SLAC MeV-UED operation. We thank M. Bisher and D. Mankus at Robert A. Swanson (1969) Biotechnology Center in the Koch Institute for technical support on sample preparation. This work was primarily supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-SC0012509 (UED and ultrafast electron microscopy (UEM) measurements, ultrafast optical measurements, data analysis and modelling, sample preparation and manuscript preparation by A.Z., Q.Z., F.Z., Y.S., K.H., D.X., X.X., N.G. and H.W.). A.Z., Y.S. and N.G. acknowledge funding by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division (keV UED data acquisition and analysis) and the Gordon and Betty Moore Foundation’s EPiQS Initiative grant GBMF9459 (keV UED instrumentation). Bulk crystal growth is supported by NSF MRSEC 1719797. X.X. and J.-H.C. acknowledge the support from the State of Washington-funded Clean Energy Institute. A.Z. acknowledges support from the Miller Institute for Basic Research in Science for data acquisition, analysis and manuscript preparation. H.W. acknowledges support for time-resolved X-ray diffraction by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. Works at the Advanced Photon Source (powder X-ray diffraction and time-resolved X-ray diffraction) and the Center for Nanoscale Materials (UEM), both US Department of Energy Office of Science User Facilities, were supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. X.S., M.E.K., D.L., A.H.R., J.Y., S.P. and X.W. acknowledge support from the US Department of Energy, Basic Energy Sciences, Scientific User Facilities Division Accelerator & Detector R&D programme, the Linac Coherent Light Source facility and SLAC under contract nos. DE-AC02-05-CH11231 and DE-AC02-76SF00515 (MeV-UED at SLAC).
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Contributions
A.Z., Q.Z., X.X. and H.W. conceived the study. Q.J. grew the single crystals under the supervision of J.-H.C. K.H. prepared the thin films used in the ultrafast electron diffraction experiments. A.Z. and Y.S. performed the keV ultrafast electron diffraction experiment. A.Z., Q.Z., K.H., X.S., M.E.K., D.L., A.H.R., J.Y., S.P., X.W., X.X. and H.W. performed the MeV ultrafast electron diffraction experiment. F.Z., H.L., T.E.G., A.Z., I.A. and H.W. performed the ultrafast electron microscopy experiment and analysed the data. Q.Z. and K.H. performed the time-resolved optical polarimetry under the supervision of X.X. F.Z., D.A.W. and H.W. performed time-resolved X-ray diffraction experiments. A.Z., Y.S., F.Z. and S.H.L. performed powder X-ray diffraction measurements. A.Z., Q.Z., F.Z. and Y.S. performed data analysis and interpreted the data. A.Z. wrote the manuscript, with critical inputs from Q.Z., F.Z., D.X., X.X., N.G., H.W. and all other authors. The project was supervised by X.X., N.G. and H.W.
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Extended data figures and tables
Extended Data Fig. 1 Spin-mediated shear oscillation detected by MeV ultrafast electron diffraction.
a, Equilibrium diffraction pattern at 100 K in the [1 0 3] zone axis, measured by 4.2-MeV electrons. High-intensity Bragg peaks are labelled; peaks with red or blue labels have their photoinduced dynamics plotted in panel c. Note that the scale bar for momentum transfer includes the 2π factor. b, Differential intensity following photoexcitation by a 400-nm, 2-mJ-cm−2 pulse, in which the diffraction pattern before the pulse incidence was subtracted from the one at 50-ps pump–probe delay. Dashed line indicates the approximate axis of rotation parallel to the b* axis for the photoinduced seesaw motion in reciprocal space. c, Photoinduced change in intensity of three Friedel pairs, exhibiting oscillatory dynamics with several frequencies. The intensity changes were calculated with respect to the values before photoexcitation. d, Fourier transform amplitude of the oscillatory components of the intensity dynamics in c, featuring a prominent mode at 10 GHz with two secondary modes at higher frequencies. e, Temperature-dependent amplitude of the 10-GHz mode extracted from the three Friedel pairs in c and d. The mode was amplified after cooling below TN and the overall trend is consistent with that in Fig. 3d. f, Initial change in peak intensity following photoexcitation, showing a fast Debye–Waller suppression over approximately 750 fs, as indicated by the arrow. Data in this panel were taken at 30 K with an incident fluence of 9 mJ cm−2. Intensity was averaged over all labelled Bragg peaks in a and the curve is a guide to the eye.
Extended Data Fig. 2 Illustration of interlayer shear in electron microscopy and diffraction.
a,b, Schematics of the real-space and reciprocal-space lattice of FePS3. Owing to the monoclinic unit cell, peaks with Miller indices (H = ∓3, L = ±1) are in the zeroth-order Laue zone (ZOLZ) for the [1 0 3] zone axis. The curvature of the Ewald’s sphere relative to the reciprocal lattice is drawn to scale in panel b for the 26-keV electron beam used in the figures in the main text (it is not drawn to scale in the other panels). c, In ultrafast electron microscopy measurement, bend contours corresponding to peaks A and B in panel d move towards the same direction (that is, in-phase motion) under the reciprocal lattice tilt depicted in panel d caused by interlayer shear. In this example, both bend contours move to the left because the film locally curves downwards; the contours will both move to the right if the film locally curves up. d, Schematic of seesaw tilt of relrods in ZOLZ as a result of interlayer shear. Red arrows indicate the movement direction of the relrods. Peaks A and B form a Friedel pair. Under this seesaw tilting motion, the intensity of peak A in a two-dimensional detector increases, whereas the intensity of peak B decreases. Drawings in c and d are exaggerated for visual clarity.
Extended Data Fig. 3 Bend contour assignment with dark-field electron microscopy.
a, Bright-field electron micrograph taken at 98 K with continuous-wave electrons. Colour-coded solid and dashed curves trace the bend contours that correspond to panels c–h. The blue line demarcates the tip of the sample that is separated from the rest of the sample by folds. This region develops bend contours that are qualitatively different from those in Fig. 1f because of slightly modified strain condition between thermal cycles. b, Selected area electron diffraction taken in the sample shown in a. The seesaw rotation axis after photoexcitation is shown as the dashed line. c–h, Dark-field electron micrographs corresponding to peaks in b. All dark-field images share the same colour scale.
Extended Data Fig. 4 Bend contour movement during sample tilt.
The panels are a series of equilibrium bright-field electron micrographs at 98 K, taken from the same flake as shown in Fig. 1f at different sample holder tilt angles around the axis indicated in the top-left image (dashed line). This axis is parallel to the line connecting the (±3 ±3 ∓1) peaks (Extended Data Fig. 3b). Coloured dots mark the bend contour movements at different spatial locations associated with peaks \((\bar{3}\,3\,1)\) (red) and \((3\,\bar{3}\,\bar{1})\) (green and blue).
Extended Data Fig. 5 Coherent oscillations in all micro-patches of the free-standing film.
a, High-resolution bright-field electron micrograph of the FePS3 thin film at 98 K studied in the main text. Dashed red lines trace several defects present in the film, such as wrinkles and folds. b–f, Evolution of the bend contour position along several line cuts in panel a following photoexcitation by a 515-nm, 2.4-mJ-cm−2 pulse. The corresponding Bragg order for each bend contour is labelled. Note the in-phase oscillations of the contour pair in panel c.
Extended Data Fig. 6 Distinct fluence-dependent plateau levels below and above TN.
The photoinduced intensity plateau (p0) of the \((\bar{3}\,3\,1)\) peak is measured as a function of incident fluence of the 260-nm pump pulse, taken at 30 K (a), 79 K (b) and 136 K (c). At 136 K, the dominant contribution to p0 is the Debye–Waller factor. Hence, the plateau value from 136 K was subtracted at each fluence in a and b to remove the Debye–Waller effect. Green shades denote the saturation regime in which a further increase in fluence does not result in a larger p0.
Extended Data Fig. 7 Extracted optical constants of FePS3.
a,b, Solutions to equations (3) and (4) using experimental values of reflectivity R and the imaginary part of the dielectric function ε2 (ref. 62). Solid and dashed curves are two possible solutions for the complex refractive index n + iκ. c, Computed penetration depth δ for the two solutions of κ. Note the logarithmic scale of the vertical axis. d, Real part of the dielectric function computed from equation (5) using the two solutions in panels a and b. In the low-energy range (<5 eV), the solid curves of all panels are the physical solutions.
Extended Data Fig. 8 Temperature-dependent and fluence-dependent time-resolved polarimetry.
a, Time evolution of the change in polarization rotation (Δφ) after the incidence of 400-nm, 0.8-mJ-cm−2 pulses at different temperatures, as indicated on the right. As Δφ is negative, the vertical axis shows −Δφ. Each trace is vertically offset by 0.015 rad for clarity. b, Maximum change in the photoinduced polarization rotation angle (|Δφ|max) within the pump–probe delay window in panel a, measured for two different incident fluences. Points in purple are reproduced from Fig. 3c and data are normalized between 0 and 1 to highlight the peak position shift. Curves are guides to the eye. c, Left axis, temperature-dependent polarization rotation φ across the antiferromagnetic phase transition, reproduced from Fig. 3a. Right axis, −δφ/δT ≡ (φ(T) − φ(T + δT))/δT with different values of δT, normalized between 0 and 1. The peak positions, as marked by the triangles, shift towards TN as δT decreases.
Extended Data Fig. 9 Lattice parameters from temperature-dependent powder X-ray diffraction.
a–d, Extracted lattice parameters a, b, c and β. e, Temperature-dependent microstrains in the sample, assuming an isotropic microstrain distribution, namely, assuming the tensor surface in panel j is a sphere. This value can be interpreted as the local variation of unit cell dimensions averaged over all crystallographic directions. f–h, Temperature evolutions of S400, S040 and S004 that correspond to microstrains along the a*, b* and c* axes, respectively. All other SHKL parameters are kept independent of temperature. Error bars in a–h represent 1 s.d. in the refinement fitting; error bars are smaller than the marker size in b. i, Scattered X-ray intensity as a function of the diffraction angle 2θ, collected at 15 K. j, Tensor surface representing the microstrain distribution in different directions (μx, μy and μz) at 15 K. Grids are equally spaced. The surface is calculated from the following SHKL values71: S400 = 0.0557, S040 = 0.00164, S004 = 0.0167, S220 = 0.00618, S202 = 0.0323, S022 = 0.0136, S301 = 0.0607, S103 = −0.00769, S121 = 0.0105.
Extended Data Fig. 10 Finite-element simulation of free-standing film motion following photoinduced interlayer expansion and interlayer shear.
a, Schematic of the model, in which the film is represented by 60 × 6 blocks. Both nearest-neighbour and next-nearest-neighbour interactions are considered, in which the effective spring constants used in the simulation are k0 = 10, k1 = 1, k2 = k3 = 2, all in arbitrary units. b,d, Time-dependent change in the interlayer spacing (b) and interlayer shear (d) for each location along the lateral dimension of the film (x axis in panel a). In b, the spacing change is computed with respect to the initial interlayer spacing. In both panels, values at each x position are calculated as the average through all layers of the film. c,e, Temporal evolution of change in the interlayer spacing and shear, integrated from b and d over all lateral positions. The oscillatory signals have distinct frequencies. See Methods section for simulation details.
Supplementary information
Supplementary Information
Full crystal structure of FePS3 (Supplementary Note 1), including Supplementary Fig. 1. Derivation of the relation between reciprocal-space tilt and real-space shear (Supplementary Note 2), including Supplementary Fig. 2. Comparison between interlayer breathing and interlayer shear (Supplementary Note 3), including Supplementary Fig. 3. Further discussion about the change of the monoclinic angle on demagnetization (Supplementary Note 4), including Supplementary Fig. 4. Evidence for photoinduced interlayer shear oscillations in FePSe3 (Supplementary Note 5), including Supplementary Figs. 5 and 6. Further references.
Supplementary Video 1
Spatially resolved photoinduced shear oscillation in FePS3 visualized by ultrafast electron microscopy. The video shows photoinduced shifts in the bend contours below and above the Néel temperature, exhibiting pronounced oscillation only in the antiferromagnetic state. In the video taken at 98 K, dashed white curves mark a pair of stationary contours corresponding to the (0 ±6 0) peaks. The 515-nm pump laser had an incident fluence of 2.4 mJ cm−2 and the data were taken with a 200-keV electron beam.
Supplementary Video 2
Photoinduced shear oscillation in FePSe3. The video shows a similarly pronounced contour position oscillation in the antiferromagnetic state of FePSe3, taken at 98 K with the same pump and probe condition as that in Supplementary Video 1.
Supplementary Video 3
Simulated film motion following photoexcitation. The video shows the instantaneous velocity (a), horizontal displacement (b), vertical displacement (c), angular momentum (d) and interlayer shearing angle (e) of each coarse-grained region in a free-standing thin film, following a photoexcitation event at the zeroth time step. The film is depicted in the a–c plane. Angular momentum is computed with respect to the axis going out of the page at the film centre of mass. Displacement values are normalized with respect to the horizontal or vertical spacing between adjacent blocks. See Methods for simulation details.
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Zong, A., Zhang, Q., Zhou, F. et al. Spin-mediated shear oscillators in a van der Waals antiferromagnet. Nature 620, 988–993 (2023). https://doi.org/10.1038/s41586-023-06279-y
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DOI: https://doi.org/10.1038/s41586-023-06279-y
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