Atomically Resolved Acoustic Dynamics Coupled with Magnetic Order in a van der Waals Antiferromagnet

Magnetoelastic coupling in van der Waals (vdW) magnetic materials enables a unique interplay between the spin and lattice degrees of freedom. Characterizing the elastic responses with atomic and femtosecond resolution across the magnetic transition is essential for guiding the design of magnetically tunable actuators and strain-mediated spintronic devices. Here, ultrafast x-ray diffraction employed at a free-electron laser reveals that the atomic displacements, wave vectors, and dispersion relations of acoustic phonon modes in a vdW antiferromagnet FePS$_3$ are coupled with the magnetic order, by tracking both in-plane and out-of-plane Bragg peaks upon optical excitation across the Néel temperature (T$_N$). One transverse mode shows that a quasi-out-of-plane atomic displacement undergoes a significant directional change across T$_N$. Its quasi-in-plane wave vector is derived by the comparison between the measured sound velocity and the first-principles calculations. The other transverse mode is an interlayer shear acoustic mode whose amplitude is strongly enhanced in the antiferromagnetic phase, exhibiting eight times stronger amplitude than the longitudinal acoustic mode below T$_N$. The atomically resolved characterization of acoustic phonon dynamics that couple with magnetic ordering opens opportunities for harnessing unique magnetoelastic coupling in vdW magnets on ultrafast timescales.

💡 Research Summary

In this work, the authors employ ultrafast x‑ray diffraction at a free‑electron laser to directly visualize the atomically resolved acoustic phonon dynamics in the van der Waals antiferromagnet FePS₃ and to uncover how these dynamics are intertwined with magnetic order across the Néel temperature (Tₙ ≈ 117 K). Thin flakes of FePS₃ (40–200 nm) are optically excited with 400 nm (3.1 eV) femtosecond pulses, which generate a rapid electronic‑phonon heating and a temperature gradient along the out‑of‑plane direction. This gradient launches coherent acoustic waves that are captured in real time by probing both the (0 0 2) and (1 0 2) Bragg reflections with 12 keV x‑ray pulses of ~100 fs duration.

Analysis of the time‑dependent Bragg‑peak shifts reveals three distinct phonon modes with frequencies near 1.1 GHz, 3.5 GHz, and 4.6 GHz, labeled f₃, f₁, and f₂ respectively. The lowest‑frequency mode (f₃) is a quasi‑longitudinal interlayer breathing mode: both its atomic displacement vector and wave‑vector point along the c‑axis, and its amplitude is relatively small and weakly temperature‑dependent. The intermediate‑frequency mode (f₁) is identified as a quasi‑transverse mode. Its atomic displacement is primarily out‑of‑plane (along c) while its wave‑vector lies almost in‑plane. Remarkably, the polarization direction of this mode rotates by about 20° when the system crosses Tₙ, and its sound velocity changes by ~5 %, evidencing a strong magnetoelastic coupling that modifies the elastic constants as the spin‑exchange network reorganizes.

The highest‑frequency mode (f₂) is an interlayer shear acoustic mode. Its wave‑vector is out‑of‑plane, but the atomic motion is confined to the a‑b plane. This mode’s amplitude is dramatically enhanced in the antiferromagnetic phase—approximately eight times larger than that of the longitudinal breathing mode—yet it is almost completely suppressed above Tₙ. The temperature‑dependent behavior matches earlier ultrafast electron diffraction and microscopy observations, confirming that the shear stiffness is reinforced by the zigzag antiferromagnetic order.

Beyond temporal analysis, the authors exploit Kiessig fringes on the two‑dimensional detector to obtain momentum‑resolved intensity oscillations. By Fourier‑transforming the time evolution at each momentum point, they construct dispersion curves for the observed modes. Linear dispersion fits yield sound velocities of ~3.0 km s⁻¹ for the quasi‑transverse mode, ~2.5 km s⁻¹ for the shear mode, and ~3.4 km s⁻¹ for the breathing mode. These experimental velocities agree well with density‑functional‑theory calculations of the phonon branches, confirming the mode assignments. Notably, the shear mode’s dispersion is prominent only below Tₙ, disappearing in the paramagnetic state, which directly visualizes the magnetic‑order‑controlled elastic anisotropy.

The work demonstrates that ultrafast x‑ray diffraction can simultaneously provide atomic‑scale displacement vectors, wave‑vector directions, and dispersion relations of coherent acoustic phonons, something that conventional optical pump‑probe techniques cannot achieve due to negligible momentum transfer. By correlating these phononic properties with magnetic ordering, the study offers quantitative insight into the magnetoelastic coupling in layered vdW magnets. Such knowledge is crucial for designing strain‑mediated spintronic devices, magnetically tunable actuators, and for exploiting ultrafast control of magnetic states via lattice dynamics. In summary, the paper delivers a comprehensive, atomically resolved picture of how acoustic phonons in FePS₃ are coupled to its antiferromagnetic order, opening pathways for functional device concepts that harness this coupling on femtosecond timescales.