Spin Reorientation Driven Renormalization of Spin-Phonon Coupling in Fe$_4$GeTe$_2$

Abstract

Quasi-2D van der Waals ferromagnet Fe$_4$GeTe$_2$, featuring the simultaneous presence of high Curie temperature ($T_\mathrm{C}$ $\sim 270$ K) and a spin-reorientation transition at $T_\mathrm{SR}$ $\sim 110$ K, is a rare system where strong interplay of spin dynamics, lattice vibrations, and electronic structure leads to a wide range of interesting phenomena. Here, we investigate the lattice response of exfoliated Fe$_4$GeTe$_2$ nanoflakes using temperature-dependent Raman spectroscopy. Polarization-resolved measurements reveal that, while one Raman mode exhibits a purely out-of-plane character, the rest display mixed symmetry, reflecting interlayer vibrational nonuniformity and symmetry-driven mode degeneracies. Below $T_\mathrm{C}$, phonons harden, and the linewidth narrows, consistent with reduced anharmonicity, while across the spin reorientation transition at $T_\mathrm{SR}$ they display anomalous softening, linewidth broadening, and a peak in lifetime, which are signatures of strengthened spin-phonon coupling. Complementary DFT+DMFT calculations and atomistic spin dynamical simulations reveal temperature-dependent spin excitations whose energies overlap with the Raman-active phonons, providing a natural route for the observed magnon-phonon interaction. Together, these insights establish Fe$_4$GeTe$_2$ as a versatile platform for exploring intertwined spin, lattice, and electronic degrees of freedom, with relevance for dynamic spintronic and magneto-optic functionalities near technologically meaningful temperatures.

Figures (4)

• Figure 1: Characterization of Raman modes of Fe4GeTe2 at 300 K.(a) Temperature-dependent magnetization data of Fe4GeTe2 (at 100 Oe) showing ferromagnetic transition at $T_\mathrm{C}$$\sim$ 270 K and spin-reorientation transition at $T_\mathrm{SR}$. (b) Raman spectrum (blue circles) of an Fe4GeTe2 flake measured with $\lambda_{\mathrm{ex}}=532$ nm, fitted using eleven Raman modes (P0–P10). The fitted curve is shown in red. Upper left inset: AFM height profile and image of the flake showing corresponding thickness of $\sim$190 nm. Right inset: Crystal structure of Fe4GeTe2, consisting of seven-atom-thick monolayers stacked in an ABC sequence, forming the rhombohedral structure (space group R$\bar{3}$m, No. 166). (c) Linear polarization–resolved Raman spectra (inset: magnified view of P0–P3). (d) Helicity-resolved Raman spectra at 300 K (inset: magnified view of P0–P3). (e) Phonon dispersion of Fe4GeTe2, calculated using Phonopy-VASP. (f) Calculated phonon frequencies and representative vibrational patterns for selected modes of Fe4GeTe2 obtained from Phonopy–VASP, highlighting mode-specific symmetry and atomic displacements.
• Figure 2: Temperature dependent Raman response of Fe4GeTe2.(a) Two-dimensional density map of Raman intensity as a function of temperature, along with representative spectra at 83, 180, and 300 K. Blue denotes maximum spectral intensity, while white corresponds to zero intensity. Each spectrum is individually normalized within the 200–400 cm$^{-1}$ range. (b) Semi-logarithmic plot of temperature-dependent Raman spectra highlighting the systematic shifts of the dominant modes (P4 and P5); the red dashed line serves as a guide to the eye. (c,d) Temperature evolution of the phonon frequencies $\omega_{\mathrm{ph}}$ for modes P4 and P5. Both modes exhibit clear deviations from the standard anharmonic behavior (red fits; see text). Insets: Temperature-dependent phonon linewidths for the same modes, fitted to the anharmonic model in the 120–300 K range.
• Figure 3: Temperature-dependent deviations of phonon properties. Temperature evolution of the phonon frequency deviations $\Delta \omega_{\mathrm{ph}}(T) = \omega \mathrm(T) - \omega _\mathrm{anh}(T)$(a,d) and linewidth deviations $\Delta\Gamma_{\mathrm{ph}}(T) = \Gamma \mathrm(T) - \Gamma _\mathrm{anh}(T)$(b,e) (left axes) from the standard anharmonic model for the Raman modes P4 and P5. Both modes exhibit pronounced deviations below $T_\mathrm{SR}$ and minor deviations above $\sim$$T_\mathrm{C}$. The right axes in (b,e) show the temperature dependence of the phonon relaxation time $\tau$ for P4 and P5, displaying marked changes around $T_\mathrm{SR}$. The color gradient highlights distinct temperature regions across $T_\mathrm{SR}$, consistent with the $M$–$T$ behavior. The black dotted line marks $T_\mathrm{SR}$. (c,f) Temperature-dependent changes in the mode intensities of P4 and P5. Dashed lines serve as guides to the eye.
• Figure 4: Theoretical calculation of magnon and phonon dynamics in Fe4GeTe2.(a,b) Calculated dynamical structure factors, $S(\mathbf{q},\omega)$, plotted along high-symmetry paths for Fe4GeTe2 at (a) $T = 10$ K and (b) $T = 80$ K. Regions with higher intensity (blue) indicate the adiabatic magnon dispersion lines. (c,d) Calculated phonon and magnon density of states at (c) 10 K and (d) 80 K. (e) Schematic representation of magnon, phonon, and magnon–phonon coupling, illustrating the interaction pathways resolved in the calculations.