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.