Elucidating the origin of long-range ferromagnetic order in Fe${}_3$GeTe${}_2$ by low-energy magnon excitation studies

Abstract

We report a detailed high-field/high-frequency ferromagnetic resonance (HF-FMR) study of low-energy magnon excitations in the van der Waals ferromagnet Fe${}_3$GeTe${}_2$. At 2 K, the field dependence of the magnon branches is well described by a semiclassical domain-based model, from which we extract key microscopic parameters including the anisotropy gap $\Delta =170\pm 4$ GHz, the anisotropy field $B_{\mathrm{A}}=5.85\pm 0.08$ T, and the effective $g$-factor $g_{\mathrm{ab}}\simeq g_{\mathrm{c}}=2.07(4)$. Furthermore the uniaxial anisotropy constant was determined to be $K=(10.5\pm 0.23)\times 10^{-6}$ erg/cm${}^3$. Anisotropic short-range magnetic order persists above $T_{\mathrm{C}}$ up to approximately 270 K, as evidenced by a finite anisotropy gap and anisotropic shifts in the FMR resonance fields. Both results clearly show the presence of anisotropic local magnetic fields well above $T_{\mathrm{C}}$. Our findings underscore the crucial role of magneto-crystalline anisotropy in driving long-range magnetic order in Fe${}_3$GeTe${}_2$.