Thermal and magnetoelastic properties of the van der Waals ferromagnet Fe 3 − δ GeTe 2 : Anisotropic spontaneous magnetostriction and ferromagnetic magnon excitations

By determining the lattice parameters as a function of temperature of the hexagonal van der Waals ferromagnet Fe 2.92 ( 1 ) Ge 1.02 ( 3 ) Te 2 we obtain the temperature dependence of the spontaneous in-plane magnetostriction in the ferromagnetic and the linear thermal expansion coefficients in the paramagnetic state. The spontaneous magnetostriction is clearly seen in the temperature dependence of the in-plane lattice parameter a ( T ) , but less well pronounced perpendicular to the planes along c . Below T C the spontaneous magnetostriction follows a power law M ( T ) 3 / 2 of the magnetization and leads to an expansion of the hexagonal layers. Extrapolating to T → 0 K we obtain a spontaneous in-plane saturation magnetostriction of λ sp , a ( T → 0 ) ≈ − 220 × 10 − 6 . In the paramagnetic state the linear thermal expansion coefficients amount to 13.9 ( 1 ) × 10 − 6 K − 1 and to 23.2 ( 2 ) × 10 − 6 K − 1 for the in-plane and out-of-plane direction, respectively, indicating a linear volume thermal expansion coefficient of 50.8 ( 4 ) × 10 − 6 K − 1 which we use to estimate the volume thermal expansion contribution to the heat capacity determined at constant pressure. A Sommerfeld-type linear term in the low-temperature heat capacities can be quantitatively ascribed to two-dimensional (2D) ferromagnetic magnon excitations.