A spin dynamics study in layered van der Waals single crystal, Cr${}_2$Ge${}_2$Te${}_6$

Abstract

We study the magnetisation dynamics of a bulk single crystal Cr${}_2$Ge${}_2$Te${}_6$ (CGT), by means of broadband ferromagnetic resonance (FMR), for temperatures from 60 K down to 2 K. We determine the Kittel relations of the fundamental FMR mode as a function of frequency and static magnetic field for the magnetocrystalline easy - and hard - axis. The uniaxial magnetocrystalline anisotropy constant is extracted and compared with the saturation magnetisation, when normalised with their low temperature values. The ratios show a clear temperature dependence when plotted in the logarithmic scale, which departs from the predicted Callen-Callen power law fit of a straight line, where the scaling exponent \textit{n}, $K_u(T)\propto [M_s(T)/M_s(2$ K$){]}^n$, contradicts the expected value of 3 for uniaxial anisotropy. Additionally, the spectroscopic g-factor for both the magnetic easy - and hard - axis exhibits a temperature dependence, with an inversion between 20 K and 30 K, suggesting an influence by orbital angular momentum. Finally, we qualitatively discuss the observation of multi-domain resonance phenomena in the FMR spectras, at magnetic fields below the saturation magnetisation.

13 pages, main text: page 1-8 with 6 figures, supplementary material: page 9-13 with 4 figures. Revised Manuscript: - Added references - Corrected Typos - Replaced figure 4 with a new figure - Modified discussion about figure 5