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

## TL;DR

This study investigates the magnetisation dynamics of Cr$_2$Ge$_2$Te$_6$ single crystals using broadband ferromagnetic resonance across a wide temperature range, revealing temperature-dependent anisotropy, g-factor variations, and multi-domain phenomena.

## Contribution

It provides detailed experimental insights into the temperature-dependent magnetic anisotropy and resonance behaviors of Cr$_2$Ge$_2$Te$_6$, highlighting deviations from theoretical models and observing multi-domain effects.

## Key findings

- Uniaxial anisotropy constant shows temperature dependence inconsistent with Callen-Callen law.
- g-factor exhibits temperature dependence with inversion around 20-30 K.
- Multi-domain resonance phenomena observed below saturation magnetisation.

## 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.