Evaluating Gilbert damping in magnetic insulators from first-principles
Liangliang Hong, Changsong Xu, Hongjun Xiang
Abstract
Magnetic damping poses a significant impact on the performance of various magnetic and spintronic devices, making it a longstanding focus of research. The strength of magnetic damping is usually quantified by the Gilbert damping constants in the Landau-Lifshitz-Gilbert equation. Here we propose a first-principles-based approach to evaluate the damping constant contributed by spin-lattice coupling in magnetic insulators. The approach involves effective Hamiltonian models and spin-lattice dynamics simulations. As a case study, we applied our method to ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}, {\mathrm{MnFe}}_{2}{\mathrm{O}}_{4}$, and ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$. Their damping constants were calculated to be $0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}, 0.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}, 2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, respectively at a low temperature. The results for ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ and ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ are very close to the experimental results, while the large discrepancy in ${\mathrm{MnFe}}_{2}{\mathrm{O}}_{4}$ can be attributed to the inhomogeneity and small band gap in real samples. The stronger damping observed in ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, compared to ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$, essentially results from its stronger spin-lattice coupling. In addition, we confirmed a proportional relationship between damping constants and the temperature difference of subsystems, which had been reported in previous studies. These successful applications suggest that our approach can be a viable candidate for estimating the Gilbert damping constant in magnetic insulators.