Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets

Abstract

We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments: ${\vec{e}}_i\cdot {\vec{e}}_j$, $({\vec{n}}_{ij}\cdot {\vec{e}}_i)({\vec{n}}_{ij}\cdot {\vec{e}}_j)$, ${\vec{n}}_{ij}\cdot ({\vec{e}}_i\times {\vec{e}}_j)$, $({\vec{e}}_i\cdot {\vec{e}}_j{)}^2$, ${\vec{e}}_i\cdot ({\vec{e}}_j\times {\vec{e}}_k)$..., where some terms are subjected to the spin-orbit field ${\vec{n}}_{ij}$ in first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.

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Cited by in corpus (2)

• Influence of non-local damping on magnon properties of ferromagnets
• Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime