Gilbert damping phenomenology for two-sublattice magnets

TL;DR

This paper develops a comprehensive phenomenological model for Gilbert damping in two-sublattice magnets, applicable across ferro-, ferri-, and antiferromagnetic materials, incorporating intra- and cross-sublattice effects.

Contribution

It introduces a matrix-based damping description within a Lagrangian framework, including spin-pumping effects and explaining experimental linewidth enhancements near compensation points.

Findings

Reproduces linewidth enhancement near compensation temperature.

Predicts new damping contributions in antiferromagnets.

Suggests linewidths as probes of sublattice asymmetry.

Abstract

We present a systematic phenomenological description of Gilbert damping in two-sublattice magnets. Our theory covers the full range of materials from ferro- via ferri- to antiferromagnets. Following a Rayleigh dissipation functional approach within a Lagrangian classical field formulation, the theory captures intra- as well as cross-sublattice terms in the Gilbert damping, parameterized by a 2$\times$2 matrix. When spin-pumping into an adjacent conductor causes dissipation, we obtain the corresponding Gilbert damping matrix in terms of the interfacial spin-mixing conductances. Our model reproduces the experimentally observed enhancement of the ferromagnetic resonance linewidth in a ferrimagnet close to its compensation temperature without requiring an increased Gilbert parameter. It also predicts new contributions to damping in an antiferromagnet and suggests the resonance linewidths as a direct probe of the sublattice asymmetry, which may stem from boundary or bulk.