Dynamic micromagnetism a la Ericksen-Leslie, allowing the Einstein-de Haas and Barnett effects

TL;DR

The paper develops a frame-indifferent continuum theory that unifies dynamic micromagnetism with finite-deformation elasticity by deriving LLg-type magnetization dynamics from fundamental balance laws, with an effective field that incorporates elastic contributions. It introduces a power-less rotational inertia term to realize Einstein-de Haas and Barnett effects within the same framework and proposes a constrained polar-material formulation in which the director spin aligns with the material spin. It further shows that a nonlinear hard-magnetic soft-material model by Zhao and co-workers fits naturally as a special case of the constrained theory, bridging magnetoelastic stress structure with established results. The framework provides a systematic route to model magnetization dynamics under angular-momentum exchange and large deformation, with potential applications to magnetorheological elastomers and hard-magnetic composites.

Abstract

A model of dissipative micromagnetics coupled to elasticity is developed, following the procedures of the Ericksen-Leslie theory of nematic liquid crystals allowing for angular momentum due to magnetization. An outcome is the Landau-Lifshitz-Gilbert theory coupled to material spin. A further power-less augmentation to the angular momentum of the theory with classical kinetic energy density is also considered, which allows for plausible approaches to model the Einstein-de Haas and Barnett effects within continuum mechanics, as well as hard magnetic soft materials treated as constrained polar materials within the overall framework.