Dynamic Micromagnetism à la Ericksen-Leslie, and the Constrained Polar Continuum Mechanics of Hard Magnetic Soft Materials

Abstract A model of dissipative micromagnetics coupled to (visco-)elasticity is explored, 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, with a preliminary exploration of its potential in representing the Einstein-de Haas and Barnett effects within continuum mechanics. A treatment of the continuum mechanics of hard magnetic soft materials as a constrained polar material is presented. The models of DeSimone and James [22] and Zhao et al. [66] are discussed as two different, namely energetically and kinematically, constrained models of magnetoelasticity encompassed within the overall framework.