A continuum theory of deformable ferrimagnetic bodies. II. Thermodynamics, constitutive theory

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Abstract
In order to close the system of differential field equations developed in Paper I, this article proposes a rational development of the relevant macroscopic thermodynamics and of a constitutive theory. In particular, by following Coleman’s thermodynamics, exact nonlinear constitutive equations for thermoelastic antiferromagnetic insulators are formulated. According to the deductive scheme adopted in Paper I, the important case of elastically isotropic antiferromagnets with a magnetic easy axis, and possibly endowed with the property of weak ferromagnetism, is developed in detail by using approximations. In order to supplement the description of thermodynamically recoverable processes and in accordance with the Onsager–Casimir theory of irreversible processes, the constitutive equations governing phenomena such as viscosity, electric and heat conduction, and spin relaxation, the latter either for strong or weak damping, are obtained. Regarding the latter effect, it is shown, thanks to the formalism adopted in Paper I, that both viscosity and spin relaxation participate in the Cauchy equations. The relaxation term of Gilbert is thus generalized to the case of deformable antiferromagnets.