Theory of Magnetoelastic Effects in Ferromagnetism

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Abstract
Standard magnetostriction theory constructs a free energy from three terms: the energy of a rigid magnetized body, the energy of a nonmagnetic elastic body, and the volume integral of an interaction energy‐density linear in the strains. This procedure is open to three criticisms. First, strains invalidate the magnetic calculation; in particular, the magnetostatic self‐energy is strain‐dependent. Second, magnetization invalidates the elastic calculation; the stresses (whose definition is somewhat arbitrary) need not be symmetric or even constitute a tensor. Third, small‐strain formulas, valid only to the first order of small quantities, are being used in energy terms that must be correct to the second order and that are linear in the strains. Previous studies make possible a rigorous treatment, by finite‐strain theory, and a small‐strain approximation with assumptions explicitly stated. The mechanical equilibrium equations contain the usual terms plus others; the ``form effect'' is a special case. The theory is easily related to microscopic models and is suited to nucleation‐field calculations.

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