Anisotropy of constrained magnetostrictive materials

The magnetic anisotropy of a ferromagnetic material that is free to deform is defined as the effective anisotropy, which is the sum of intrinsic anisotropy and magnetostriction-induced anisotropy. Prior works [1] and [2] (Baltzer, 1957; Kittel, 1949) indicate that if the material is undeformed then the measured anisotropy is same as its intrinsic anisotropy. When magnetostrictive materials are used as actuators or sensors they are often mechanically loaded, resulting in a restriction on the deformation. To capture their behavior in such scenarios, a modelling approach is required. Therefore, in this work, the thermodynamic accuracy of the common expressions for magnetostriction-induced and stress-induced anisotropies is first investigated. A 3D magnetoelastic model is then developed using Armstrong's implementation of an energy model. This 3D magnetoelastic model is capable of predicting the stresses induced when the magnetostriction of these materials is constrained. Using this model, it is shown that when the bulk magnetostriction of the material is clamped, the measured anisotropy will not in general be the same as the intrinsic anisotropy. It is also shown that when the magnetostriction is clamped at the microscopic level, i.e. if the material is locally constrained at the exchange length scales, then the measured anisotropy is the intrinsic anisotropy.