Magneto-elastic Anisotropy

The magneto-elastic effect arises from the spin-orbit interaction. The spin moments are coupled to the lattice via the orbital electrons. If the lattice is changed by strain the distances between the magnetic atoms is altered and hence the interaction energies are changed. This produces magneto-elastic anisotropy.

Magnetostriction constants, $\lambda_{hkl}$, are defined for various crystal directions. For an elastically isotropic medium, with isotropic magnetostriction, the magneto-elastic energy per unit volume is given by[8]

$$E = -\frac{3}{2}\lambda\sigma\cos^{2}\theta$$ (5.7)

where $\sigma$ is the stress and $\theta$ is the angle between the magnetisation and stress directions. For positive $\lambda$, as in metallic iron, the easy magnetic direction will be along a direction of tensile stress, or perpendicular to a compressive stress.

Strain in thin films and multilayers can be produced by the growth conditions, such as lattice mismatch between layers or thermal stress caused by differences in thermal expansion coefficients of adjacent layers.