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A quantitative mathematical model for the critical thickness of strainedepitaxial metal films is presented, at which the magnetic moment experiences areorientation from in-plane to perpendicular magnetic anisotropy. The model isbased on the minimum of the magnetic anisotropy energy with respect to theorientation of the magnetic moment of the film. Magnetic anisotropy energiesare taken as the sum of shape anisotropy, magnetocrystalline anisotropy andmagnetoelastic anisotropy, the two latter ones being present as constantsurface and variable volume contributions. Other than anisotropy materialsconstants, readily available from literature, only information about the strainin the films for the determination of the magnetoelastic anisotropy energy isrequired. Application of the epitaxial Bain path allows to express the strainin the film in terms of substrate lattice constant and film lattice parameter,and thus to obtain an approximate closed expression for the reorientationthickness in terms of lattice mismatch. The model can predict the critical spinreorientation transition thickness with surprising accuracy.

Quantitative model for anisotropy and reorientation thickness of the magnetic moment in thin epitaxially strained metal films