Shape Anisotropy

The magnetic dipolar anisotropy, or shape anisotropy, is mediated by the dipolar interaction. This interaction is long range and so its contribution is dependent upon the shape of the sample. Hence shape anisotropy becomes important in thin films and often produces inplane alignment of moments.

In a thin film considered as a magnetic continuum the dipolar anisotropy energy per unit volume is given by[20]

$$E = \frac{1}{2}\mu_{0}M_{s}^{2}\cos^{2}\theta$$ (5.3)

where $M_{s}$ is the saturation magnetisation, assumed to be uniform throughout the layer. The magnetisation subtends an angle, $\theta$, to the plane normal. The dipolar anisotropy energy is thus minimised for an angle of $90^{\circ }$ ie moments lying in the plane of the layer.