The Stoner-Wohlfarth model

The Stoner-Wohlfarth model (Stoner and Wohlfarth, 1948) is the model of coherent rotation of magnetisation. This makes the assumption that the direction of magnetisation of all moments within the system are parallel leaving only two degrees of freedom and reducing the exchange energy factor to zero. One then only need consider the interaction with the applied field and the anisotropic energy of the system (Aharoni, 2000):

$$\mathcal{E} = K_1V \sin^2(\theta - \phi)-\mu H \cos\phi$$ (2.35)

where $K_1$ is the anisotropy energy density, $V$ is a particle volume, $\mu$ is the magnetic moment, $\phi$ is the direction of the magnetic moment to the easy axis (that is, the axis with which the magnetisation prefers to align), $\theta$ is the angle between the easy axis and the applied field.

The Stoner-Wohlfarth model is applicable to smaller systems with a comparatively large contribution to anisotropy, where one can consider all magnetic moments to be aligned. If single-domain behaviour can be expected then the Stoner-Wohlfarth model is appropriate. For larger systems the approximation breaks down as it neglects the dipolar component and consequently more complicated magnetic microstructures, such as domains and vortices, are unable to form with this model.