Stoner–Wohlfarth model

The Stoner–Wohlfarth model is a widely used model for the magnetization of single-domain ferromagnets. It is a simple example of magnetic hysteresis and is useful for modeling small magnetic particles in magnetic storage, biomagnetism, rock magnetism and paleomagnetism.

The Stoner–Wohlfarth model was developed by Edmund Clifton Stoner and Erich Peter Wohlfarth and published in 1948. It included a numerical calculation of the integrated response of randomly oriented magnets. Since this was done before computers were widely available, they resorted to trigonometric tables and hand calculations.

In the Stoner−Wohlfarth model, the magnetization does not vary within the ferromagnet and it is represented by a vector M. This vector rotates as the magnetic field H changes. The magnetic field is only varied along a single axis; its scalar value h is positive in one direction and negative in the opposite direction. The ferromagnet is assumed to have a uniaxial magnetic anisotropy with anisotropy parameter K_u. As the magnetic field varies, the magnetization is restricted to the plane containing the magnetic field direction and the easy axis. It can therefore be represented by a single angle φ, the angle between the magnetization and the field (Figure 1). Also specified is the angle θ between the field and the easy axis.

The energy of the system is

${\displaystyle E=K_{u}V\sin ^{2}\left(\varphi -\theta \right)-\mu _{0}M_{s}VH\cos \varphi ,\,}$

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