Figure 5.3: Schematic of SW particle.

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Figure 5.4: Variation of magnetic hysteresis loop of a SW particle with angle, Φ, between the field direction and easy axis.

Stoner-Wohlfarth Model:

This is a simple analytical model describing the hysteresis. Consider a uniformly magnetized ellipsoid with uniaxial anisotropy of shape or magnetocrystalline origin (called as SW particle, as shown in Fig.5.3) in a field applied at an angle Φto the anisotropy axis. The energy density is

(5.1)

Minimizing the E _total with respect to θ gives either one or two energy minima. The hysteresis arises in the field range where two minima are present. Switching is the irreversible jump from one minimum to another, which occurs when d² E/d Φ² = 0. The typical hysteresis loop for the SW particle is shown in Fig.5.4. The loop shape is perfectly square when α = 0 and in such case the coercivity is equal to the anisotropy field, i.e.,

(5.2)

where K_u is the sum of the magnetocrystalline anisotropy, K₁ and the shape anisotropy, K_sh, having same axis.