Hysteretic properties of a magnetic particle with strong surface anisotropy

We study the influence of surface anisotropy on the zero-temperature hysteretic properties of a small single-domain ferromagnetic particle, and investigate limiting cases where deviations from the Stoner-Wohlfarth model are observed due to nonuniform reversal of the particle’s magnetization. We consider a spherical particle with simple cubic crystal structure, a uniaxial anisotropy for core spins, and radial anisotropy on the surface. The hysteresis loop is obtained by solving the local (coupled) Landau-Lifshitz equations for classical spin vectors. We find that when the surface anisotropy constant $K_s$ assumes large values, e.g., of the order of the exchange coupling J, large deviations are observed with respect to the Stoner-Wohlfarth model in the hysteresis loop and thereby the limit-of-metastability curve, since in this case the magnetization reverses its direction in a nonuniform manner via a progressive switching of spin clusters. This characteristic value of $K_s$ depends on the surface-to-volume ratio of exchange coupling and the angle between the applied field and core easy axis.