Theoretical hysteresis loops for single-domain particles with cubic anisotropy

The magnetic properties of randomly oriented assembly of noninteracting single-domain particles with cubic anisotropy are studied in detail. Both signs of the cubic anisotropy constant are considered. We analyze the irreversible jumps of particle magnetization by means of direct solution of the Landau-Lifshitz-Gilbert (LLG) equation in case when several equilibrium positions are available for a disappearing magnetization slate. It is shown that a particular hysteresis loop of a particle with cubic anisotropy may depend on the value of the damping parameter in the LLG equation. On the other hand, the upper and lower bounds for the coercive force of an assembly stated in the paper turn out to be very close to each other. The physical reason for the closeness of the upper and lower bounds is the fact that, for particles with cubic type of magnetic anisotropy, the fraction of the uniquely determined particular hysteresis loops is rather large. As a result, the coercive force of randomly oriented assembly with cubic anisotropy is almost independent of the value of the damping parameter. It is also shown that it has only weak dependence on the value of the second cubic anisotropy constant.