Crossover condition in the coherent rotation model and the Preisach-type models

The crossover of the hysteresis branches in the classical coherent rotation model is analyzed. The analysis is extended when the truncated Stoner-Wohlfarth astroid is used. The physical explanation of the crossover occurrence is given. More accurate expressions of the anisotropy free energy density are required to better describe the behavior of the system when the angle between the easy axis and the magnetic moment of the particle is near 90°. A simple approximate formula for the hysteresis loop branches, which are in good agreement with those obtained when the discussed corrections are made, is given. The effect of the use of the Stoner-Wohlfarth astroid in the calculus of the equilibrium state in some vector Preisach-type models is analyzed