Mean-field theory for spin-reorientation phase transitions in magnetic thin films

A mean-field theory for spin-reorientation phase transitions in magnetic thin films is worked out, solving analytically the relevant differential equation. The role of the exchange stiffness A in the competition between the in-plane shape anisotropy Kv and the perpendicular surface anisotropy Ks is addressed. The spin-reorientation transition from the perpendicular configuration to the in-plane one with increasing thickness is derived. Two different stable spin configurations are presented at large thickness for Ks< AKv and vice versa. The phase transition with temperature is also explored. Asymptotic formulas are given for energy stocked in the film per unit area, which enable one to evaluate the surface anisotropy.