Spontaneous magnetization of amorphous ferromagnets with anisotropy

The mean field approximation was used to calculate by iteration (for simple cubic lattices of up to 1728 spins) the spontaneous magnetization of a spin one ferromagnet in which the amorphousness is simulated by fluctuating the magnitude of the uniaxial anisotropy term (of strength D and average value D̄). Fluctuations with D=0 as well as about a positive value of D̄ were considered. Nearest neighbor (n.n) Ising exchange interactions with periodic boundary conditions were used. In the approximation considered, each spin interacted withe the local mean field created by its 6 n.n.’s and it also experienced a randomly fluctuating uniaxial anisotropy. Generally, the fluctuations caused a decrease in the magnetization from the crystalline mean field case. For D̄=0 convergence problems were encountered near the Curie temperature. By examining both the free energy and the magnetization it is shown that increasing D̄ suitably higher values of D̄, there is no thermodynamically stable magnetized state. The magnetization curve depends also on the amplitude of the D fluctuations.