Phase Transition of an Anisotropic Ferromagnet

Abstract

The phase transition of an Ising Ferromagnet with uniaxial single ion anisotropy with spin one has been investigated extensively by Capel. Here we consider a similar but a more general system with anisotropic exchange interaction. The Hamiltonian can be written as $$\mathcal{H}\mathrm{=D\hspace{0.17em}}{\displaystyle \sum _i}{\mathrm{\hspace{0.17em}(S}}_i^z{)}^2\mathrm{-\hspace{0.17em}}{\displaystyle \sum _{\mathrm{ij}}}{\mathrm{\hspace{0.17em}J}}_{\mathrm{ij}}{S}_i^z{S}_j^z\mathrm{-\hspace{0.17em}}{\displaystyle \sum _{\mathrm{ij}}}{\mathrm{\hspace{0.17em}K}}_{\mathrm{ij}}{\mathrm{(S}}_i^x{S}_j^x{\mathrm{+S}}_i^y{S}_j^y)$$ , where J, K, and D are positive parameters. We show that in addition to the more familiar phase transition from an ordered phase to the paramagnetic phase, as temperature is raised, a first‐order phase transition can occur. Depending upon the relative magnitude of D, J, and K, a phase transition from the ferromagnetic state with spin ordering along (perpendicular to) the z axis to a ferromagnetic state with spin ordering perpendicular to (along) the z axis can take place at a critical temperature lower than the Curie temperature where a transition to the paramagnetic phase occurs. The boundaries of the three phases have been calculated in the molecular field approximation.