Characterization of the Reorientation Transition in Classical Heisenberg Models with Dipole Interaction

In this paper the thermodynamics of thin ferromagnetic lms are studied in the framework of the classical Heisenberg model with uniaxial anisotropy and long{range dipole interaction. The dependence of the order of the reorientation transition in these systems on the number of layers and on the distribution of anisotropies is investigated using both mean eld theory and Monte{Carlo simulations. Thin magnetic lms with a ground state magne-tization perpendicular to the surface can undergo a phase transition into a phase with in-plane mag-netization at a temperature T R < T C , the Curie temperature of the lm, due to the competition of dipole interaction and surface anisotropy 1]. This reorientation transition has already been investigated theoretically in the framework of the two{ dimensional anisotropic Heisenberg model with di-pole interaction using classical 2] and quantum mechanical 3] mean eld theory, renormalization group theory 4], spin wave theory 5], and Monte{ Carlo simulations 6, 7]. While all calculations for a monolayer except 6] show a rst order reorientation transition, the calculations in 3] show a second order transition for a system with L = 3 layers and vanishing anisotropy in the middle layer. In a recent paper on the order of the reorientation transition Moschel et al. 8] proposed that the order depends on the distribution of anisotropies through the layer. In this paper we present ground state aspects and detailed phase diagrams obtained from both mean eld theory and Monte{Carlo simulations in a classical anisotropic Heisenberg model with long range dipole interactions. The system consists of L two{dimensional layers and it is described by the Hamiltonian