The influence of the number of atomic sheet on the direction of magnetization in thin ferromagnetic film

The competition between dipole-dipole interaction and surface anisotropy in a thin ferromagnetic film is described by two spin s = 1 layered Ising systems. The spin is perpendicular to the layers in one system,and is in-plane in the other system. Free energy densities in the two systems are calculated by use of VCE method. The results show that the magnetization will transfer from perpendicular to in-plane when the number of layers increase. In this process, the influence of dipole-dipole interaction which favors the in-plane magnetization is approximately a constant and that of surface anisotropy which favors the perpendicular magnetization decreases apparently. Finally the dipole-dipole interaction prevails over the surface anisotropy,and then the reorientation transition occurs.