Thin Ferromagnetic Films

The magnetic properties of thin films of ferromagnetic materials have been studied by means of the Bloch spin-wave theory. The spontaneous magnetization depends upon the number of atomic layers, $G_z$, in the film. For thicknesses below a "critical" thickness, which depends on the temperature and film dimensions, the spontaneous magnetization decreases rapidly as the number of atomic layers is decreased. The temperature dependence of the spontaneous magnetization varies from a $T^{\frac{3}{2}}$ law for very thick films to a linear function of $T$ for a monolayer film. The spontaneous magnetization, at fixed temperature and film thickness, decreases as the film dimension increases.