Dipolar interactions and the magnetic behavior of two-dimensional ferromagnetic systems

A simple model is presented for spin-wave excitations and the low-temperature magnetization of ferromagnetic ultrathin films. The films are assumed to be quasi-two-dimensional arrays of fixed magnetic moments and both exchange and dipolar interactions are taken into account. Discrete and continuous models are used to examine the wave-vector dependence of the spin-wave frequency in the long-wavelength limit. This spin-wave theory can be used to calculate the temperature dependence of the saturation magnetization in the limit of small fluctuations. The role of dipolar interactions is examined for a single monolayer and for thin films consisting of two or three atomic layers.