Once we analyzed the temperature dependence of the magnetization and the magnetic anisotropy of a thin film with only surface moments, we continue our study with a more complex system. Namely, we model a thin film with simple cubic lattice structure with spins (). Now we distinguish between bulk and surface spins. We first investigate the case where the bulk anisotropy is of the uniaxial type and the easy axis is parallel to Z axis. The Néel surface anisotropy has an easy axis parallel to the easy axis of the bulk anisotropy and perpendicular to the surface of the thin film (see Fig. 4.9).
When both bulk and surface anisotropies are uniaxial, the torque curves are similar to those corresponding to a pure uniaxial system. However, the effective anisotropy constant is different from the bulk or the surface ones. It can be calculated by fitting the torque curves to the expression (4.19). We calculate the total, bulk and the surface magnetization, see Fig. 4.10 (left graph) and the total anisotropy, see Fig. 4.10 (right graph), dependencies on temperature. The surface magnetization is more sensitive than the total magnetization to the temperature increase, but both have the same Curie temperature, we can find similar results in the literature [130,131].
Next we present a more complicated situation, where an fcc thin film has cubic bulk anisotropy and a Néel surface anisotropy. The plane of the thin films is cut along the (001) direction, thus for an fcc crystalline structure the spins that belong to the surface have lost 4 first neighbors. This yields a further reduction of the exchange field and therefore the sensibility of the surface magnetization with temperature is increased. One of the easy axes of the cubic anisotropy coincides with the surface anisotropy axis and is perpendicular to the thin film surface. The torque curve is clearly a sum of the uniaxial and cubic contributions as is seen in Fig. 4.11 (Left).
The temperature dependence of the uniaxial and cubic macroscopic contributions to the anisotropies of the system are present in Fig. 4.11 (Right). According to the general theory and our previous results, the cubic anisotropy is decreasing faster with temperature than the uniaxial surface one. Consequently, at low temperatures the cubic anisotropy dominates, while at high temperatures the uniaxial surface one. This leads to a change in the global easy axis of the system with temperature.