Temperature Dependence of Magnetization in Transition Metal Ultrathin Films of Various Thicknesses

Temperature dependence of the local magnetization in the spin-wave regime is calculated within the framework of the multiband model for ultrathin films consisting of 5, 7 and 9 monolayers. The temperature range in which the calculated results can be fitted to the Bloch T$\text{}^{3}$ $\text{}^{/}$ $\text{}^{2}$ law is found in all cases. The Bloch coefficient Bay corresponding to temperature dependence of the average film magnetization is found to be proportional to 1/D, where D is the thickness of the film. The spatial distribution of the local magnetization is obtained. The Bloch coefficient corresponding to the surface layer appears to be greater than the one corresponding to the central layer, namely B$\text{}_{s}$ > B$\text{}_{c}$. The ratio B$\text{}_{s}$/B$\text{}_{c}$ is increasing with an increase of the film thickness. The calculated results are well consistent with experimental ones obtained for ultrathin films of various thicknesses