Temperature Dependence of Magnetocrystalline Anisotropy in Itinerant Ferromagnets

We theoretically investigated magnetocrystalline anisotropy (MA) at a finite temperature T in ferromagnetic metals. Assuming a Rashba-type ferromagnet with uniaxial MA, we defined the MA constants K-u(T) derived from several different concepts. Our purpose was to examine the equality between them and to confirm a power law between K (u)(T) and magnetization M(T) in the form of K-u(T)/K-u(0) = [M(T)IM(0)](alpha). We demonstrate that a equals 2 in the itinerant-electron limit and increases with the localized feature of electrons passing through alpha = 3, predicted for the single-ion MA in spin models.