Site occupancy and magnetic properties of Al-substituted M-type strontium hexaferrite

We use first-principles total-energy calculations based on density functional theory to study the site occupancy and magnetic properties of Al-substituted M-type strontium hexaferrite SrFe_12−xAl_xO₁₉ with x = 0.5 and x = 1.0. We find that the non-magnetic Al³⁺ ions preferentially replace Fe³⁺ ions at two of the majority spin sites, 2a and 12k, eliminating their positive contribution to the total magnetization causing the saturation magnetization M_s to be reduced as Al concentration x is increased. Our formation probability analysis further provides the explanation for increased magnetic anisotropy field when the fraction of Al is increased. Although Al³⁺ ions preferentially occupy the 2a sites at a low temperature, the occupation probability of the 12k site increases with the rise of the temperature. At a typical annealing temperature (>700 °C) Al³⁺ ions are much more likely to occupy the 12k site than the 2a site. Although this causes the magnetocrystalline anisotropy K₁ to be reduced slightly, the reduction in M_s is much more significant. Their combined effect causes the anisotropy field H_a to increase as the fraction of Al is increased, consistent with recent experimental measurements