First-principles prediction of structural, magnetic properties of Cr-substituted strontium hexaferrite, and its site preference

To investigate the structural and magnetic properties of Cr-doped M-type strontium hexaferrite (SrFe$_{12}$O$_{19}$) with x = (0.0, 0.5, 1.0), we perform first-principles total-energy calculations relied on density functional theory. Based on the calculation of the substitution energy of Cr in strontium hexaferrite and formation probability analysis, we conclude that the doped Cr atoms prefer to occupy the 2a, 12k, and 4f$_{2}$ sites which is in good agreement with the experimental findings. Due to Cr$^{3+}$ ion moment, 3 {$\mu_B$}, smaller than that of Fe$^{3+}$ ion, 5 {$\mu_B$}, saturation magnetization (M$_{s}$) reduce rapidly as the concentration of Cr increases in strontium hexaferrite. The magnetic anisotropic field $\left(H_{a}\right)$ rises with an increasing fraction of Cr despite a significant reduction of magnetization and a slight increase of magnetocrystalline anisotropy $\left(K_{1}\right)$.The cause for the rise in magnetic anisotropy field $\left(H_{a}\right)$ with an increasing fraction of Cr is further emphasized by our formation probability study. Cr$^{3+}$ ions prefer to occupy the 2a sites at lower temperatures, but as the temperature rises, it is more likely that they will occupy the 12k site. Cr$^{3+}$ ions are more likely to occupy the 12k site than the 2a site at a specific annealing temperature (>700{\deg}C).