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The site preference and magnetic properties of Zn, Sn and Zn-Sn substitutedM-type strontium hexaferrite (SrFe$_{12}$O$_{19}$) have been investigated usingfirst-principles total energy calculations based on density functional theory.The site occupancy of substituted atoms were estimated by calculating thesubstitution energies of different configurations. The distribution ofdifferent configurations during the annealing process at high temperature wasdetermined using the formation probabilities of configurations to calculatemagnetic properties of substituted strontium hexaferrite. We found that themagnetization and magnetocrystalline anisotropy are closely related to thedistributions of Zn-Sn ions on the five Fe sites. Our calculation show that inSrFe$_{11.5}$Zn$_{0.5}$O$_{19}$, Zn atoms prefer to occupy $4f_1$, $12k$, and$2a$ sites with occupation probability of 78%, 19% and 3%, respectively, whilein SrFe$_{11.5}$SnO$_{19}$, Sn atoms occupy the $12k$ and $4f_2$ sites withoccupation probability of 54% and 46%, respectively. We also found that inSrFe$_{11}$Zn$_{0.5}$Sn$_{0.5}$O$_{19}$, (Zn,Sn) atom pairs prefer to occupythe ($4f_1$, $4f_2$), ($4f_1$, $12k$) and ($12k$, $12k$) sites with occupationprobability of 82%, 8% and 6%, respectively. Our calculation shows that theincrease of magnetization and the reduction of magnetic anisotropy in Zn-Snsubstituted M-type strontium hexaferrite as observed experimentally is due tothe occupation of (Zn,Sn) pairs at the ($4f_1$, $4f_2$) sites.

Correlation between site preference and magnetic properties of Zn-Sn-substituted strontium hexaferrite