We study the site occupancy and magnetic properties of Zn-Sn substituted M-type Sr-hexaferrite SrFe$_{12-x}$(Zn$_{0.5}$Sn$_{0.5}$)$_x$O$_{19}$ with x = 1 using first-principles total-energy calculations. We find that in a ground-state configuration Zn-Sn ions preferentially occupy $4f_1$ and $4f_2$ sites unlike the model previously suggested by Ghasemi et al. [J. Appl. Phys, textbf{107}, 09A734 (2010)], where Zn$^{2+}$ and Sn$^{4+}$ ions occupy the $2b$ and $4f_2$ sites. Density-functional theory calculations show that our model has a lower total energy by more than 0.2 eV per unit cell compared to Ghasemis model. More importantly, the latter does not show an increase in saturation magnetization ($M_s$) compared to the pure $M$-type Sr-hexaferrite, in disagreement with the experiment. On the other hand, our model correctly predicts a rapid increase in $M_s$ as well as a decrease in magnetic anisotropy compared to the pure $M$-type Sr-hexaferrite, consistent with experimental measurements.
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