  The site preference and magnetic properties of Zn, Sn and Zn-Sn substituted
M-type strontium hexaferrite (SrFe$_{12}$O$_{19}$) have been investigated using
first-principles total energy calculations based on density functional theory.
The site occupancy of substituted atoms were estimated by calculating the
substitution energies of different configurations. The distribution of
different configurations during the annealing process at high temperature was
determined using the formation probabilities of configurations to calculate
magnetic properties of substituted strontium hexaferrite. We found that the
magnetization and magnetocrystalline anisotropy are closely related to the
distributions of Zn-Sn ions on the five Fe sites. Our calculation show that in
SrFe$_{11.5}$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, while
in SrFe$_{11.5}$SnO$_{19}$, Sn atoms occupy the $12k$ and $4f_2$ sites with
occupation probability of 54% and 46%, respectively. We also found that in
SrFe$_{11}$Zn$_{0.5}$Sn$_{0.5}$O$_{19}$, (Zn,Sn) atom pairs prefer to occupy
the ($4f_1$, $4f_2$), ($4f_1$, $12k$) and ($12k$, $12k$) sites with occupation
probability of 82%, 8% and 6%, respectively. Our calculation shows that the
increase of magnetization and the reduction of magnetic anisotropy in Zn-Sn
substituted M-type strontium hexaferrite as observed experimentally is due to
the occupation of (Zn,Sn) pairs at the ($4f_1$, $4f_2$) sites.
