We use first-principles total-energy calculations based on density functionaltheory to study the site occupancy and magnetic properties of Al-substituted$M$-type strontium hexaferrite SrFe$_{12-x}$Al$_{x}$O$_{19}$ with $x=0.5$ and$x=1.0$. We find that the non-magnetic Al$^{3+}$ ions preferentially replaceFe$^{3+}$ ions at two of the majority spin sites, $2a$ and $12k$, eliminatingtheir positive contribution to the total magnetization causing the saturationmagnetization $M_s$ to be reduced as Al concentration $x$ is increased. Ourformation probability analysis further provides the explanation for increasedmagnetic anisotropy field when the fraction of Al is increased. AlthoughAl$^{3+}$ ions preferentially occupy the $2a$ sites at a low temperature, theoccupation probability of the $12k$ site increases with the rise of thetemperature. At a typical annealing temperature ($> 700\,^{\circ}{\rm C}$)Al$^{3+}$ ions are much more likely to occupy the $12k$ site than the $2a$site. Although this causes the magnetocrystalline anisotropy $K_1$ to bereduced slightly, the reduction in $M_s$ is much more significant. Theircombined effect causes the anisotropy field $H_a$ to increase as the fractionof Al is increased, consistent with recent experimental measurements.
展开▼
