Magnetic properties of diluted hexaferrites

Recent experimental observations of the magnetic properties of the diluted hexagonal ferrite PbFe_12-xGa_xO₁₉, have remained a puzzle. Specifically, the dependence on the Ga concentration of the magnetic phase boundary and the saturation magnetization disagree with theoretical predictions. These earlier theories assume a uniform distribution of the Ga ions over all lattice sites. However, ab-initio density-functional calculations suggest a strong preference among the Ga ions towards the 12k sublattice, the most populous of the five Fe sublattices. Motivated by these calculations, we perform large-scale Monte Carlo simulations for a Heisenberg model with non-uniform vacancy distribution. With appropriately chosen Ga concentration in each sublattice, the simulation results are in excellent agreement with both the magnetic phase boundary and the saturation magnetization observed in recent experiments on the ferrite. This suggests the non-uniformity of the distribution of Ga impurities to be the main reason for the unusual magnetic properties held by PbFe_12-xGa_xO₁₉. We also perform calculations for the individual sublattice magnetizations and their behavior as the system approaches the magnetic phase boundary at different Ga concentrations and different temperatures.