Atomistic and ab initio DFT modelling of the defect structures in Al³⁺/Cr³⁺-doped and co-doped Y₃Fe₅O₁₂

The defect structures when Y₃Fe₅O₁₂ is doped with either Al³⁺ or Cr³⁺, and evenly co-doped with both, which have been a matter of controversy in the literature, are modeled using atomistic and ab initio DFT methods. When Y₃Fe₅O₁₂ is doped with Al³⁺, the defect reaction energy obtained marginally favors the preferential substitution of Al³⁺ for Fe³⁺ at the tetrahedral sites as opposed to octahedral ones. This is indicative that for Al³⁺-doped samples processed at elevated temperatures, or containing undetected impurities, the substitution of Al³⁺ for octahedral Fe³⁺ is likely. To model the defect structure of the Cr³⁺ -doped Y₃Fe₅O₁₂, it was essential that the Cr³⁺ ions crystal field stabilization energy (CFSE) and the Fe³⁺-O^2-- Cr³⁺ spin-spin coupling derived from the ab initio DFT calculations,be taken into account. The results show the substitution of the Cr³⁺ ion for an octahedral Fe³⁺ ion to be energetically favorable relative to its substitution for a tetrahedral Fe³⁺ one. It is also shown that the antisite defect, where the Cr³⁺ ion substitutes for Y³⁺ at a dodecahedral site with the expelled Y³⁺ ion substituting for an octahedral Fe³⁺ ion, is possible under certain processing conditions. For the Al³⁺ /Cr³⁺ co-doped Y₃Fe₅O₁₂, the Al³⁺ and Cr³⁺ ions were found to, respectively, substitute for the tetrahedral and octahedral Fe³⁺ ions. The energy values obtained suggest this defect structure to be insensitive to the processing conditions and/or the presence of undetected impurities. The structural and magnetic implications of these defect structures are discussed.