The statistics of superexchange interaction and ionic distribution in substituted ferrimagnetic rare earth iron garnets

Abstract

Ideas on the statistics of superexchange interaction developed and applied to substituted yttrium-iron garnets by Gilleo are extended and applied to substituted rare earth iron garnets. It is shown by means of structural considerations that only four interactions per c site ion with d site ions are important in determining the contribution of the c site ions to the 0°K saturation magnetization. The statistical theory accounts especially well for the behavior of n B (0°K) vs. x(= y + z) of the system {Gd 3}[Al y Fe 2− y ](Al z Fe 3− z )O 12 and for {Gd 2.4Ca 0.6}[Al y Fe 2− y ](Al z−0.6 Si 0.6Fe 3− z )O 12 corrects the previously obtained ionic distribution which had been considered anomalous. Other systems are also considered. Crystal chemical aspects of some of the results, compensation points and some minor limitations of the treatment are discussed.