High Temperature Susceptibility of Garnets: Exchange Interactions in YIG and LuIG

Publisher Website
Google Scholar
Abstract
Power series expansions of the high temperature susceptibility and its inverse in ascending powers of the reciprocal temperature have been obtained through the use of an extension of the method of Rushbrooke and Wood. The Heisenberg form of exchange is adopted and interactions between neighboring spins from different sublattices (a-d exchange) only are included. The coefficients in the series are derived for arbitrary spins on the two sublattices. The calculations have been carried out to terms including the fifth power of the exchange divided by the temperature; the molecular field theory by contrast is rigorously valid only to the first power term of its expansion. The inverse susceptibility series have been used to determine the magnitude of the a-d exchange interactions in the ferrimagnetic garnets, YIG and LuIG. The intra-sublattice interactions are assumed to be zero, in keeping with the increasing suspicion on the part of numerous investigators that these interactions have been seriously overestimated by molecular field considerations. The data of Aléonard was analyzed by a least-squaring method, and the following values for the a-d exchange were obtained: J/k=−35.0°K for YIG, and J/k=−34.5°K for LuIG. The deviation of theory from experiment is about 1%. In addition, the value for YIG is in satisfactory agreement with the Landau-Lifschitz constant determined from the heat capacity and spin-wave spectrum. It is concluded that these results support the hypothesis of relatively weak intrasublattice exchange in the garnets.