Origin of exchange field reductions in diluted magnetic garnets

New theory on the source of magnetic frustration that causes canting of spin alignments in diluted ferrimagnetic systems is presented, providing a fundamental basis for the widely used semiempirical relations between molecular field coefficients and sublattice dilution fractions in the ferrimagnetic garnets. The theory explains the remarkable linearity and symmetry found in the original relations between the coefficients and the sublattice dilution fractions. It also distinguishes between the dilution and canting contributions to the weakening of the exchange fields, which has remained an unresolved issue. As part of the analysis, a probability is defined for each sublattice to characterize the canting effect on a particular spin caused by the removal of a neighboring magnetic ion from the opposing sublattice. The canting probabilities are found to be almost identically 0.07 for both the octahedral and tetrahedral garnet Fe3+ sublattices, thereby confirming the overall reciprocity of the garnet magnetic system. (C) 1999 American Institute of Physics. [S0021-8979(99)42108-5].