The methods of determining the spin-lattice coupling coefficients G11 and G44 from the formulae for zero-field splitting

Abstract

The simple correlations between the spin-lattice coupling coefficients G11 and G44 and the axial (tetragonal and trigonal) crystal-field splittings have been established. According to the correlations, the methods of calculating the coefficients G11 and G44 from the formulae for zero-field splitting, which are easier to use than the usual correlations obtained directly from the strain tensor elements, are given. As an example, the analytic expressions of G11 and G44 for S-state ions in cubic crystals are obtained from two distinctive perturbation schemes based on the spin-orbit coupling mechanism. It can be found that the formulae for G44 obtained by Yu and Zhao (1987, 1988) from the same two schemes are not correct. The reason is perhaps that they confuse the actual shear strains eij (i not=j) with the strain tensor elements. The values of G44 for Mn2+ ions in MgO and CaO crystals are calculated. On comparison with the experimental results, it can be seen that the results are better than those of Yu and Zhao.