Calculation methods for the spin-lattice coupling coefficient F 44 in cubic symmetry for two cases

Abstract

Similar to the case of coupling coefficients G ij , the relationships between the spin-lattice coupling coefficients F ij ( F 11, F 12 and F 44) in cubic symmetry and the g-factors in cubic and low symmetries have been found and hence simple and unified methods of calculating these coefficients from the formulas of the anisotropic g-factor are given. On this basis, the coefficient F 44 can be calculated very easily for two cases, i.e., for the g-factor formulas in trigonal field and for those in rhombic field. Thus, we can, in a certain degree, check whether the formulas of the g-factor in trigonal and rhombic symmetries are consistent and reliable by comparing the values of F 44 calculated for the two cases. As an example, the formulas of anisotropic g-factor for d 8 ions based on the strong-field coupling scheme have been inspected. Because the calculated values of F 44 for MgO:Ni 2+ crystal for the two cases are not only close to each other, but also in good agreement with the estimated experimental value, these formulas for the g-factor in trigonal and rhombic fields obtained by different authors can be regarded as reasonable.