Spin-Lattice Coupling Coefficients of a3d5Ion in Trigonal Symmetry: Study ofMn++in Zinc Sulfide

The spin-lattice coupling coefficients of ${\mathrm{Mn}}^{++}$ in $C_{3\nu }$ symmetry have been measured by a uniaxial-stress method. The two axial sites studied experimentally correspond to an axial-field parameter $D=-130.9\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Since the structure of these sites is not yet known, we performed theoretical calculations of the spin-lattice coupling coefficients for all the different sites which can exist in ZnS. The coefficients were calculated in an ionic model, following a perturbation method proposed by Blume and Orbach and generalized to any pressure-induced distortion. It appears clearly that the components of rank four of the internal crystal field give the preponderant contribution of the spin-lattice coupling coefficients, the influence of the components of rank two being two orders of magnitude smaller. The major contribution to the spin-lattice coupling coefficients $C_{\mathrm{ij}}$ is given by the pressure-induced even fields. We show that the equivalent even fields arising from the composition of the internal crystal fields of odd parity with the pressure-induced crystal fields of odd parity contribute significantly to the values of the $C_{\mathrm{ij}}$'s. Several other mechanisms such as spin-spin mechanism and higher-order effects have also been considered. We have shown that the $C_{\mathrm{ij}}$'s would be roughly identical for the different axial sites existing in our samples.