Calculation of the Spin-Lattice Coefficients ofGd3+in CaF2Using a Point-Charge Model for the Crystalline Field

The contribution of the Blume-Orbach mechanism to the second-order spin-lattice coefficients for ${\mathrm{Gd}}^{3+}$ in cubic sites of Ca${\mathrm{F}}_2$ has been calculated with a point-charge approach for the orbit-lattice interaction. Our results, $G_{3g}^{\mathrm{}\left(2\right)\mathrm{}}=-0.006\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $G_{5g}^{\mathrm{}\left(2\right)\mathrm{}}=-0.07\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, agree in sign with the experimental values of $G_{3g}^{\mathrm{}\left(2\right)\mathrm{}}=-0.22\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $G_{5g}^{\mathrm{}\left(2\right)\mathrm{}}=-0.11\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Differences in magnitude of $G_{3g}^{\mathrm{}\left(2\right)\mathrm{}}$ can be understood in view of the opposite contribution of the fourth- and sixth-order terms of the orbit-lattice Hamiltonian. We conclude that the Blume-Orbach mechanism predicts values for the spin-lattice coefficients $G_{3g}^{\mathrm{}\left(2\right)\mathrm{}}$ and $G_{5g}^{\mathrm{}\left(2\right)\mathrm{}}$ of ${\mathrm{Gd}}^{3+}$ in Ca${\mathrm{F}}_2$ in reasonable agreement with the experimental data, and that the cubic crystalline field must be considered in any calculation of the spin-lattice parameters.