Dynamic Orbit-Lattice Interactions for PbF$\text{}_{2}$:Gd$\text{}^{3+}$ Single Crystals

Temperature dependence of the second-order spin-lattice coefficients for PbF$\text{}_{2}$:Gd$\text{}^{3+}$ is reported. It is shown that the thermal expansion of the crystal lattice contributes only in about 14 % to the observed dependence and the rest should be ascribed to a dynamic coupling between the 4f$\text{}^{7}$ electrons and lattice vibrations. The results are parametrized in both the Einstein and the Debye models and it is shown that the phenomenological parameters obtained from such parametrization can be made to coincide in both models if a specific value of the Einstein frequency ω$\text{}_{E}$ is properly chosen. Both models of parametrization show that the Γ$\text{}_{3_{g}}$ vibrating mode couples to the 4f$\text{}^{7}$ electrons much weaker than the Γ$\text{}_{5_{g}}$ one.