Temperature Dependence of the Hyperfine Coupling of Rare-EarthS-State Ions in Cubic Crystals

Measurements of the hyperfine coupling constant $A$ of Ca${\mathrm{F}}_2$: ${\mathrm{Eu}}^{2+}$ were made for temperatures between 4.2 and 715°K by means of EPR techniques. It was found that $\mathrm{}\left|A\right|\mathrm{}$ decreased in magnitude by approximately 2% over this temperature range. A calculation of the temperature dependence of $A$ following Šimánek and Orbach was also performed. The orbit-lattice interaction for a molecular cluster with eightfold cubic coordination was expanded in third-order spherical harmonics and normal coordinates which are antisymmetrical under inversion through the origin. This interaction was used to admix excited $\mathrm{ns}$ states into the ground $4f$ orbitals so as to give rise to a temperature-dependent hyperfine coupling constant given by the relation $A\left(T\right)=A\left(0\right)[1-C{T}^6\int 0^{\frac{\Theta }{t}}{x}^5{(e^x-1)}^{-1\mathrm{}}\mathrm{dx}]$ Good agreement was obtained between the temperature dependence predicted by this expression and our experimental data on Ca${\mathrm{F}}_2$: ${\mathrm{Eu}}^{2+}$. However, the strength of the constant $C$, calculated on the basis of a nearest-neighbor point-charge model and the long-wavelength approximation, was smaller than the experimentally determined value by approximately one order of magnitude.