Generalized Theory for the Temperature-Dependent Hyperfine Coupling Constant of Iron-GroupS-State Ions

The orbit-lattice interaction theory describing the temperature dependence of the hyperfine coupling constant of iron-group $S$-state ions in cubic crystals is generalized by means of the same $k$-space averaging method employed in the generalization of the theory for rare-earth $S$-state ions. This generalized theory provides a good qualitative fit to experimental data on the temperature behavior of the hyperfine constant of ${\mathrm{Mn}}^{2+}$ in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$, but the calculated magnitude of the decrease in the hyperfine constant with temperature is considerably smaller (with respect to its observed value) than is the corresponding magnitude calculated from the long-wavelength theory. This disagreement between theory and experiment increases with increasing interionic distance in the host lattice. In addition, the generalized theory for iron-group $S$-state ions confirms our previous finding that optical phonons make a significant contribution to both the thermal and rigid-lattice values of the hyperfine coupling constant, and enables us to determine the range of validity of the long- and short-wavelength treatments.