Overlap contribution to the axial field of ${\mathrm{Mn}}^{2+}$ in ${\mathrm{K}}_2$Mg${\mathrm{F}}_4$

The values of transferred hyperfine parameters for both equatorial and axial ligands are obtained for ${\mathrm{K}}_2$Mg${\mathrm{F}}_4$:${\mathrm{Mn}}^{2+}$. These values are used to compute the overlap contributions to $D$, arising via spin-spin and spin-orbit interactions. Both local and nonlocal contributions are considered. The calculations indicate that, while both local and nonlocal contributions arising via spin-spin interactions are important, the nonlocal contribution arising via spin-orbit interaction is very small. The total overlap contribution to $D$ arising through these two mechanisms is 62.25 X ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, while the experimental value of $D$ is (107±2) X ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$.