Zero-Field Splitting ofS-State Ions. III. Corrections to Parts I and II and Application to Distorted Cubic Crystals

The procedures developed in two previous papers by the authors for calculating the parameters $D$ and $E$ in the spin Hamiltonian ${\mathcal{H}}_s=D[3\mathrm{}{S_z}^2-S(S+1\mathrm{}\left)\right]+E({S_x}^2-{S_y}^2)$ for iron-group $3d^5\left({}_{}{}^6{}_{}{}^{}S\right)$ ions are applied to a distorted cubic system, namely, that of a ${\mathrm{Mn}}^{++}$ ion in a MgO host lattice under uniaxial stress. The parameters $D$ and $E$ for this system are specified respectively by two stress coefficients $C_{11}$ and $C_{44}$, which contain contributions from point-charge and overlap mechanisms of the amounts: $C_{11} \left(\mathrm{point}\mathrm{charge}\right)=2.10\mathrm{}$, $C_{11} \left(\mathrm{overlap}\right)=-0.14\mathrm{}$, $C_{44} \left(\mathrm{point}\mathrm{charge}\right)=-1.44\mathrm{}$, $C_{44} \left(\mathrm{overlap}\right)=-0.28\mathrm{}$ all in units of ${10}^{-13\mathrm{}}$ cm/dyn. The totals, $C_{11}=1.96\mathrm{}$, $C_{44}=1.16\mathrm{}\times {10}^{-13\mathrm{}}$ cm/dyn are in resonable agreement with the values $C_{11}=7.1\mathrm{}$, $C_{44}=-2.1\mathrm{}\times {10}^{-13\mathrm{}}$ cm/dyn measured by Feher. An Appendix is included which lists corrections to the spin-spin contributions to $D$ and $E$ that were derived in two earlier papers.