Zero-Field Splitting of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-State Ions. III. Corrections to Parts I and II and Application to Distorted Cubic Crystals

Abstract

The procedures developed in two previous papers by the authors for calculating the parameters $D$ and $E$ in the spin Hamiltonian ${\mathcal{H}}_{s}=D[3{{S}_{z}}^{2}\ensuremath{-}S(S+1)]+E({{S}_{x}}^{2}\ensuremath{-}{{S}_{y}}^{2})$ for iron-group $3{d}^{5}(^{6}S)$ 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: ${C}_{11} (\mathrm{point}\mathrm{charge})=2.10$, ${C}_{11} (\mathrm{overlap})=\ensuremath{-}0.14$, ${C}_{44} (\mathrm{point}\mathrm{charge})=\ensuremath{-}1.44$, ${C}_{44} (\mathrm{overlap})=\ensuremath{-}0.28$ all in units of ${10}^{\ensuremath{-}13}$ cm/dyn. The totals, ${C}_{11}=1.96$, ${C}_{44}=1.16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm/dyn are in resonable agreement with the values ${C}_{11}=7.1$, ${C}_{44}=\ensuremath{-}2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ 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.