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- W2051208788 abstract "A general formulation including both overlap and charge-transfer covalency effects is developed for the parameters $D$ and $E$ in the spin Hamiltonian ${mathcal{H}}_{S}=D(3{{S}_{z}}^{2}ensuremath{-}S(S+1))+E({{S}_{x}}^{2}ensuremath{-}{{S}_{z}}^{2})$ for a $^{6}S$ ion surrounded by six singly charged negative closed-shell ions. The contributions to $D$ and $E$ arise in second order from the spin-orbit interaction and in first order from the spin-spin interaction. These contributions can be broken down into three categories: local, nonlocal, and distant, depending on whether the ligand orbitals are involved not at all, once, or twice. Specific application is made to the case of a ${mathrm{Mn}}^{2+}$ ion surrounded by six ${mathrm{F}}^{ensuremath{-}}$ ions (${mathrm{Mn}}^{2+}$:Zn${mathrm{F}}_{2}$). The calculations are performed for the recent crystal-structure parameters given by Baur. We find, on the one hand, that for the spin-spin interaction, the nonlocal terms predominate over the local and distant terms, and are of the same sign. On the other hand, for the spin-orbit interaction, the local and distant terms predominate over the nonlocal terms, and are of opposite sign, though similar in magnitude. The total (overlap only) contribution to $D$ is found to be -10.94ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$, which is comparable and of opposite sign to the point-charge contribution 24.01ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$ calculated in our earlier publication on this problem. The sum of the two contributions (point charge and overlap) is found to be 13.07ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$, very close to the experimental value of +10.5ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$. The overlap contribution to $E$ is found to be -19.77ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$, which is rather smaller than the point-charge contribution of -102.32ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$. The combined result, $E=ensuremath{-}122.09ifmmodetimeselsetexttimesfi{}{10}^{ensuremath{-}04}$ ${mathrm{cm}}^{ensuremath{-}1}$, is also close to the experimental value of -113.5ifmmodetimeselsetexttimesfi{}${10}^{ensuremath{-}4}$ ${mathrm{cm}}^{ensuremath{-}1}$." @default.
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- W2051208788 title "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. II. Overlap and Covalency Model" @default.
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- W2051208788 doi "https://doi.org/10.1103/physrev.155.338" @default.
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