Ground State of a $\textit{d}\varepsilon$ Electron in an Elastic Octahedron of Ligands

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The ground state of a $\textit{d}\varepsilon$ electron in an elastic octahedral ligand is discussed. The increases in both crystalline field potential and elastic energy due to the deformation of the ligand are respectively taken into account up to the terms linear and quadratic to the magnitude of deformation. The $E_{g}$ and $T_{2g}$ types of deformation, as well as spin–orbit coupling, are to be considered. There are four types of ground state characterized by the direction (parallel or perpendicular to $\langle 001\rangle$ or $\langle 111\rangle$) and magnitude of orbital angular momentum, and the sign (elongation or shrinkage) and direction ($\langle 001\rangle$ or $\langle 111\rangle$) of the main deformation, parallel or perpendicular to the orbital angular momentum. A phase diagram is given in a plane of the relative magnitudes of couplings, $\Delta\varepsilon_{e}^{0}/|\lambda S|$ and $\Delta\varepsilon_{t}^{0}/|\lambda S|$, where $\Delta\varepsilon_{e}^{0}$ and $\Delta\varepsilon_{t}^{0}$ indicate the largest energy decrease due to each type of deformation. By considering these types of ground state, the reported large tilting of Co spins from $\langle 100\rangle$ in antiferromagnetic CoO is discussed briefly in the last section. The present result is consistent with the multi-spin-axis model of van Laar [Phys. Rev. 138 (1965) A584] and the antiferroelastic character of the antiferromagnetic CoO is suggested.
2010-11-15