Theoretical spin-orbit coupling constants for 3d ions in crystals.

Abstract

Theoretical spin-orbit constants for the ${\mathrm{V}}^{2+}$, ${\mathrm{Cr}}^{\mathrm{z}+}$ (z=1--3), and ${\mathrm{Mn}}^{2+}$ ions in ${\mathrm{KMgF}}_{3}$ have been calculated by means of the theory of Blume and Watson [Proc. R. Soc. London, Ser. A 270, 127 (1962); 271, 565 (1963)] and the approximate cluster Hamiltonian of Misetich and Buch [J. Chem. Phys. 41, 2524 (1964)]. The modified one-center spin-orbit parameters appearing in the latter Hamiltonian have been obtained by means of Hartree-Fock-Roothaan calculations on the octahedral M${\mathrm{F}}_{6}$ clusters (M is the 3d ion) including the cluster-lattice interaction. The 3d-orbital deformation, deduced from the cluster calculations, appears as a key factor in determining the spin-orbit constants and their reduction with respect to the free-ion values. Covalency effects are less important in this highly ionic compound. Ligand contributions to the spin-orbit constants are smaller than 10%. The variation of these constants with the metal-ligand distance R has also been determined from calculations at different values of R. According to the results of this and previous work, the spin-orbit constants behave as local observables, fairly independent of the effects of the rest of the lattice on the cluster wave function. The theoretical coupling constants agree rather well with available experimental values.