Calculation of Some Ytterbium-Oxygen-Iron Superexchange Integrals

Past calculations of the anisotropic superexchange interaction between Yb3+ and Fe3+ in the garnets have made use of drastic assumptions about the form of the exchange potential. A more fundamental calculation has been impossible until now because of a lack of detailed knowledge of the relative magnitudes of the superexchange integrals. We have calculated the nineteen exchange integrals between the different combinations of O2− p orbitals and Yb3+ f orbitals. The O2− wave functions were taken from Watson's analytic Hartree-Fock calculation and the Yb3+ wave functions were calculated using a Hartree-Fock computer program of F. Herman. The values of the integrals span a range of three orders of magnitude. They exhibit a strong dependence on the azimuthal quantum numbers m and m′ of the oxygen p orbitals along the bond, and a much weaker dependence on the f-electron quantum numbers. The integrals involving m = 0 and m′ = 0 clearly predominate, and those involving m = 0 and m′ = ±1 are smaller by almost an order of magnitude. The transfer integrals and the implications of these results for the form of the exchange potential are discussed.