Calculation of Some Ytterbium-Oxygen-Iron Superexchange Integrals

Abstract

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.