Direct Exchange betweendElectrons

Abstract

The empirical data necessary to determine all the parameters in the exchange interaction between a pair of orbitally degenerate ions do not exist for any system. Given this paucity, we have resorted to using the best available theoretical estimates of the two-center exchange integrals for $d$ electrons which have been calculated for particular cases of cobalt atoms and ions. With these data we have quantitatively substantiated the recent assertions made about the importance of anisotropic and higher-degree isotropic-exchange interactions. We demonstrate that a bilinear scalar spin hamiltonian is totally inadequate to describe exchange interactions in systems containing orbitally degenerate ions. The higher-degree isotropic terms considerably alter the positions of the centers of gravity of the energy levels of exchange-coupled pairs. We estimate that the exchange interaction accounts for 25% of the discrepancy between the spin-orbit coupling constant $\lambda$ required to explain the magnon spectra of cobalt in KCo${\mathrm{F}}_3$ and the $\lambda$ for free cobalt ions. For orbitally degenerate ions in magnetically inequivalent sites, it is shown that antisymmetric exchange is as large as the symmetric terms.