Quantitative interpretation of the Goodenough-Kanamori rules: A critical analysis

Expressions in the early literature for kinetic exchange in magnetically coupled systems are critically analyzed by second-order perturbation theory and substituted by corrected versions. The widely held belief that kinetic exchange is always antiferromagnetic is found to be incorrect. Ferromagnetic kinetic exchange terms are found to be more important than hitherto assumed. The quantity J/U, where J stands for intraatomic exchange interactions and U is the energy difference between the ground electron configuration and a charge-transfer configuration, plays a crucial role in the competition between ferromagnetic and antiferromagnetic contributions, J/U readily exceeds the value 1/5 considered as an upper limit by Anderson. J is found to be proportional to the number of unpaired electrons on a given magnetic center.