Exchange and Superexchange Coupling between Conduction Electrons anddElectrons in Magnetic Materials

Abstract

An analysis is made of the magnetization of the conduction electrons in a ferromagnetic material induced by their exchange interaction with the $d$ electrons. The problem is set up by using the density matrix, some special properties of which are proved in the Appendix. When this formalism is used, the exchange interaction between a conduction electron and the inner as well as the $d$ electrons associated with a given atom are found as a function of the relative spin orientation of the atom and the conduction electron. The problem is treated for $T\ensuremath{\ll}{T}_{C}$ and for $T\ensuremath{\sim}{T}_{C}$. Results for Fe have been calculated by using the nearly free electron method and the cellular methods. The effect of correlation is taken into account by the Bohm and Pines technique. A magnetization of about ${0.20}_{\mathrm{\ensuremath{\mu}}0}$ per atom is found. An antiferromagnetic coupling is found to be possible between magnetic ions in dilute alloys such as has been found experimentally in Cu-Mn. The mechanism is a superexchange coupling of the magnetic ions through the conduction electrons. A molecular field theory has been worked out for this case on the basis of an antiferromagnetic coupling between the magnetic ions and a ferromagnetic coupling between these ions and the conduction electrons. This theory is found to admit the possibility of an antiferromagnetic-ferromagnetic transition. Application of this theory to the Cu-Mn alloys shows that it is unnecessary to assume that the $s\ensuremath{-}d$ exchange interaction is as weak as previously believed. It is, furthermore, suggested that the combination of direct and superexchange interactions between the $4f$ and conduction electrons in the rare earths is responsible for their magnetic properties and in particular is the source of the observed antiferromagnetic-ferromagnetic transitions in erbium and dysprosium.