Theory of Antiferromagnetic-Ferromagnetic Transitions in Dilute Magnetic Alloys and in the Rare Earths

In a previous paper a theory of direct exchange and superexchange coupling between $d$ or $f$ electrons and conduction electrons was given. This led to the possibility of an antiferromagnetic-ferromagnetic transition. The present paper is devoted to a more complete treatment of this magnetic transition by way of examining a particular case. Both the molecular-field theory and a cluster theory due to Oguchi are applied. Each leads to a magnetic transition and both predict that for all such transitions the ferromagnetic state must have a lower free energy at 0°K than the antiferromagnetic state. The transition is found to be of second order. Expressions are given for the parallel and perpendicular susceptibility in the neighborhood of the Néel point. A discussion is given showing how the direct exchange interaction with the conduction electrons makes a magnetic transition possible. A comparison is made between the theory given here and recent experimental results in Cu-Mn alloys.