Interaction Between the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>Shells in the Transition Metals

TLDR

The interaction between incomplete d shells in transition metals is assumed to be weak enough to preserve intra‑shell coupling, with exchange interactions of fixed sign, leading to an inherent antiferromagnetic tendency of adjacent d spins. The authors explain the body‑centered cubic structures of V, Cr, Co, Mo, Ta, and W, and show that coupling between d shells and conduction electrons produces ferromagnetic alignment, offering simple rules to predict ferromagnetism or antiferromagnetism in alloys.

Abstract

It is assumed (1) that the interaction between the incomplete $d$ shells of the transition elements is insufficient to disrupt the coupling between the $d$ electrons in the same shells, and (2) that the exchange interaction between adjacent $d$ shells always has the same sign irrespective of distance of separation. The direct interaction between adjacent $d$ shells then invariably leads to a tendency for an antiferromagnetic alignment of $d$ spins. The body-centered cubic structure of the transition metals V, Cr, Cb, Mo, Ta, and W is thereby interpreted, as well as more complex lattices of certain alloys. It is demonstrated that the spin coupling between the incomplete $d$ shells and the conduction electrons leads to a tendency for a ferromagnetic alignment of $d$ spins. The occurrence of ferromagnetism is thereby interpreted in a much more straightforward manner than through the ad hoc assumption of a reversal in sign of the exchange integral. The occurrence of antiferromagnetism and of ferromagnetism in various systems is readily understood, and certain simple rules are deduced for deciding which type of magnetism will occur in particular alloys.