Direct Exchange in Ferromagnets

Abstract

The direct exchange integral which occurs in the Heisenberg theory of ferromagnetism is evaluated for all internuclear spacings. We find that it is always positive, whereas Bethe originally suggested it would be positive only at large spacing and more recently it has been suggested that the integral should always be negative. However, at the observed internuclear separation the magnitude calculated is of the order of 70 times too small to explain the experimentally determined exchange constant in ferromagnetic metals, and we therefore conclude that direct exchange is not responsible for ferromagnetism in these metals.