STATISTICAL EXCHANGE AND THE HEISENBERG EXCHANGE INTEGRAL

Abstract
A method is proposed for using the statistical Xα exchange approximation to the self-consistent field for studying magnetic excitations in crystals. The remarks are illustrated by the example of the ferromagnetism of EuS. In the ground state this crystal is known to be ferromagnetic, in agreement with the energy-band calculations of Cho, each Eu⁺² ion having a half-filled shell of 4 f electrons, all with parallel spin. From experiment, one can find the energy difference between this state, and a state with the magnetic moment of one Eu⁺² ion reversed. This energy difference can be expressed in terms of the Heisenberg exchange integral J. A method is proposed for using existing computer programs to find this same energy difference by fundamental a priori methods, thus determining J. This new method is based on two recent developments. One is the study of a so-called transition state, a state in which the electrons taking part in the transition are half in the initial state, half in the final state. In the present case, where the transition is from a state with the spin of a given ion up, to that with the spin down, the transition state is non-spin-polarized. A self-consistent solution is to be found for a crystal with one atom in this transition state. It has been shown that the energy difference between the initial and final states of such a transition can be given very accurately from differences of one-electron states computed for this transition state. To study these energy levels, one can use recently-developed methods for treating a crystal with an impurity atom. Use of these methods should be capable of leading even to the very small energy differences characteristic of the low Curie temperature (16.5 °K) known to hold for EuS. The method should be adaptable to many other similar problems.