The Heisenberg exchange operator for ferromagnetic and antiferromagnetic systems
Abstract
The Heisenberg exchange operator has never been derived by methods which are applicable to the general case of arbitrary spin, although this operator has served as a starting postulate of theories of ferromagnetism and antiferromagnetism. A derivation of the Heisenberg operator, valid for the interaction of ions or atoms of arbitrary spin in a crystalline environment, is given which is intended to meet the principal theoretical objections to earlier derivations. The "exchange integral" is shown to be a linear combination of two types of terms, ordinarily of opposite sign, arising respectively from the ordinary exchange integrals in the Hartree-Fock approximation and from a superchange effect which occurs in the first order of configuration interaction corrections to the Hartree-Fock approximation. The Heisenberg exchange operator, according to the present derivation, can represent the interaction between ions or atoms in a crystal only when an unfilled shell of orthogonalized atomic orbitals remain uncombined with orbitals on other atoms in the single determinant approximation at the equilibrium internuclear distance. The formula obtained for the "exchange integral" is used to calculate the transition temperatures of the antiferromagnetic oxides MnO, FeO, NiO, and CoO. The ratios between these temperatures are shown to depend primarily on spectroscopic data for the ions, and are found to be in reasonable agreement with experimental values.
- Publication:
-
Annals of Physics
- Pub Date:
- May 1958
- DOI:
- 10.1016/0003-4916(58)90039-3
- Bibcode:
- 1958AnPhy...4...87N