Exchange interactions in two-state systems: rare earth pyrochlores

TL;DR

This paper derives the general form of nearest neighbour exchange interactions for two-state systems in rare earth pyrochlores, treating the ground state doublets as pseudo-spins and providing a methodology applicable to other high-symmetry two-state systems.

Contribution

It presents a symmetry-based derivation of exchange interactions for pseudo-spins in rare earth pyrochlores, applicable to various two-state high-symmetry systems.

Findings

Derived the general form of exchange interactions for pseudo-spins.

Applicable methodology to other two-state systems with high symmetry.

Clarified the role of crystal electric field in degeneracy lifting.

Abstract

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.