A strong coupling theory for electron-mediated interactions in double-exchange models

TL;DR

This paper develops a systematic theoretical framework to evaluate effective interactions between localized spins mediated by itinerant electrons in double-exchange models, especially in the large Hund's coupling limit.

Contribution

It introduces a new expansion method for constructing effective spin models in double-exchange systems, validated against numerical solutions and extendable to various spin types.

Findings

Accurate effective spin models derived in the large Hund's coupling limit.

Validation against numerical solutions shows high accuracy.

Method extendable to Heisenberg and XY spin models.

Abstract

We present a theoretical framework for evaluating effective interactions between localized spins mediated by itinerant electrons in double-exchange models. Performing the expansion with respect to the spin-dependent part of the electron hopping terms, we show a systematic way of constructing the effective spin model in the large Hund's coupling limit. As a benchmark, we examine the accuracy of this method by comparing the results with the numerical solutions for the spin-ice type model on a pyrochlore lattice. We also discuss an extension of the method to the double-exchange models with Heisenberg and $XY$ localized spins.