Magnon-mediated interactions between fermions depend strongly on the lattice structure

TL;DR

This paper introduces exact methods to analyze two charge carriers in a ferromagnetic background, revealing that lattice structure critically influences magnon-mediated interactions and bipolaron formation.

Contribution

It demonstrates that lattice structure determines the strength of magnon-mediated interactions, showing that two-sublattice models exhibit strong binding not captured by single-lattice models.

Findings

Magnon-mediated interactions are strong in two-sublattice models.

Fermions form triplet bipolarons in two-sublattice configurations.

Single-lattice models fail to capture low-energy two-carrier spectra.

Abstract

We propose two new methods to calculate exactly the spectrum of two spin-${1\over 2}$ charge carriers moving in a ferromagnetic background, at zero temperature. We find that if the spins are located on a different sublattice than that on which the fermions move, magnon-mediated effective interactions are very strong and can bind the fermions into low-energy bipolarons with triplet character. This never happens in models where spins and charge carriers share the same lattice, whether they are in the same band or in different bands. This proves that effective one-lattice models do not describe correctly the low-energy part of the two-carrier spectrum of a two-sublattice model, even though they may describe the low-energy single-carrier spectrum appropriately.