# Competition of the Coulomb and hopping based exchange interactions in granular magnets

## TL;DR

This paper investigates how Coulomb and hopping-based exchange interactions between ferromagnetic grains in an insulator compete and influence magnetic coupling, with the total interaction depending complexly on the dielectric properties of the matrix.

## Contribution

It introduces a comprehensive analysis of Coulomb exchange interaction in granular magnets and its competition with hopping-based exchange, highlighting the dielectric dependence.

## Key findings

- Coulomb and hopping exchange interactions are comparable in magnitude.
- These interactions often have opposite signs, leading to competition.
- The total exchange interaction varies significantly with dielectric constant, causing magnetic phase transitions.

## Abstract

We study exchange coupling due to the interelectron Coulomb interaction between two ferromagnetic grains embedded into insulating matrix. This contribution to the exchange interaction complements the contribution due to virtual electron hopping between the grains. We show that the Coulomb and the hopping based exchange interactions are comparable. However, for most system parameters these contributions have opposite signs and compete with each other. In contrast to the hopping based exchange interaction the Coulomb based exchange is inversely proportional to the dielectric constant of the insulating matrix $\varepsilon$. The total intergrain exchange interaction has a complicated dependence on the dielectric permittivity of the insulating matrix. Increasing $\varepsilon$ one can observe the ferromagnet-antiferromagnet (FM-AFM) and AFM-FM transitions. For certain parameters no transition is possible, however even in this case the exchange interaction has large variations, changing its value by three times with increasing the matrix dielectric constant.