Non-perturbative $J_{pd}$ model and ferromagnetism in dilute magnets

TL;DR

This paper non-perturbatively calculates magnetic couplings in the $J_{pd}$ model for dilute magnets, revealing how parameters influence ferromagnetism and challenging weak coupling assumptions, with implications for materials like Ga(Mn)As.

Contribution

It introduces a non-perturbative method for calculating magnetic interactions in dilute magnets, bridging first-principles and model approaches, and highlights the role of bandwidth and resonant structures.

Findings

Magnetic exchange interactions differ qualitatively from weak coupling predictions.

Increasing $J_{pd}$ does not necessarily increase Curie temperature.

Ga(Mn)As exhibits a resonant structure conducive to high-temperature ferromagnetism.

Abstract

We calculate magnetic couplings in the $J_{pd}$ model for dilute magnets, in order both to identify the relevant parameters which control ferromagnetism and also to bridge the gap between first principle calculations and model approaches. The magnetic exchange interactions are calculated non-perturbatively and disorder in the configuration of impurities is treated exacly, allowing us to test the validity of effective medium theories. Results differ qualitatively from those of weak coupling. In contrast to mean field theory, increasing $J_{pd}$ may not favor high Curie temperatures: $T_C$ scales primarily with the bandwidth. High temperature ferromagnetism at small dilutions is associated with resonant structure in the p-band. Comparison to diluted magnetic semiconductors indicate that Ga(Mn)As has such a resonant structure and thus this material is already close to optimality.