Magnetic Percolation and the Phase Diagram of the Disordered RKKY model

TL;DR

This paper maps the phase diagram of a disordered RKKY model with randomly placed magnetic moments, revealing a magnetic percolation transition and the effects of various interactions on ferromagnetism.

Contribution

It provides the first detailed Monte Carlo phase diagram of the disordered RKKY model including superexchange and damping effects.

Findings

Ferromagnetism vanishes when carrier concentration exceeds 0.1 times impurity density.

The ferromagnetic-nonferromagnetic boundary is a zero-temperature critical line.

Superexchange and damping significantly influence the phase diagram.

Abstract

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain via Monte Carlo the magnetic phase diagram as a function of the impurity moment density $n_{i}$ and the relative carrier concentration $n_{c}/n_{i}$. As evidenced by the diverging correlation length and magnetic susceptibility, the boundary between ferromagnetic (FM) and non-ferromagnetic (NF) phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for $n_{c}/n_{i}>.1$. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities, and examine the impact of a damping factor in the RKKY range function.