Why RKKY exchange integrals are inappropriate to describe ferromagnetism in diluted magnetic semiconductors

TL;DR

This paper critically examines the use of RKKY exchange integrals for modeling ferromagnetism in diluted magnetic semiconductors, showing that previous mean-field approaches overestimate stability and Curie temperatures, and proposing a more accurate semi-analytical method.

Contribution

The authors introduce a semi-analytical SC-L RPA approach to better account for fluctuations and disorder, challenging the validity of RKKY-based models in describing ferromagnetism in these materials.

Findings

Mean-field theories overestimate Curie temperatures.

RKKY oscillations lead to underestimated frustration effects.

RKKY-like interactions near the Fermi level better explain experimental ferromagnetism.

Abstract

We calculate Curie temperatures and study the stability of ferromagnetism in diluted magnetic materials, taking as a model for the exchange between magnetic impurities a damped Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and a shor t range term representing the effects of superexchange. To properly include effects of spin and thermal fluctuations as well as geometric disorder, we solve the effective Heisenberg Hamiltonian by means of a recently developed semi-analytical approach. This approach, ``self-consistent local Random Phase Approximation (SC-L RPA)'', is explained. We show that previous mean-field treatments, which have been widely used in the literature, largely overestimate both the Curie temperatures and the stability of ferromagnetism as a function of carrier density. The discr epancy when compared to the current approach was that effects of frustration in RKKY oscillations had been strongly underestimated by such simple mea n-field theories. We argue that the use, as is frequent, of a weakly-disordered RKKY exchange to model ferromagnetism in diluted III-V systems is inconsistent with the observation of ferromagnetism over a wide region of itinerant carrier densities. This may be puzzling when compared to the apparent success of calculations based on {\it ab-initio} estimates of the coupling; we propose a resolution to this issue by taking RKKY-like interactions between resonant states close to the Fermi level.