Clustering in disordered ferromagnets: The Curie temperature in diluted magnetic semiconductors

TL;DR

This paper develops an analytical formula for the Curie temperature in highly disordered diluted magnetic semiconductors, revealing that impurity correlations have minimal impact and that magnetic clustering near the transition resembles a percolation process.

Contribution

It provides a new analytical expression for the Curie temperature in dilute magnetic semiconductors and clarifies the effects of impurity correlations and magnetic clustering.

Findings

Impurity correlations have minor effects on $T_c$.

Neutrally correlated disorder yields the highest $T_c$.

Magnetic order emerges via a percolation-like clustering transition.

Abstract

We theoretically investigate impurity correlation and magnetic clustering effects on the long-range ferromagnetic ordering in diluted magnetic semiconductors, such as $\textrm{Ga}_{1-x}\textrm{Mn}_{x}\textrm{As}$, using analytical arguments and direct Monte Carlo simulations. We obtain an analytic formula for the ferromagnetic transition temperature $T_{c}$ which becomes asymptotically exact in the strongly disordered, highly dilute (i.e. small $x$) regime. We establish that impurity correlations have only small effects on $T_{c}$ with the neutrally correlated random disorder producing the nominally highest $T_{c}$. We find that the ferromagnetic order is approached from the high temperature paramagnetic side through a random magnetic clustering phenomenon consistent with the percolation transition scenario.