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

Abstract

We theoretically investigate impurity correlation and magnetic clustering effects on the long-range ferromagnetic ordering in diluted magnetic semiconductors, such as ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$, 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.

5 pages, 4 figures