Ferromagnetism of Ga$_{1-x}$Mn$_x$As and Weiss theory of Curie temperature in the coherent potential approximation

TL;DR

This paper investigates ferromagnetism in Ga$_{1-x}$Mn$_x$As using CPA with an exact DOS transformation, predicting a nonlinear Curie temperature relation and matching experimental data.

Contribution

It introduces an exact DOS transformation in CPA and applies Weiss theory to derive a nonlinear Curie temperature relation, improving upon previous semicircular DOS models.

Findings

Ferromagnetism is favored at low temperatures.

Impurity bands form only with strong Kondo coupling.

Predicted Curie temperature aligns well with experiments.

Abstract

The zinc-blende GaAs-based III-V diluted magnetic semiconductors (DMS)are studied in the coherent potential approximation(CPA). In this work, we use the exact Hilbert transformation of the face-centered cubic(fcc) density of states (DOS), which is different from the usual semi-circle density of states employed in our previous work. Our calculated relation of ground-state energy and impurity magnetization shows that ferromagnetism is always favorable at low temperatures. For very weak Kondo coupling, the density of states (DOS) of the host semiconductor is modified slightly. Impurity band can be generated at the host band bottom only when Kondo coupling is strong enough. Using Weiss molecular theory, we predict a nonlinear relation of Curie temperature with respect to Kondo coupling, as is different from the conclusion of our previous calculations based on semicircle DOS. The agreement of our calculated $T_{\rm C}$ with measured values is convincing.