Disorder, spin-orbit, and interaction effects in dilute ${\rm Ga}_{1-x}{\rm Mn}_x{\rm As}$

TL;DR

This paper develops an effective Hamiltonian for dilute GaMnAs that incorporates spin-orbit coupling, disorder, and interactions, revealing a localization transition of impurity band states at low Mn concentrations.

Contribution

The authors derive a non-perturbative effective Hamiltonian for GaMnAs that includes spin-orbit effects and disorder, providing new insights into magnetic and localization properties.

Findings

Impurity band remains well separated from valence band up to x_active ≈ 0.015.

Localization transition occurs at low Mn concentrations, even with strong interactions.

Magnetic properties show non-collinear states influenced by disorder and interactions.

Abstract

We derive an effective Hamiltonian for ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ in the dilute limit, where ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ can be described in terms of spin $F=3/2$ polarons hopping between the {\rm Mn} sites and coupled to the local {\rm Mn} spins. We determine the parameters of our model from microscopic calculations using both a variational method and an exact diagonalization within the so-called spherical approximation. Our approach treats the extremely large Coulomb interaction in a non-perturbative way, and captures the effects of strong spin-orbit coupling and Mn positional disorder. We study the effective Hamiltonian in a mean field and variational calculation, including the effects of interactions between the holes at both zero and finite temperature. We study the resulting magnetic properties, such as the magnetization and spin disorder manifest in the generically non-collinear magnetic state. We find a well formed impurity band fairly well separated from the valence band up to $x_{\rm active} \lesssim 0.015$ for which finite size scaling studies of the participation ratios indicate a localization transition, even in the presence of strong on-site interactions, where $x_{\rm active}<x_{\rm nom}$ is the fraction of magnetically active Mn. We study the localization transition as a function of hole concentration, Mn positional disorder, and interaction strength between the holes.