Effective Hamiltonian for Ga_{1-x}Mn_xAs in the Dilute Limit

TL;DR

This paper derives an effective Hamiltonian for dilute GaMnAs, modeling spin polarons hopping between Mn sites, incorporating Coulomb interactions, spin-orbit coupling, and disorder, suitable for low Mn concentrations.

Contribution

The paper introduces a non-perturbative effective Hamiltonian for dilute GaMnAs that includes Coulomb interactions, spin-orbit effects, and disorder, based on microscopic calculations.

Findings

Model applies to Mn concentrations up to 3%.

Captures effects of spin-orbit coupling and disorder.

Parameters derived from microscopic calculations.

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. Our approach treats the large Coulomb interaction in a non-perturbative way, captures the effects of spin-orbit coupling and disorder, and is appropriate for other p-doped magnetic semiconductors. Our model applies to uncompensated {\rm Mn} concentrations up to $x \sim 0.03$.