Multi-Orbital Lattice Model for (Ga,Mn)As and Other Lightly Magnetically Doped Zinc-Blende-Type Semiconductors

TL;DR

This paper introduces a real-space Hamiltonian model for lightly Mn-doped III-V semiconductors, capturing hole behavior and magnetic interactions, validated by large-scale simulations matching experimental results.

Contribution

The authors develop a novel lattice Hamiltonian incorporating spin-orbit and impurity interactions, enabling detailed numerical studies of magnetic doping effects in zinc-blende semiconductors.

Findings

Model reproduces experimental Curie temperatures for GaMnAs and GaMnSb.

Shows Curie temperature does not increase monotonically with doping level.

Provides insights into Mn doping effects in GaP and GaN.

Abstract

We present a Hamiltonian in real space which is well suited to study numerically the behavior of holes introduced in III-V semiconductors by Mn doping when the III$^{3+}$ ion is replaced by Mn$^{2+}$. We consider the actual lattice with the diamond structure. Since the focus is on light doping by acceptors, a bonding combination of III and V p-orbitals is considered since the top of the valence band, located at the $\Gamma$ point, has p character in these materials. As a result, an effective model in which the holes hop between the sites of an fcc lattice is obtained. We show that around the $\Gamma$ point in momentum space the Hamiltonian for the undoped case is identical to the one for the Luttinger-Kohn model. The spin-orbit interaction is included as well as the on-site interaction between the spin of the magnetic impurity and the spin of the doped holes. The effect of Coulomb interactions between Mn$^{2+}$ and holes, as well as Mn$^{3+}$ doping are discussed. Through large-scale Monte Carlo simulations on a Cray XT3 supercomputer, we show that this model reproduces many experimental results for ${\rm Ga_{\it 1-x}Mn_{\it x}As}$ and ${\rm Ga_{\it 1-x}Mn_{\it x}Sb}$, and that the Curie temperature does not increase monotonically with $x$. The cases of Mn doped GaP and GaN, in which Mn$^{3+}$ is believed to play a role, are also studied.