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

Abstract

We derive an effective Hamiltonian for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ in the dilute limit, where ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ 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 $x_{\mathrm{active}}\lesssim 0.015$ for which finite size scaling studies of the participation ratios indicate a localization transition, even in the presence of strong on-site interactions, where $x_{\mathrm{active}}<x_{\mathrm{nom}}$ 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.

15 pages, 12 figures

References in corpus (5)

• Spatial structure of an individual Mn acceptor in GaAs
• Multiband tight-binding model of local magnetism in GaMnAs
• Ellipsometric study of the Electronic Structure of GaMnAs and LT-GaAs
• Positional Disorder, Spin-Orbit Coupling and Frustration in GaMnAs
• Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

Cited by in corpus (5)

• Optical Properties of III-Mn-V Ferromagnetic Semiconductors
• Electron-hole contribution to the apparent s-d exchange interaction in III-V diluted magnetic semiconductors
• Carrier induced ferromagnetism in diluted local-moment systems
• Heitler-London model for acceptor-acceptor interactions in doped semiconductors
• Enhanced ferromagnetism from electron-electron interactions in double exchange type models