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.

arXiv comment15 pages, 12 figures

References in corpus (24)

• Spintronics: Fundamentals and applications
• Ferromagnetic Semiconductors: Moving Beyond (Ga,Mn)As
• Mn Interstitial Diffusion in (Ga,Mn)As
• Effects of Disorder on Ferromagnetism in Diluted Magnetic Semiconductors
• Effects of annealing time on defect-controlled ferromagnetism in Ga1-xMnxAs
• Highly enhanced Curie temperatures in low temperature annealed (Ga,Mn)As epilayers
• Bound Magnetic Polaron Interactions in Insulating Doped Diluted Magnetic Semiconductors
• Spatial structure of an individual Mn acceptor in GaAs
• Transition temperature of ferromagnetic semiconductors: a dynamical mean field study
• First-principles investigation of the assumptions underlying Model-Hamiltonian approaches to ferromagnetism of 3d impurities in III-V semiconductors
• Disorder effects in diluted magnetic semiconductors
• Multiband tight-binding model of local magnetism in GaMnAs
• Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN
• Correlated defects, metal-insulator transition, and magnetic order in ferromagnetic semiconductors
• Ellipsometric study of the Electronic Structure of GaMnAs and LT-GaAs
• Griffiths phase in diluted magnetic semiconductors
• Monte Carlo simulations of an impurity band model for III-V diluted magnetic semiconductors
• Influence of non-local exchange on RKKY interactions in III-V diluted magnetic semiconductors
• Photoemission studies of Ga${}_{1-x}$Mn${}_x$As: Mn-concentration dependent properties
• Metal-Insulator Transition and Ferromagnetism in Diluted Magnetic Semiconductors
• Effective Hamiltonian for Ga_{1-x}Mn_xAs in the Dilute Limit
• Optical properties of metallic (III,Mn)V ferromagnetic semiconductors in the infrared to visible range
• 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 (12)

• Optical Properties of III-Mn-V Ferromagnetic Semiconductors
• Spatial structure of Mn-Mn acceptor pairs in GaAs
• The influence of electrostatic potentials on the apparent s-d exchange energy in III-V diluted magnetic 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
• Combined approach of density functional theory and quantum Monte Carlo method to electron correlation in dilute magnetic semiconductors
• The influence of structural short-range order on the phase diagrams of diluted FCC magnet with arbitrary spin and modified RKKY interaction
• Theory of optical conductivity for dilute GaMnAs
• Impurity bands and the character of the electronic states in ferromagnetic GaMnAs layers
• Heitler-London model for acceptor-acceptor interactions in doped semiconductors
• A semiquantitative approach to the impurity-band-related transport properties of GaMnAs nanolayers
• Enhanced ferromagnetism from electron-electron interactions in double exchange type models