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

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

2005-03-16

arxiv.org/abs/cond-mat/0503382v1

Phys. Rev. B 72, 045212 (2005)

Physics

Condensed Matter

Materials Science

15 pages, 12 figures

Scientific paper

10.1103/PhysRevB.72.045212

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}

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