Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN

Abstract

We present calculations of magnetic exchange interactions and critical temperature T c in Ga 1−x Mn x As, Ga 1−x Cr x As and Ga 1−x Cr x N. The local spin density approximation is combined with a linear-response technique to map the magnetic energy onto a Heisenberg hamiltonion, but no significant further approximations are made. Special quasi-random structures in large unit cells are used to accurately model the disorder. T c is computed using both a spin-dynamics approach and the cluster variation method developed for the classical Heisenberg model.We show the following: (i) configurational disorder results in large dispersions in the pairwise exchange interactions; (ii) the disorder strongly reduces T c ; (iii) clustering in the magnetic atoms, whose tendency is predicted from total-energy considerations, further reduces T c . Additionally the exchange interactions J(R) are found to decay exponentially with distance R 3 on average; and the mean-field approximation is found to be a very poor predictor of T c , particularly when J(R) decays rapidly. Finally the effect of spin-orbit coupling on T c is considered. With all these factors taken into account, T c is reasonably predicted by the local spin-density approximation in MnGaAs without the need to invoke compensation by donor impurities.

Disorder and the effectiveMn−Mnexchange interaction inGa1−xSilva1, Fazzio2, Santos3 et al. 2005Phys. Rev. B15150View full textAdd to dashboardCite

“…The nonmonotonic behavior is attributed to directionality effects; by the same token, deviations in the sign of J n were found only at large n (=5), when its magnitude is already greatly reduced with respect to the nearest neighbor value. The discrepancy of the present results with respect to recent calculations by Xu et al, 18 may be attributed to the fact that their muffin-tin calculations are not full potential; they therefore do not fully reproduce the crucial role played by the directional sp 3 bonds and by the hole p-states. Also, due to the quite significant variations of the calculated exchange couplings with configurations and Mn concentration, we emphasize that estimates of the critical temperature obtained via exchange couplings thus obtained are clearly open to question.…”

“…18,19,20,21,22,23,24,25,26 Some predict an alternating sign for the exchange coupling, but these predictions should be taken with extreme care, since these theoretical calculations are based on non-fullpotential muffin-tin-type potentials which are not reliable to treat the electronic structure of covalent semiconductor systems such as (Ga,Mn)As DMS. Also, disorder quite certainly is not adequately taken into account within simple effective-medium approaches such as VCA or CPA, as fluctuations in the Mn positions essentially lead to variations in the Mn-Mn exchange-coupling parameters, as apparent from Fig.…”

“…Van Schilfgaarde and Mryasov 17 have performed calculations of total energies, within the atomic spheres approximation, to extract exchange couplings, J's, for specific (i.e., not randomly chosen) clusters of closely spaced Mn ions; their results suggest a tendency of a decrease in |J| when more Mn atoms are added to nearby sites. More recently, Xu et al 18 used muffin-tin orbitals to investigate the dependence of the exchange coupling with the Mn-Mn distance at much larger (8.3%) concentrations of Mn atoms; they found a considerable scatter in the values of the exchange couplings. In a series of theoretical studies, in which the effect of randomness/disorder is described by the coherent-potential approximation (CPA), Kudrnovský et al 19,20 and Bergqvist et al 21 have used a tight-binding linear muffin-tin orbital method, together with the magnetic force theorem, to study the dependence of the Mn-Mn exchange couplings and critical temperatures with the concentration of Mn impurities in III-V and group IV DMS.…”

Ab-initiostudy of exchange constants and electronic structure in diluted magnetic group-IV semiconductors

“…Environmental effects were also recently reported by Sato et al in DMS via a cluster-embedding method [15]. Of course, these findings imply that a careful prediction of the Curie ordering temperature requires an accurate knowledge of the real distribution of the Mn atoms in the host matrix [16,17]. In order to have a deep understanding of the exchange constants in group-IV DMS, we focus on the dependence on (i) the concentration (by examining Mn doping varying from 12.5 up to 50%); (ii) the semiconducting host (by examining difference and similarities of Mn-doped Ge and Mn-doped GaAs) and (iii) the impurity (by examining a different behavior of Mn-doped versus Cr-doped Ge).…”

Carrier-induced ferromagnetism in diluted local-moment systems

“…Moreover, dynamical mean-field theory (DMFT) 29,30,31 is used to investigate the carrier spin polarization of the impurity band and the Curie temperature of Ga 1−x Mn x As. In addition to these theories, ab-initio approaches 32,33,34,35 , spin-wave theories 36,37,38,39 , Monte Carlo (MC) simulations 13,40,41,42,43 have been applied to understand the physics of DMSs.…”