Magnetic properties and disorder effects in diluted magnetic semiconductors

We present calculations of the exchange interactions and critical temperatures for several diluted magnetic semiconductor systems. It is shown that the exchange interactions are dominated by short-ranged interactions that have a strong directional dependence. Using a combination of first-principles calculations of the exchange interactions together with Monte Carlo simulations of the classical Heisenberg model, in which the positional disorder and spin fluctuations are properly included, the calculated critical temperatures are in good agreement with experimantal observations. It is shown that agreement between theory and experiment, as regards ordering temperatures, is obtained only when the magnetic atoms are randomly positioned in a simulation cell which proves that disorder effects play a very important role. The effect of strong electron-electron interaction has been studied by means of the $\mathrm{LSDA}+U$ scheme. We investigate in detail the nature of the anisotropic exchange interactions by means of a Fermi surface analysis.

Figure 1

Critical temperatures from MC simulations for a simple toy model (see text) with concentration $x$ of magnetic atoms, for different ranges of the magnetic interaction (given by the numbers in the inset).

Figure 2

Calculated Heisenberg exchange interactions plotted as a function of distance $d$ (measured in lattice constants) between magnetic impurities for (a) 5% Mn doped GaAs, (b) 5% Mn doped GaN, (c) Cr-doped ZnTe, and (d) 25% Co doped ZnO using LDA. In (a) and (b) both interactions calculated with LDA and $\mathrm{LDA}+U$ are displayed. In (c) the exchange parameters for three different concentrations $x$ of Cr atoms are displayed. In (d) both the intrasublattice interaction between Co atoms and the intersublattice interaction between Co and O are displayed.

Figure 3

Spin-spin correlation function $G\left(\mathbf{r}\right)$ of GaAs doped with 5% Mn plotted as a function of distance $d$ (measured in lattice constants), for two temperatures $T=160\mathrm{K}$ and $T=190\mathrm{K}$, above the critical temperature $\left(148\mathrm{K}\right)$.

Figure 4

Critical temperatures of Mn-doped GaAs as a function of Mn concentration $x$ in (a) LDA and (b) the $\mathrm{LDA}+U$ approximation. The LRPA values are from Ref. 30. Experimental data are from Refs. 4, 5, 6.

Figure 5

Exchange parameters using LDA in 5% Mn-doped GaAs plotted as a function of $(d∕a)$ for several different As-antistite concentrations $y$ (inset).

Figure 6

Critical temperatures of 5% Mn-doped GaAs plotted as a function of As-antisite concentration $y$ in (a) LDA and (b) $\mathrm{LDA}+U$ approximation.

Figure 7

Critical temperatures of Mn-doped GaN plotted as a function of Mn concentration $x$ in (a) LDA and (b) the $\mathrm{LDA}+U$ approximation.

Figure 8

The Bloch spectral function of GaMnAs from the $\Gamma$ point outwards in the [001], [011], and [111] directions. Darker color corresponds to higher intensity of the BSF.

Figure 9

The Bloch spectral function of ordered GaAs from the $\Gamma$ point outwards in the [001], [011], and [111] directions. Darker color corresponds to higher intensity of the BSF.

Figure 10

The Bloch spectral function, at the Fermi energy, of $\left({\mathrm{Ga}}_{0.95}{\mathrm{Mn}}_{0.05}\right)\mathrm{As}$ along the [001], [011], and [111] directions.

Figure 11

Approximations of the Fermi surfaces for $\left({\mathrm{Ga}}_{0.95}{\mathrm{Mn}}_{0.05}\right)\mathrm{As}$, constructed by taking isosurfaces of the spectral function $A(E_F,k)$ for $A=1.0$, 2.0, and 3.0, respectively. While the shape of the Fermi surface for the highest value is spherical free-electron-like, the two other surfaces are clearly anisotropic.