Disorder-enhanced spin polarization in diluted magnetic semiconductors

We present a theoretical study of diluted magnetic semiconductors that includes spin-orbit coupling within a realistic host band structure and treats explicitly the effects of disorder due to randomly substituted Mn ions. While spin-orbit coupling reduces the spin polarization by mixing different spin states in the valence bands, we find that disorder from Mn ions enhances the spin polarization due to formation of ferromagnetic impurity clusters and impurity bound states. The disorder leads to large effects on the hole carriers which form impurity bands as well as hybridizing with the valence band. For Mn doping $0.01\lesssim x\lesssim 0.04$, the system is metallic with a large effective mass and low mobility.

Figure 1

(Color online) Energy levels of Mn-Mn pairs calculated in a supercell consisting of approximately $600\text{unit}$ cells. ${\mathrm{Mn}}_i$ indicates the $i\text{th}$ nearest-neighbor Mn pair configuration. The horizontal red (dashed) line indicates the position of the valence band maximum of host GaAs. The figure shows only the highest valence energy levels higher than $-0.2\mathrm{eV}$ below the GaAs valence band maximum. The top two levels are occupied by holes.

Figure 2

(Color online) Density of states (DOS) of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$. [(a) and (c)] EBOM with randomly placed Mn ions. [(b) and (d)] EBOM with one Mn ion in a supercell. (a) and (b) are for $x=0.010$ and (c) and (d) are for $x=0.037$. Red (solid) and blue (dashed) curves correspond to the majority and minority spin DOSs. 100 disorder configurations were used for the disorder average. Energies are relative to the host GaAs valence band maximum energy. The dashed vertical lines indicate the position of the chemical potential for uncompensated charge density. Notice that magnetic impurities generate a large DOS in the GaAs band gap region $[0,1.52]\mathrm{eV}$ due to strong hybridization with the valence band. At both dopings, there is a peak in the DOS at $\approx 0.55\mathrm{eV}$ [indicated by arrows in (a) and (c)] originating from the bound states of nearest-neighbor Mn ion pairs.

Figure 3

(Color online) Inverse participation ratio (IPR) of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$. Left panels (a) and (c) are for $x=0.010$, and right panels (b) and (d) are for $x=0.037$. [(a) and (b)] $\mathrm{IPR}\left(ϵ\right)$ plotted in logarithmic scale as a function of the carrier energy $ϵ$. [(c) and (d)] Scaling of ${\mathrm{IPR}}_N$, where $N$ is the size of the system. The horizontal lines show the ${\mathrm{IPR}}_{N_2}∕{\mathrm{IPR}}_{N_1}\propto N_1∕N_2$, expected for extended wave functions. The energies are relative to the GaAs valence band maximum located at $0\mathrm{eV}$. The dashed vertical lines denote the position of the chemical potential at given charge fraction $p=(\text{hole}\text{density}∕\mathrm{Mn}\text{density})$. Strong size dependence indicates extended states, whereas localized states show little size dependence. For each system size, the participation ratio was averaged over 100 disorder realizations.

Figure 4

(Color online) Disorder effects on spin polarization. (a) Density of states (DOS) of GaAs with the magnetic impurity concentration $x=0.037$ and the exchange coupling $J_{pd}=-1.5\mathrm{eV}$. Upper panel, disordered array; lower panel, ordered array. Red (solid) and blue (dashed) lines denote majority and minority spin DOSs, respectively. The energy is relative to the undoped GaAs valence band maximum. The vertical lines are the position of the chemical potential. The hole states with energy above the chemical potential are occupied. (b) The carrier spin polarization as a function of impurity concentration for two values of $J_{pd}=-2.48\mathrm{eV}$ (triangles) and $J_{pd}=-1.5\mathrm{eV}$ (circles). The filled (empty) symbols denote disordered (ordered) systems.