Enhanced carrier scattering rates in dilute magnetic semiconductors with correlated impurities

In III-V dilute magnetic semiconductors such as ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$, the impurity positions tend to be correlated, which can drastically affect the electronic transport properties of these materials. Within the memory function formalism we have derived a general expression for the current relaxation kernel in spin and charge disordered media and have calculated spin and charge scattering rates in the weak-disorder limit. Using a simple model for impurity clustering, we find a significant enhancement of the charge scattering. The enhancement is sensitive to cluster parameters and may be controllable through postgrowth annealing.

Figure 1

Momentum-dependent impurity structure factor (13) for different values of cluster radius $R_c$. Number of ions within the cluster $N=10$; average impurity concentration in the sample $x=0.05$. Inset: Schematic plot of the pair distribution function (11).

Figure 2

Frequency dependence of charge (15) and spin (16) scattering relaxation rates, for impurity clusters with $R_c=10\mathrm{\AA }$, $x_c=0.1$, and hole concentration $p=0.5$ hole per magnetic ion. Inset: Illustration of the frequency dependence of the cluster enhancement; see text.

Figure 3

Charge contribution to the relaxation rate as a function of the degree of compensation (number of holes per substitutional Mn ion). Solid lines include effects of ionic screening. The cluster model assumed $R_c=10\mathrm{\AA }$ and $x_c=0.1$.

Figure 4

Charge relaxation rate as a function of compensation for different cluster sizes (average number of ${\mathrm{Mn}}_{\mathrm{Ga}}$ ions within the cluster is fixed to $N=10$). The interplay between ionic and band carrier screening results in a nonmonotonic dependence for dense clusters.

Figure 5

Relaxation rate enhancement (21) due to correlation in impurity positions as a function of cluster size. The average number of magnetic ions within the cluster is fixed to $N=10$.