Electronic structure of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ analyzed according to hole-concentration-dependent measurements

We study the effects of variable hole concentration on the transport, thermoelectric, and magnetic properties of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$. The hole concentration in samples with fixed Mn content has been varied using high energy particle irradiation, which introduces donorlike defects that compensate Mn acceptors without changing the concentration of localized Mn spins. As expected, a decrease of the hole concentration results in a reduction of the Curie temperature and an increase in electrical resistivity and thermoelectric power. The mobility and thermopower data are then analyzed in terms of models based on free holes in the valence band and holes localized in a Mn impurity band. The energetic structure of the impurity band is described by the valence-band anticrossing model. We show that the electronic structure provided by the impurity band model is consistent with the experimental results.

Figure 1

(Color online) Carrier concentration as a function of vacancy concentration generated by irradiation. ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ concentration (red squares) is calculated by combining initial ECV measurements with the carrier removal rate monitored by Hall effect in the GaAs:Zn and GaAs:Be samples (triangles).

Figure 2

(Color online) (a) Magnetization as a function of temperature for a series of irradiated ${\text{Ga}}_{0.955}{\text{Mn}}_{0.045}\text{As}$. (b) Curie temperature for each sample as a function of hole concentration.

Figure 3

(Color online) (a) Resistivity as a function of temperature of irradiated ${\text{Ga}}_{0.955}{\text{Mn}}_{0.045}\text{As}$. (b) Room temperature (300 K) mobility as a function of concentration for two samples of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ and Hall effect-measured mobility for nonmagnetic GaAs:Be and GaAs:Zn samples. Fits (dashed lines) are based on the ionized impurity model; the blue dashed lines (shorter dashes) use an effective mass derived from VBAC, while the black dashed lines represent calculations based on valence-band transport.

Figure 4

(Color online) Thermopower as a function of temperature of irradiated ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$. Colored points indicate measured data while solid lines are fits based on the VBAC model.

Figure 5

(Color online) (a) Approximated density of states used in transport calculations with reference to the original GaAs valence band. Blue line represents delocalized states of the original impurity band (red line). (b) Close-up image of the impurity band [same energy scale as (a), arbitrary units on $y$ axis] with the Fermi level denoted in terms of concentration for selected samples of the $x=0.038$ irradiated series.

Figure 6

(Color online) Thermopower as a function of concentration. Circles indicate measured data for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ samples, while squares show GaAs:Be data. The solid red line (convex) shows the calculation developed from both exchange and diffusion thermopower based on valence-band anticrossing, while the dashed curve shows only the anticrossing calculation without the empirically determined exchange contribution. The blue line shows a thermopower calculation for a system with valence-band transport.

Figure 7

(Color online) Mn acceptor level (red dashed line) with respect to III-V semiconductor band edges.