Infrared Probe of Itinerant Ferromagnetism in ${\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{M}\mathrm{n}}_x\mathrm{A}\mathrm{s}$

The doping and temperature dependence of the complex conductivity is determined for the ferromagnetic semiconductor ${\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{M}\mathrm{n}}_x\mathrm{A}\mathrm{s}$. A broad resonance develops with Mn doping at an energy scale of $\sim 200\mathrm{m}\mathrm{e}\mathrm{V}$, well within the GaAs band gap. Possible origins of this feature are explored in the context of a Mn induced impurity band and intervalence band transitions. From a sum rule analysis of the conductivity data the effective mass of the itinerant charge carriers is found to be at least a factor of 3 greater than what is expected for hole doped GaAs. In the ferromagnetic state a significant decrease in the effective mass is observed, demonstrating the role played by the heavy carriers in inducing ferromagnetism in this system.

Figure 1

Top panel: ${\sigma }_1(\omega )$ for all samples at $T=292\mathrm{K}$. The gray line is the conductivity of undoped GaAs. All Mn doped samples show a substantial broadening of the GaAs gap edge, likely due to As disorder. Ferromagnetic samples also show a broad resonance near $2000{\mathrm{c}\mathrm{m}}^{-1}$. The dashed line corresponds to ${\sigma }_1(\omega )$ for a nonmagnetic, very dilute Mn concentration sample, where the absorption band is due to electronic transitions between the valence band and Mn acceptor level [13]. Bottom panels: Both panels show ${\sigma }_1^m(\omega )$ for the $x=0.052$ sample at $T=292\mathrm{K}$. Two different methods of separating the intraband and interband conductivity are demonstrated, as described in the text. Dashed lines in the right panel correspond to Eq. (2) with ${\omega }_{p,1}^2=1.7\times {10}^7{\mathrm{c}\mathrm{m}}^{-2}$, ${\omega }_{o,1}=1900{\mathrm{c}\mathrm{m}}^{-1}$, ${\Gamma }_1=3200{\mathrm{c}\mathrm{m}}^{-1}$, ${\omega }_{p,2}^2=7\times {10}^6{\mathrm{c}\mathrm{m}}^{-2}$, ${\omega }_{o,2}=8000{\mathrm{c}\mathrm{m}}^{-1}$, ${\Gamma }_2=5000{\mathrm{c}\mathrm{m}}^{-1}$, while the thick line is determined from Eq. (2) with ${\omega }_{p,D}^2=5.1\times {10}^7{\mathrm{c}\mathrm{m}}^{-2}$, ${\omega }_{o,D}=0{\mathrm{c}\mathrm{m}}^{-1}$, ${\Gamma }_D=6000{\mathrm{c}\mathrm{m}}^{-1}$. The dashed line in the left panel is a single Lorentz oscillator [Eq. (2)] with ${\omega }_p^2=6\times {10}^7{\mathrm{c}\mathrm{m}}^{-2}$, ${\omega }_o=1675{\mathrm{c}\mathrm{m}}^{-1}$, $\Gamma =5050{\mathrm{c}\mathrm{m}}^{-1}$. The thick lines with shading underneath are different estimates of the intraband conductivity used to determine a likely range of the carrier mass.

Figure 2

Temperature dependence of ${\sigma }_1(\omega )$ for $x=0.052$ sample on a log scale. Left panel shows $T\ge T_C$, while the right panel displays $T\le T_C$. At temperatures above $T_C$ all the spectra cross near $900{\mathrm{c}\mathrm{m}}^{-1}$. In contrast, below $T_C$ no crossing is observed below $3000{\mathrm{c}\mathrm{m}}^{-1}$, indicating an overall increase in the low-$\omega$ spectral weight. Top left inset shows correlation between carrier density [Eq. (1)] at 292 K and $T_C$. Right inset demonstrates that the redistribution of spectral weight is confined to energies below $8000{\mathrm{c}\mathrm{m}}^{-1}$.

Figure 3

Change in $n/m^{*}$ below $T_C$ calculated using both the maximum and minimum intraband spectral weight (Fig. 1), and from simply integrating the entire ${\sigma }_1(\omega )$ spectrum to $4000{\mathrm{c}\mathrm{m}}^{-1}$, for the $x=0.052$ sample. Below $T_C$, the magnitude of $n/m^{*}$ increases strongly with decreasing temperature. This increase of spectral weight can be interpreted in terms of a lowering of the charge carrier effective mass in the ferromagnetic state. The strong increase in $n/m^{*}$ is observed in all samples, regardless of the method used to determine the intraband conductivity. Inset: Scaling relation between $\delta (n/m^{*})$, normalized to the value of $n/m^{*}$ at$T_C$, and the magnetization squared.