Observation of a blue shift in the optical response at the fundamental band gap in Ga${}_{1-x}$Mn${}_x$As

We report the observation of a sharp band-edge response in spectrally resolved differential reflectivity experiments on GaMnAs, in contrast to linear optical experiments in which large band-tail effects are known to dominate. The differential reflectivity response exhibits a blue shift relative to results in GaAs and LT-GaAs, consistent with the valence-band model of ferromagnetism. Our results demonstrate the utility of nonlinear optical techniques for studying the electronic structure of III-Mn-V diluted magnetic semiconductors.

Figure 1

(a) Schematic diagram of the pump probe apparatus. (b) Results of differential reflectivity experiments at a probe photon energy of 1.65 eV for SI GaAs (circles) and the 150-nm-thick GaMnAs sample (triangles). (c) Results of model calculations of differential reflectivity spectra using an effective mass model and a thermalized carrier distribution with a temperature of 80 K, separating contributions due to SF, BGR, FCA, and DIA. For the BGR curve, a small band edge shift of 13 meV was introduced by hand following Ref.38. For DIA, $\Delta \alpha$ was assumed to be proportional to the conduction-band density of states with an onset of absorption from the As${}_{\mathrm{Ga}}$ band at half the band-gap energy.

Figure 2

Results of spectrally resolved differential reflectivity experiments on (a) SI GaAs, (b) GaMnAs (150 nm thickness) (c) LT-GaAs and (d) GaMnAs (20 nm thickness). The band gap of SI-GaAs at 80 K (1.507 eV) is indicated by a vertical dashed line. The contour scale indicates the size (and sign) of $\Delta R/R_0$, which extends from $-1.0\%$ to $+1.0\%$ in (a) and from $-0.4\%$ to $0.4\%$ in (b)–(d). $\Delta R/R_0$ is positive (dark grey, red online) or zero (light grey, green online), except for a rapid negative response (black, blue online) below 1.507 eV in (a) and around 1.507 eV in (c).

Figure 3

The differential reflectivity response at a probe pulse delay of 500 ps is shown for (a) SI-GaAs (circles) and (b) the two GaMnAs samples (150 nm thickness, triangles; 20 nm thickness, circles). The calculated differential reflectivity signals are also shown (solid curves), where (a) the full optically injected carrier density is included, and the $\Delta R/R_0$ includes only SF; and (b) the fraction of carriers trapped into the As${}_{\mathrm{Ga}}$ band is 95$\%$, and SF, DIA, and FCA were included. For the calculated curve in (b), the magnitude of the FCA contribution has been enhanced to account for the influence of defects, and the Moss-Burstein effect has been approximated by a rigid shift of the band gap of 55 meV. (c) Contributions to the $\Delta R/R_0$ response for SI-GaAs (left) and p-type LT-GaAs (right). The arrows indicate optical transitions induced by the probe pulse following excitation by the pump.