Electronic structure near the Fermi level in the ferromagnetic semiconductor GaMnAs studied by ultrafast time-resolved light-induced reflectivity measurements

Clarification of the electronic structure near the Fermi level is important in understanding the origin of ferromagnetism in the prototypical ferromagnetic semiconductor GaMnAs. Here, we perform ultrafast transient reflectivity spectra measurement, which is a powerful tool for selective detection of absorption edges in GaMnAs. The results show that the Fermi level of GaMnAs exists in the band gap. By using the Kramers-Kronig relation, we find the Mn-induced electronic states around the Fermi level, confirming that the ferromagnetism is stabilized by spin-polarized impurity-band holes.

Figure 1

(a), (b) Schematic illustration of the band structures of (a) GaAs and (b) GaMnAs with the optical transitions from the VB to the CB (black arrows) and from the IB to the CB (red arrow). The black dashed, red dashed-dotted, and black dashed-dotted horizontal lines represent the energy of the bottom of the CB, Fermi level, and the top of the VB, respectively. The gray region represents the IB region. (c), (e) Schematic absorption spectra; energy spectra of α (black solid curve), ${\alpha }_{\mathrm{BGR}}^{\prime }$ (green dotted curve), and ${\alpha }_{\mathrm{BF},\mathrm{BGR}}^{\prime }$ (orange dashed curve) associated with the optical transitions (c) from the VB to the CB and (e) from the IB to the CB. (d), (f) Calculated $\mathrm{\Delta }R/R$ spectrum associated with the optical transitions (d) from the VB to the CB and (f) from the IB to the CB.

Figure 2

(a), (b) Time evolution of $\mathrm{\Delta }R/R$ (solid curves) as a function of the photon energy $E$ measured at 5 K (a) for SI GaAs and (b) for $\mathrm{G}{\mathrm{a}}_{0.94}\mathrm{M}{\mathrm{n}}_{0.06}\mathrm{As}$. The estimated $E_{\mathrm{g}}$ and $E_{\mathrm{F}}$ positions are indicated by the black and red arrows.

Figure 3

(a) Absorption (α) spectra derived from the analysis of the TRS for $\mathrm{G}{\mathrm{a}}_{0.94}\mathrm{M}{\mathrm{n}}_{0.06}\mathrm{As}$ (black curve). This is composed of the optical transitions from the IB to the CB ($E>E_{\mathrm{F}}$) and from the VB to the CB ($E>E_{\mathrm{g}}$). The absorption spectrum when assuming that only the BGR occurs is shown by the (green) dotted curve. It is changed to the one shown by the (orange) dashed curve due to the BF in addition to the BGR. (b) Δα spectrum obtained for the $\mathrm{G}{\mathrm{a}}_{0.94}\mathrm{M}{\mathrm{n}}_{0.06}\mathrm{As}$ film. (c) $\mathrm{\Delta }R/R$ spectra measured at 5 K for the SI GaAs substrate and for the $\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$ films ($x=0.1\%$, 1%, 3%, and 6%) at $t=166\mathrm{ps}$ (plotted data). The solid curves are the fitting curves.

Figure 4

$x$ dependence of $E_{\mathrm{diff}}$ (red diamonds). The blue solid circles are the values reported in Ref. [4].