Near-Resonance Spontaneous-Spin-Flip Light Scattering in InSb

The properties of near-resonance spontaneous-spin-flip Raman scattering in InSb have been studied both experimentally using a 5-6-\ensuremath{\mu}m CO laser and theoretically. The polarization selection rules for both linearly and circularly polarized light have been investigated. The experimental results are in good agreement with the theoretical predictions. The resonance enhancement of the spontaneous-scattering cross section for an input photon energy near the InSb energy gap has been studied as a function of input photon energy and magnetic field. Good agreement is found between the experimental data and a theoretical treatment which includes both the effects of varying population factors and the ${k}_{z}$ dependence of the spin-flip cross section. The linewidth and, where it could be resolved, the line shape of spontaneous-spin-flip Raman scattering was studied experimentally as a function of electron concentration (1-3 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), temperature (2-50 K), and magnetic field (20-80 kG). Two different geometries were studied. In both geometries, the incident photon propagated normal to the magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. In one geometry the scattered light was collected colinear with the incident light ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=0$), while in the other geometry it was collected along $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ at right angles to the incident light ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\ne}0$). The linewidth in the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=0$ geometry was very narrow (0.2-0.4 ${\mathrm{cm}}^{\ensuremath{-}1}$) and almost independent of magnetic field. The linewidth in the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\ne}0$ geometry was strongly dependent on magnetic field. It varied from a maximum of 6.5 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 21 kG to a minimum of 0.2-0.3 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 80.5 kG. The linewidth in the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=0$ geometry was almost independent of temperature, while the linewidth in the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\ne}0$ geometry broadened appreciably at higher temperatures. These features of the spin-flip Raman-scattering line shape are shown to be inconsistent with the simplest spin-relaxation theory of the line shape that includes the inhomogeneous broadening due to the nonparabolicity of the InSb conduction band (present in both geometries) and the Doppler shift (in the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\ne}0$ geometry only). A theory which includes orbital collisions that alter the ${k}_{z}$ state of the spin excitation is considered and is found to give results that are in good agreement with the experiment.