Spin-Flip Raman Scattering by Carriers in PbTe, PbSe, and Pbs

Because of spin-orbit coupling, an incident light wave can flip the effective spin of carriers in a semiconductor. In the presence of a strong dc magnetic field $H$, the frequency shift for the scattered light due to this process corresponds to the intraband excitation energy $g_{\mathrm{eff}}\beta H$. Using the band-edge structure of PbTe, PbSe, and PbS at the $L$ point in the Brillouin zone, the spin-flip Raman cross sections are calculated for both electrons and holes in these materials. Scattering amplitudes, which can be assumed to be independent of the magnetic field, are calculated by considering six bands near the band gap. The predictions of a simple two-band model including the spin-orbit effect are also analyzed to try to relate the scattering amplitudes directly to energy gaps and effective masses. Theoretical values for the cross sections in PbTe and PbSe for a C${\mathrm{O}}_2$ laser are comparable to those in InSb. The nature of the variation of these cross sections with the carrier concentration $n$ and the magnetic field $H$ is discussed.