Two-photon spin injection in semiconductors

A comparison is made between the degree of spin polarization of electrons excited by one- and two-photon absorption of circularly polarized light in bulk zinc-blende semiconductors. Time- and polarization-resolved experiments in (001)-oriented GaAs reveal an initial degree of spin polarization of 49% for both one- and two-photon spin injection at wavelengths of 775 and 1550 nm, in agreement with theory. The macroscopic symmetry and microscopic theory for two-photon spin injection are reviewed, and the latter is generalized to account for spin-splitting of the bands. The degree of spin polarization of one- and two-photon optical orientation need not be equal, as shown by calculations of spectra for GaAs, InP, GaSb, InSb, and ZnSe using a $14\ifmmode\times\else\texttimes\fi{}14\phantom{\rule{0.3em}{0ex}}\mathbf{k}∙\mathbf{p}$ Hamiltonian including remote band effects. By including the higher conduction bands in the calculation, cubic anisotropy and the role of allowed-allowed transitions can be investigated. The allowed-allowed transitions do not conserve angular momentum and can cause a high degree of spin polarization close to the band edge; a value of 78% is calculated in GaSb, but by varying the material parameters it could be as high as 100%. The selection rules for spin injection from allowed-allowed transitions are presented, and interband spin-orbit coupling is found to play an important role.