Spin precession of light holes in the spin-orbit field of strained GaAs nanowires

We have used a polarized spatially resolved microluminescence technique to investigate photocarrier charge and spin transport at 6 K in a GaAs nanowire (NW; n-type doping level $\ensuremath{\approx}{10}¹⁷\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). Because of the difference in expansion coefficients of the NW and of its ${\mathrm{SiO}}₂$ substrate, the NW is under strain, as revealed by the splitting between light- and heavy-hole emissions in the luminescence intensity spectrum. Light valence levels lie above the heavy valence ones, which is attributed as being caused by a tensile strain along both the axial and the lateral directions of the NW, equivalent to a compressive strain in the direction of light excitation. The symmetry group of the perturbed nanowire is then lowered to ${C}_2v$. No spin polarization can be evidenced for the heavy valence levels. The electron spin polarization decays up to a distance of $5\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{m}$ from the excitation spot, because of spin relaxation, and stays constant for larger distances because of the increased value of the drift velocity. Remarkably, the light-hole spin polarization exhibits damped spatial oscillations over as much as $5\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{m}$. Analysis of the effect of strain on valence states shows that these oscillations are caused by the spin-orbit interaction in the light valence level. It is found that, for the ${C}_2v$ point group, the corresponding Hamiltonian is linear in momentum. This spin-orbit interaction causes coherent oscillations rather than a spin relaxation process since transport essentially has a drift character in the internal electric field. The equivalent effective magnetic field induced by spin-orbit interaction and strain is, taking a light-hole $g$ factor of 1, of the order of $60\phantom{\rule{0.28em}{0ex}}\mathrm{mT}$.