Zero-magnetic-field spin splittings inAlxGa1−xAs/GaAs heterojunctions

The observation of zero-magnetic-field spin splitting of the lowest electron subband in an ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ As/ GaAs heterojunction, detected as a beating pattern in the Shubnikov–de Haas oscillations, is reported. The observed effect is induced by a combination of the bulk ${\mathrm{k}}^3$ term, ascribed to the inversion asymmetry of the host crystal and the spin-orbit Rashba term, ${\mathrm{H}}_{\mathrm{so}}$ =α(σ×k)⋅z, introduced by the electric field at the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ As/GaAs interface. The magnitude of the spin splitting depends on both the built-in electric field and the electron concentration in the two-dimensional electron gas.