Evidence for spin splitting in In x Ga 1-x As/In 0.52 Al 0.48 As heterostructures as B-->0

TLDR: In this paper, the splitting in zero magnetic field between the up-and down-spin electrons in a two-dimensional electron gas is obtained for a series of three different modulation-doped heterostructures with high electron densities.

Abstract: The splitting in zero magnetic field between the up- and down-spin electrons in a two-dimensional electron gas is obtained for a series of three different ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}/{\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ modulation-doped heterostructures with high electron densities [${n}_{s}\ensuremath{\sim}(1.5\ensuremath{-}1.8)\ifmmode\times\else\texttimes\fi{}{10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$]. We have observed a characteristic beating modulation in the amplitude of the Shubnikov-de Haas oscillations in this system and up to six nodes have been measured in the Shubnikov-de Haas data for magnetic fields in the range $0.15 \mathrm{T}lBl1.0 \mathrm{T}$. Analysis of these data indicates that one subband is primarily occupied and the two beating frequencies arise from a spin splitting of the lowest subband. A spin splitting of 1.5-2.5 meV as $B\ensuremath{\rightarrow}0$ is deduced from the data. For magnetic fields applied at an angle $\ensuremath{\theta}$ to the interface, the beat positions scale as $cos\ensuremath{\theta}$ for small angles but increase steeply after a critical angle.