Tuning of the spin-orbit interaction in two-dimensional GaAs holes via strain

We report direct measurements of the spin-orbit interaction-induced spin splitting in a modulation-doped GaAs two-dimensional hole system as a function of anisotropic, in-plane strain. The change in spin-subband densities reveals a remarkably strong dependence of the spin splitting on strain, with up to about 20% enhancement of the splitting upon the application of only about $2\times {10}^{-4}$ strain. The results are in very good agreement with our numerical calculations of the strain-induced spin splitting.

Figure 1

(Color online) (a) Shubnikov–de Haas oscillations, measured in the $\left[01\overline{1}\right]$ direction, for seven different piezo voltages in steps of $100\mathrm{V}$. The traces are offset vertically for clarity. (b) Normalized Fourier power spectra of the oscillations in the range $0.2⩽B⩽2\mathrm{T}$. The positions of the peaks $f_{-}$ and $f_{+}$ correspond to the densities of the minority- and majority-spin subbands, while the peak labeled $f_{\mathrm{tot}}$ gives the total 2D hole density. (c) Experimental setup. The poling direction for the piezo is along $\left[01\overline{1}\right]$. (d) Spin splitting versus applied strain. The black squares $(\Delta f=f_{+}-f_{-})$ and the red circles $(\Delta f=f_{\mathrm{tot}}-2f_{-})$ are from two different methods used to determine the spin splitting.

Figure 2

(Color online) The black squares $(\Delta f=f_{+}-f_{-})$ and the red circles $(\Delta f=f_{\mathrm{tot}}-2f_{-})$ are the experimentally measured spin splitting. The solid curves are $\Delta f$ determined from the calculated magneto-oscillations. The three different densities, from lowest to highest, are obtained at front-gate biases of 0.3, 0, and $-0.7\mathrm{V}$, respectively.