Strain-induced spin relaxation anisotropy in symmetric (001)-oriented GaAs quantum wells

We show experimentally, using spin quantum beat spectroscopy, that strain applied to an undoped symmetric (001) GaAs/AlGaAs multiple quantum well causes an in-plane anisotropy of the spin-relaxation rate ${\Gamma }^s$, but leaves the electron Landé $g$ factor isotropic. The spin-relaxation-rate anisotropy gives a direct measure of the bulk inversion asymmetry and the strain contributions to the conduction-band spin splitting. The comparison of the measured strain-splitting coefficient $C_3$ for the quantum well with the value for bulk GaAs suggests a dependence on electron quantum confinement. The isotropic $g$ factor implies a symmetric conduction electron wave function, whereas the anisotropic spin-relaxation rate requires a nonzero expectation value of the valence-band potential gradient on the conduction-band states. Therefore, the experiment suggests that strain generates an effective valence-band potential gradient, while the conduction-band potential remains symmetrical to a good approximation.

Figure 1

A typical decay curve (open circles) with a 5-T magnetic field oriented at $\theta ={90}^{\circ }$, at a temperature of 180 K and an applied strain of ${\epsilon }_{xy}=0.0021$. The solid curve is a fit of $A·\cos \left({\omega }_{Lt}\right)e^{-{\Gamma }^{s}t}$, as discussed in the text.

Figure 2

Dependence of the electron $g$ factor (open circles) and the spin-relaxation rate (solid circles) on the magnetic-field orientation. (a) Zero applied strain and (b) a shear strain ${\epsilon }_{xy}=0.0021$. The insets show the orientation of the sample with respect to the magnetic field $B$. In both plots, the insets indicate the compressive strain along (1$\overline{1}$0) and tensile strain along (110).

Figure 3

Variation with strain ${\epsilon }_{xy}$ of (a) $g_{xy}$ (solid circles) and $g_{xx}$ (open circles) and (b) $\eta$ and $\eta /\beta$. The gradient of linear fit (line) to the points in (b) gives $C_3/\hslash =4.7\pm 1.1\times {10}^5$ ms${}^{-1}$.