Spin Noise Spectroscopy in GaAs (110) Quantum Wells: Access to Intrinsic Spin Lifetimes and Equilibrium Electron Dynamics

In this Letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The nondemolition measurement technique gives access to the otherwise concealed intrinsic, low temperature electron spin relaxation time of $n$-doped GaAs (110) quantum wells and to the corresponding low temperature anisotropic spin relaxation. The Brownian motion of the electrons within the spin noise probe laser spot becomes manifest in a modification of the spin noise line width. Thereby, the spatially resolved observation of the stochastic spin polarization uniquely allows to study electron dynamics at equilibrium conditions with a vanishing total momentum of the electron system.

Figure 1

Spin decay rate ${\gamma }_z=1/{\tau }_z$ and relative integrated spin noise power at $T=20\mathrm{K}$ as a function of the laser wavelength. Solid line: Integrated spin noise power according to model [9] (details in text). The inset shows a typical spin noise spectrum.

Figure 2

Absolute integrated spin noise power as a function of laser wavelength and temperature, measured (left panel) and calculated (right panel, details in text).

Figure 3

Effective spin decay rate ${\gamma }_{\mathrm{eff}}=1/{\tau }_{\mathrm{eff}}$ ($T=20\mathrm{K}$) as a function of the applied magnetic field with fits according to Eq. (1). Inset: Anisotropy determined by the fits as function of laser wavelength ($T=20\mathrm{K}$). Open symbols indicate measurements with an enlarged laser spot in which time of flight broadening is strongly reduced.

Figure 4

Effective spin decay rate ${\gamma }_z=1/{\tau }_z$ ($T=20\mathrm{K}$) as a function of sample position $z$ for a laser wavelength of $\lambda =815\mathrm{nm}$ (squares), $\lambda =816\mathrm{nm}$ (circles) and $\lambda =816\mathrm{nm}$ with doubled laser power (triangles). The $z=0$ position is set to the maxima of the measured curves. The lines show calculations according to the model given by Eq. (2) for $D=100{\mathrm{cm}}^2/\mathrm{s}$ (solid line), $200{\mathrm{cm}}^2/\mathrm{s}$ (dash-dotted line), $400{\mathrm{cm}}^2/\mathrm{s}$ (dashed line) and $1000{\mathrm{cm}}^2/\mathrm{s}$ (dotted line).