Spin Manipulation of Free Two-Dimensional Electrons in $\mathrm{Si}/\mathrm{SiGe}$ Quantum Wells

Understanding the mechanisms controlling the spin coherence of electrons in semiconductors is essential for designing structures for quantum computing applications. Using a pulsed electron paramagnetic resonance spectrometer, we measure spin echoes and deduce a spin coherence time ($T_2$) of up to $3\mu \mathrm{s}$ for an ensemble of free two-dimensional electrons confined in a $\mathrm{Si}/\mathrm{SiGe}$ quantum well. The decoherence can be understood in terms of momentum scattering causing fluctuating effective Rashba fields. Further confining the electrons into a nondegenerate (other than spin) ground state of a quantum dot can be expected to eliminate this decoherence mechanism.

Figure 1

(a) Oscillating shape of the in-phase and quadrature echo signals in a two-pulse spin-echo experiment after the 30 K anneal at $\theta =0°$. Only the decaying portion of the echo shape is shown with the echo center at $0.1\mu \mathrm{s}$ (the echo rise and early decay are obscured by the cavity ring down and detector blanking). (b) Fourier-transform EPR lines for two interpulse delays, $\tau$. The integrated intensity of these FT-EPR lines versus delay is used to measure $T_2$.

Figure 2

(a) Two-pulse spin-echo intensity versus total delay time ($2\tau$), and (b) FID intensity in the inversion-recovery experiment as a function of interpulse delay $T$, for the as-illuminated (▪) and after 30 K anneal (●) with $\theta =0°$. The exponential fits give $T_2$ in (a) and $T_1$ in (b).

Figure 3

Electron spin relaxation times, $T_1$ (▪) and $T_2$ (●), of the 2D electron system (after the 30 K anneal) as a function of the angle ($\theta$) between the external magnetic field, $B_0$, and the normal to the 2D electron system. The lines connecting experimental points are guides to the eye. The multiple values shown for $T_1$ at 0° and $T_2$ at 90° were obtained in different experimental runs, showing about 10% variations.