Long spin relaxation time of holes in InGaAs/GaAs quantum wells probed by cyclotron resonance spectroscopy

In this paper, we report on a long, ms range, hole spin relaxation time in InGaAs/GaAs quantum wells probed by cyclotron resonance spectroscopy in pulsed magnetic fields. In our experiments, we found strong hysteresis in the spectral weights of cyclotron resonance absorption lines when rapidly changing magnetic field is used for the experiment. The hysteresis vanishes when a much slower changing magnetic field is used. We attribute this behavior to a long energy relaxation time between the two lowest spin-split hole Landau levels, i.e., a long hole spin relaxation time. We also present transition frequencies calculated using a $4\times 4$ Luttinger Hamiltonian, which confirm our findings.

Figure 1

Magnetic-field profiles for the two coils used: Type 1 has a 12 ms rise time and $\sim$75 ms total pulse duration, and type 2 has a 34 ms rise time and 150 ms total pulse duration.[14]

Figure 2

Cyclotron-resonance absorption spectra, taken at $T=4.2$ K, with excitation wavelength $\lambda =75$ $\mu$m and using (a) fast coil type 1 and (b) slow coil type 2. Dotted curves indicate data taken for rising magnetic field, solid lines for decreasing field. The inset shows the calculated relative position of the two lowest Landau levels; arrows indicate transitions corresponding to the CR lines 1 and 2.

Figure 3

Transition rate $1/\tau$ between the states $0s_1$ and $3a_1$ assisted by longitudinal acoustic phonons as a function of magnetic field for the Luttinger parameter (a) $\kappa =2.01$ and (b) $\kappa =1.2$. Arrows indicate the magnetic field values where the transitions 1 and 2 occur.