Spin noise of localized electrons in CdTe/CdMgTe quantum well

TL;DR

This work uses spin noise spectroscopy to disentangle spin dephasing and relaxation of donor-bound electrons in a CdTe/CdMgTe quantum well. By analyzing a clearly resolved satellite peak at $\bar{\delta}_e/2\pi\approx27$ MHz and a Larmor peak, the authors separate hyperfine-induced dephasing from temperature-activated spin relaxation, attributing the latter to donor-to-conduction-band hopping and spin exchange among donors. The study extracts quantitative values for the average nuclear-field fluctuation $\bar{\delta}_e$, its dispersion $\alpha$, spin-relaxation rate $\gamma$, and donor density $N_d\approx 10^{10}$ cm$^{-2}$, and explains the absence of motional narrowing in this QW due to strong impurity-band broadening. The results connect SN spectral features to microscopic processes and provide a framework to estimate donor density from SN measurements in quantum wells.

Abstract

The spin dynamics of localized electrons in bulk semiconductors is governed by the interplay of effective nuclear field fluctuations, spin exchange between electrons, and spin transitions into the conduction band. Using spin noise spectroscopy, we reveal this interplay for donor-bound electrons in a CdTe/CdMgTe quantum well and spectrally separate electron spin relaxation and dephasing in zero magnetic field. We identify a specific regime of the electron spin dynamics, where temperature-induced activation of spin-independent hopping leads to a monotonic acceleration of electron spin relaxation. This behavior contrasts with bulk CdTe crystals, where the motional narrowing effect is observed. We attribute this difference to the significantly larger inhomogeneous broadening of the donor-related trion resonance in our quantum well compared to bulk samples. The theoretical analysis of the spin noise power and the strength of the spin exchange interaction provides the estimation of the donor concentration in our unintentionally doped structure.

Figures (7)

• Figure 1: (a) PL and reflectivity spectra of the QW, with donor-bound exciton, negative trion, and exciton identified. (b) Artistic view of various spin species localized in the QW: donor-bound electrons in the QW center and close to the interface (blue), as well as electrons localized at the interface roughness (magenta). The latter, as well as the electrons localized on donors close to the QW edge have the wave-function different from the spherical one, characterized by the bulk Bohr radius. Each of the spin fluctuations $\delta\bm S$ precesses around an effective field $\bm\Omega_{N,i}$ of the underlying nuclei, . (c) Sketch of the excited states energy levels. Red dashed line shows the probe laser energy, $E_p$, tuned to the bottom of the D0X energy distribution (blue band), well below $X^-$ band (magenta). Yellow lines schematize the mechanisms leading to the spin loss within the probed energy band: electron jumps via conduction band (curved arrow) and electron spin exchange within donor band (straight arrows).
• Figure 2: Sketch of the experimental setup. Four regions identified by colour show the laser excitation part (magenta), the split LO and probe beam paths (green and yellow, respectively), and the detection part (blue). The latter features optical mixing of the spin-flip Raman scattered light and the LO and its detection using the optical bridge. Legend: PBS $\equiv$ Polarizing beam splitter; BS $\equiv$ Beam splitter; VPR $\equiv$ Variable phase retarder; $\lambda/2$$\equiv$ Half-wave plate. Focal lengths are given in millimetres.
• Figure 3: SN spectrum measured at $B=0$, from which the spectrum measured under identical conditions at $B=16$ mT is substracted. Three main features are identified in this differential spectrum: the relaxational peak characterized by the width $\gamma/2\pi=1/T_1$, the satellite peak centred at frequency $\bar{\delta}_e/2\pi$, and the peak at Larmor frequency with the width depending on both $\bar{\delta}_e$ and $\gamma$. Inset shows low-frequency region in logarithmic scale. Red symbols show the experimental data, black solid lines are the results of the fit within the model of Section \ref{['sec:model']}. Probe energy $E_p=1.616$ eV.
• Figure 4: Differential SN spectra measured at two different probe energies, $E_p=1.616$ eV and $E_p=1.617$ eV. $P=400$ µW, $T=3.75$ K. At higher energy relaxational, satellite and Larmor peaks broaden significantly.
• Figure 5: Probe energy dependence of the SN: Area of the Larmor peak (brown circles, left axis) and its FWHM (blue squares, right axis) as a functions of the probe energy. PL spectrum is also shown for easier identification of the optical resonances. Green and pink vertical lines point the probe energies corresponding to the spectra shown in Fig. \ref{['fig:Fig_WL_spectra']}.