Kerr effect induced by exchange interaction of electrons separated by a tunnel barrier in a double quantum well

TL;DR

The paper investigates Kerr-effect signals in a CdTe/Cd_{0.98}Mn_{0.02}Te double quantum well with a 5 ML separator, showing that interwell electron exchange couples exciton spins in the narrow well to the wide-well electron spin ensemble. A quantitative model incorporating exchange, precession, and sample reflectivity reproduces the observed Kerr spectra and extracts the interwell exchange constant, δ_e, from fits. Theoretical estimates yield δ_e ≈ (2.1 ± 0.3) × 10^{-15} eV cm^2, while experimental fits give δ_e^{exp} ≈ 0.9 × 10^{-15} eV cm^2, supporting the exchange mechanism. Overall, the work demonstrates that resonant Kerr-rotation spectroscopy can probe interwell spin interactions in tunnel-coupled semiconductor heterostructures and clarifies the role of barrier-mediated exchange in spin dynamics.

Abstract

In a structure with two tunnel-coupled quantum wells of different widths, the spin dynamics resulting from resonant pulsed optical pumping of the narrow-well exciton includes the wide-well electron magnetization dynamics. Our analysis shows that the effect is driven by electron exchange between narrow-well excitons and spin-polarized electrons in the wide well. A theoretical model of the spin Kerr effect has been developed accounting for the interwell electron spin exchange. In the studied double-well structure with CdTe and Cd$_{0.98}$Mn$_{0.02}$Te quantum wells and a well-separating barrier thickness of 5 monolayers (1.6 nm), the model accurately describes the experimental results and allows us to estimate the interwell electron exchange constant as $δ_{e} \approx 0.9\times10^{-15}~\textrm{eV}~\textrm{cm}^{2}$.

Figures (10)

• Figure 1: Schematic energy diagram of the studied DQW.
• Figure 2: The reflection spectrum of the studied structure with DQW, measured in a zero magnetic field at temperature of $T=5$ K (solid line). The vertical arrows show the excitons resonant energies $X_{\textrm{WQW}}$ and $X_{\textrm{NQW}}$ in the wide and narrow wells, the region of excited states in the wide well is highlighted by a dashed rectangle. An incandescent lamp was used as the light source. The spectrum is recorded using a 0.5-m spectrometer interfaced with a charge-coupled-device detector. The dashed curve represents the reflection spectrum calculated using the Eq. (\ref{['eq:R']}).
• Figure 3: The scheme of experimental setup for the time-resolved spin Kerr effect measurement in pump-probe mode. Ti:Sa is the tunable Ti:Sa laser, producing 1.5 ps pulses with the repetition rate of 80 MHz, GP is the Glan prism, $\lambda/2$ and $\lambda/4$ are the half- and quarter-wave plates, WP is the Wollaston prism, BPD is the balanced photodetector, PEM1 and PEM2 are the photoelastic modulators, operating with frequencies $f_1=42$ kHz and $f_2=34$ kHz, the block ($f_1$-$f_2$) forms the reference signal for the lock-in detector with the differencial frequency ($f_1$-$f_2$), PC is the personal computer, $B$ is the external magnetic field. Electrical signals $U_1\propto I_1$, $U_2\propto I_2$.
• Figure 4: The Kerr rotation signal (black line) measured in the NQW in a transverse magnetic field (Voigt geometry) $B=0.54$ T at $T=5$ K, and its approximation by two components (red lines) shifted vertically for clarity. The pumping quantum energy is $\hbar\omega=1.656$ eV.
• Figure 5: Spectral dependence of the amplitude of oscillations of the Kerr effect fast component occurring under resonant pumping of exciton in Cd$_{0.98}$Mn$_{0.02}$Te QW in a magnetic field $B=0.54$ T in Voigt geometry at $T=5$ K. Filled circles are the experimental data, solid curve is the result of calculation.