Excitonic enhancement of spin relaxation in diluted magnetic semiconductor quantum wells

We performed pump-probe magneto-optical Kerr spectroscopy to explore the role of excitonic effects on the electron and hole spin relaxation in ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$-based quantum well structures. Particularly, important information is obtained from detailed interpretation of the temperature and wavelength dependence of the observed transient magneto-optics in specially engineered structures. In manganese-rich wells the electron spin relaxation is found to be strongly enhanced in the exciton due to the increased mass of the bound electron-hole pair, in agreement with earlier predictions. An even stronger enhancement of the relaxation time is found for the hole spin, which is explained by the additional mixing of heavy-hole and light-hole states in the bound state. In structures where Mn is confined to the barrier region, a different behavior is observed, indicative for a competition of various contributions.

Figure 1

Spectrum of the magneto-optical signal and its temperature dependence at zero field: Panel (a) shows both rotation (open circles) and ellipticity (closed squares) for the single quantum well containing 0.5% Mn (sample A) as measured at $T=5\mathrm{K}$, and in panel (b) the temperature dependence of the maximum in the rotation spectrum is shown. Panel (c) shows the magneto-optical spectrum for a multiple quantum well (sample B) with 4% Mn in the well at a temperature of 5 (open circles), 80 (closed squares), and $160\mathrm{K}$ (open diamonds). In panel (d) the temperature dependence of the extrema in the magneto-optical spectrum of the multiple quantum well is shown, with black squares denoting maxima and gray triangles denoting minima.

Figure 2

(a) Magneto-optical signal as a function of the time after the arrival of the pump pulse for sample B (the multiple quantum well containing 4% Mn) at $5\mathrm{K}$. Open gray squares represent a zero-field measurement, whereas closed circles correspond to measurements under an applied magnetic field of $0.65\mathrm{T}$. The solid line is the nonoscillating part of a fit of the in-field measurement with one exponentially decaying component for the holes and one oscillating component with an exponentially decaying amplitude for the electrons, Eq. (1). (b) Electron and hole spin relaxation times as a function of the applied transverse magnetic field for the same sample, also at $5\mathrm{K}$.

Figure 3

(a) Electron and hole spin relaxation times as a function of laser fluence used for the spin-selective excitation for the multiple 4% Mn quantum well at $5\mathrm{K}$ (sample B). (b) The fluence dependence of the electron $g$ factor for the same sample, again at $5\mathrm{K}$. The inset shows for a comparison the temperature dependence of the $g$ factor. All measurements were performed under the application of an in-plane magnetic field of $0.8\mathrm{T}$.

Figure 4

Electron (a) and hole (b) spin relaxation time, measured at $0.8\mathrm{T}$, as well as the electron-hole recombination time at zero field (c) as a function of temperature for the 4% Mn multiple quantum well (sample B).

Figure 5

Electron spin relaxation time as a function of temperature for several quantum well structures. Samples are denoted by two numbers of which the first denotes the manganese content inside the well, whereas the second indicates the amount of manganese in the barrier. Furthermore, A and B indicate samples A and B, respectively. The temperature behavior of the spin relaxation in bulk CdTe is also given for comparison. The lines are only meant as guides to the eye.

Figure 6

(a) The magneto-optical signal as a function of the time after excitation at excitation energies of 1.709 (triangles), 1.723 (circles), and $1.731\mathrm{eV}$ (squares) for a 4% Mn multiple quantum well at an applied magnetic field of $0.8\mathrm{T}$ at $5\mathrm{K}$. The drawn lines are fits with a superposition of two sine functions with damping amplitude and two simple exponentials superimposed. The offsets were added in order to spatially separate the different graphs. (b) The spectral dependence of the magneto-optical signal at a constant delay time of $3\mathrm{ps}$ in the absence of a magnetic field. The explicit time dependencies were measured at the extrema of this spectrum. (c) The amplitudes of the different constituents to the magneto-optical signal as obtained from the fits in panel (a). Open circles indicate free electrons, whereas full squares denote excitons. The lines are guides to the eye.

Figure 7

Electron spin relaxation rates for $8\text{−}\mathrm{nm}$-thick quantum wells containing various concentrations of manganese both at low temperatures $\left(5\mathrm{K}\right)$ and at room temperature. The lines represent the calculations by Bastard and Chang (Ref. 22), corrected for antiferromagnetic interactions between manganese ions, following the expression proposed by Gaj et al. (Ref. 23). Dashed lines indicate the parameter-free results, whereas solid lines represent the results after application of a global scaling parameter of 1.8. For comparison also a data point at $5\mathrm{K}$ using a higher excitation energy is given.