Electron spin dephasing in Mn-based II-VI diluted magnetic semiconductors

In various manganese-based II-VI diluted magnetic semiconductors and their quantum structures, the measured variations of electron spin dephasing time in an external magnetic field are conflicting with the most advanced spin relaxation theory based on quantum kinetic equations. We demonstrate, by time-resolved optical spin beat measurements performed on high-mobility $n$-doped CdMnTe quantum wells, that these contradictions are resolved if one takes into account the electron spin dephasing induced by laser heating of the manganese spins. We then provide a test of the spin relaxation theory in Mn-based quantum wells by a careful comparison with existing data, including our measurements. It turns out that the theory systematically underestimates the relaxation rates by a factor of 5.

Figure 1

Selected data on spin dephasing time taken from literature and present work: ($\square$) Ref. 11, ($\circ$) Ref. 7, ($▾$) Ref. 12, ($▴$) Ref. 8, ($⧫$) this work. The blue and green solid lines are calculated with the model of Ref. 15 with parameters corresponding to the experimental data ($⧫$ and $▾$, respectively).

Figure 2

Left panel: Evolution of the Fourier power spectra of the time-resolved Kerr rotation as a function of magnetic field, in conditions where the electronlike and Mn-like modes cross each other. The spectrum corresponding to the anticrossing is highlighted in green. Right panel: Frequencies and relaxation times of the two mixed modes ${\omega }_{\pm }$ in the region of the anticrossing. The green diamonds represent the electron spin relaxation time corrected from the effect of dynamic coupling with ${\text{Mn}}^{2+}$ spins (see text).

Figure 3

Magnetic field dependencies of electron precession frequency and spin relaxation time measured in samples A (left panel) and B (right panel), for different powers and helium bath temperatures. Solid lines in (a) and (b) are fits to ${\omega }_e$ with a linear Zeeman term plus a Brillouin function. Solid lines in (c) and (d) are fits to ${\tau }_e$ with the model of inhomogeneous heating described in the text. The inset shows how the variance of the temperature distribution $\Delta T$ and the effective ${\text{Mn}}^{2+}$ temperature $T_{\text{eff}}$, deduced from the fits, correlate when the laser power changes.

Figure 4

Left panel: Normalized relaxation rates (see text) vs power for the three studied samples. Right panel: Experimental (solid symbols), including data taken from literature, and theoretical (solid line) normalized relaxation rates. The dashed line corresponds to the theoretical relaxation rates multiplied by a factor of 5.