Softening of spin resonance at low temperature in $p$-doped ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ quantum wells

Time-domain spin resonances in $p$-doped CdMnTe quantum wells have been studied via time-resolved magneto-optical Kerr rotation. The resonances related to quantum well electrons Mn and electrons excited in the substrate are identified. An additional spin resonance which shows an unusual temperature dependence is detected in one of the samples. The corresponding frequency tends to zero when approaching the Curie temperature. This “soft” spin precession mode has been studied as a function of magnetic field, temperature, magnetic field orientation, and optical excitation density. Its origin is discussed in the framework of the existing collective spin excitation model.

Figure 1

(a) Time-resolved Kerr rotation in the M921a sample detected for different temperatures, photon energy $1.655\mathrm{eV}$. The slowing down of the oscillations is apparent. The variation of the signal amplitude versus photon energy (inset) indicate the signal is related to the QW. (b) Fourier spectra in the low frequency domain obtained for the three samples at $T=10\mathrm{K}$ (M921a, M952) and $T=15\mathrm{K}$ (M921b), excitation at $1.638\mathrm{eV}$. The two temperature independent resonances (Mn ions and substrate electrons) and the “soft” temperature dependent mode can be distinguished.

Figure 2

Kerr rotation in M921b at short delays, $B=5\mathrm{T}$. The rapid oscillations are related to the precession of the electrons in Mn exchange potential. Inset: The precession frequency versus magnetic field (open circles) is fitted with a modified Brillouin function at $2.4\mathrm{K}$ for lattice temperature (solid line).

Figure 3

“Soft” mode frequency as a function of magnetic field intensity and temperature in the sample M921a.

Figure 4

Effective $g$ factor versus temperature measured in the M921a sample. Open symbols correspond to the “soft” mode and were deduced from Fig. 3 (see text), close symbols correspond to electron spin resonance coming from the CdZnTe substrate.

Figure 5

Comparison between the “soft” mode frequencies measured under magnetic field in the plane of the QW (open symbols) and at $45\mathrm{deg}$ (close symbols). The inset illustrates the corresponding experimental configurations.

Figure 6

Logarithmic scale plot of the soft mode effective $g$ factor as a function of $1-\zeta$ (see text). Open symbols represent the experimental data, solid line is the best power law fit $(\nu =0.73)$, dotted line corresponds to the slope $\nu =0.5$, predicted theoretically.