Collective nature of two-dimensional electron gas spin excitations revealed by exchange interaction with magnetic ions

Time-resolved Kerr rotation experiments in CdMnTe quantum wells provide the evidence of mixed spin excitations of the two-dimensional electron gas and magnetic ions. The onset of strong coupling between electron and Mn spin modes reveals the collective (spin-wave) nature of electronic spin excitations probed by this method. We show that resonant exchange coupling between electron-spin waves and magnetic ions spin-flip excitations provide insights in the many-body physics of the two-dimensional electron gas.

Figure 1

(Color online) Schematic representation of spin precession modes in $n$-doped (Cd,Mn)Te quantum wells. The anticrossing between the collective electron mode (spin wave) and Mn spin excitations at $g_m=2$ is indicated in the rectangular frame. Other excitations of the 2DEG, such as spin-density waves and charge-density waves based on intersubband excitations, sit at higher energy.

Figure 2

(Color online) Time-resolved Kerr rotation scans measured at $B=3\text{T}$ for samples 2 (black line) and 3 (red line). Inset shows the corresponding Fourier spectra.

Figure 3

(Color online) Waterfall plots (a) of the time-resolved Kerr rotation and (b) of the corresponding Fourier spectra, measured under magnetic field in the resonance region from $B=5.1\text{T}$ to $B=6\text{T}$ on sample 2.

Figure 4

(Color online) (a) Spin precession frequencies and (b) decay times extracted from Kerr rotation measurements under magnetic field $B=1–6\text{T}$ (sample 2). Insets show the frequencies (a) and the intensities $A_{\pm }$ of the two coupled modes in the resonance region defined in Eq. (6). Symbols show the experimental data, lines are the best fit obtained using Eq. (3) assuming the parameters listed in Table .

Figure 5

(Color online) Time-resolved Kerr rotation scans (left panel) and the Fourier spectra (right panel) from sample 3 with magnetic field values ranging from 5.7 to 6.1 T (resonant conditions). Two Fourier spectra correspond to each measurement, one for the short delays ($0<t<225\text{ps}$, black line) and the other for the long delays ($225<t<450\text{ps}$, red line).

Figure 6

(Color online) Differences between (a) the frequencies and (b) relaxation times of the mixed modes for samples 1 (diamonds), 2 (circles), 3 (triangles), and 4 (squares). Solid lines are best fit using Eq. (3) with parameters listed in Table .

Figure 7

(Color online) 2DEG spin polarization extracted from the anticrossing splitting using Eq. (5) (squares) and calculated assuming a Fermi distribution (circles), as a function of the 2DEG density. Inset shows the enhancement of the spin polarization with respect to the Fermi gas as a function of dimensionless spacing between electrons $r_s$. Solid line is the theory from Ref. 17.