Spin Excitations of the Spin-Polarized Electron Gas in Semimagnetic Quantum Wells

Collective and single-particle spin-flip excitations of a two-dimensional electron gas in a semimagnetic ${\mathrm{C}\mathrm{d}}_{1-x}{\mathrm{M}\mathrm{n}}_x\mathrm{T}\mathrm{e}$ quantum well are observed by resonant Raman scattering. Application of a magnetic field splits the spin subbands and a spin polarization is induced in the electron gas. Above 1 T the collective modes, which disperse with the in-plane wave vector, dominate the spectra. The local spin-density approximation provides a good description of our results and enables us to confirm that the energy of the low wave vector collective mode is given by the bare Zeeman energy.

Figure 1

(a)–(d) In-plane dispersion of the SPE and SF excitations for four different values of the external field. For each field, experimental energies of the peak in the SPE band (triangles) and the SF line (squares) are compared, when available, to the midpoint (dashed line) in the calculated SPE energy range (shaded regions) and the SF energies in their wave vector range of existence (thick lines). (e),(f) Raman response calculated from the interacting polarizability $P(\omega ,q)$ for five different Zeeman energies ($\Delta E_Z=0$, 2, 3, 4, 5 meV) and for two different values of the transferred wave vector $q$.

Figure 2

Raman spectra as a function of the external magnetic field for $q=5.72\mu {\mathrm{m}}^{-1}$ (a) and $15.72\mu {\mathrm{m}}^{-1}$ (b). The narrow line at the vanishing Raman shift is the remnant of the laser line after the scattered light has passed through the subtractive premonochromator. (c) Variation with the applied magnetic field of the measured excitation energies: SPE (full squares), SF excitation at $20°$ (open squares), $45°$ (open circles), and $70°$ (open triangles). The diamonds indicate the energy of the low-energy line measured at $20°$. The thick full line represents a Brillouin function fit of the spin-flip line measured at $20°$. The same fit is illustrated in the inset on a larger field range. The other lines show the field variations of the SPE energy (dashed line) and the SF energies at $45°$ and $70°$ (thin narrow lines) as deduced from the model assuming the Brillouin dependence of the SF energy at $20°$.