Spin-orbit and exchange interaction in a HgMnTe magnetic two-dimensional electron gas

Spin-orbit interaction and sp-d exchange interaction are investigated by analyzing beating patterns of Shubnikov-de Hass oscillations in HgMnTe magnetic two-dimensional electron gas (2DEG) at various temperatures. The results show that (l) spin-orbit interaction results in zero-magnetic-field spin splitting in 2DEG; (2) spin-orbit interaction is dominant at low magnetic field, and the total spin-splitting decreases with increasing magnetic field due to the influence of Landau splitting and Zeeman splitting; (3) at a high magnetic field, the sp-d exchange interaction tends to saturate and the spin splitting corresponds to Zeeman splitting. The experiments demonstrate that the spin splitting deduced from fast Fourier transformation (FFT) of SdH oscillations versus. 1/B is different from zero-magnetic-field spin splitting when Zeeman spin splitting is comparable to zero-magnetic-field spin splitting.