Multi-spin-subband structure of dilute magnetic semiconductor quantum wells: Feedback mechanism

Using a fully self-consistent envelope function approach, we focus on wide conduction band NMS (non-magnetic semiconductor)/DMS (dilute magnetic semiconductor)/NMS quantum wells, under weak external parallel magnetic field, where many spin-subbands are usually present. We concentrate on small values of the magnetic field because we want to investigate the influence of the feedback mechanism due to the difference of the concentrations of spin-up and spin-down carriers which could induce spontaneous spin-polarization i.e. in the absence of a magnetic field. We study the spin-subband structure, the spin-subband populations and the spin-polarization as functions of the sheet carrier concentration, NsNs, for different values of the magnitude of the exchange interaction, |J||J|, between the itinerant carriers and the magnetic impurities. Our calculations for 0.01 T show that at 20 K the values of |J||J| necessary to make this feedback mechanism sufficiently strong are too high compared to the |J||J| values of common Mn-doped systems in the conduction band. However, the feedback mechanism will be sufficiently strong at low enough temperatures below 20 K for realistic values of |J||J|. Moreover, we explain how increasing the sheet carrier concentration the heterostructure is transformed from an almost square quantum well to a system of two coupled heterojunctions with an intermediate soft barrier.