Effects of Spin Polarization in the HgTe Quantum Well

Magnetoresistivity features connected with the spin level coincidences under tilted fields in a $\Gamma_8$ conduction band of the HgTe quantum well were found to align along straight trajectories in a $(B_\bot,B_{||})$ plane between the field components perpendicular and parallel to the layer meaning a linear spin polarization dependence on magnetic field. Among the trajectories is a noticeable set of lines descending from a single point on the $B_{||}$ axis, which is shown to yield a field of the full spin polarization of the electronic system, in agreement with the data on the electron redistribution between spin subbands obtained from Fourier transforms of oscillations along circle trajectories in the $(B_\bot,B_{||})$ plane and with the point on the magnetoresistivity under pure $B_{||}$ separating a complicated weak field dependence from the monotonous one. The whole picture of coincidences is well described by the isotropic $g$-factor although its value is twice as small as that obtained from oscillations under pure perpendicular fields. The discrepancy is attributed to different manifestations of spin polarization phenomena in the coincidences and within the exchange enhanced spin gaps. In the quantum Hall range of $B_\bot$, the spin polarization manifests in anticrossings of magnetic levels, which were found to depend dramatically nonmonotonously on $B_\bot$.