Analysis of the spin splitting of maxima of quantum oscillations of the resistivity of $n$-Bi–Sb semiconductor alloys in a magnetic field parallel to the bisector axis

In samples of semiconductor alloys $n$-Bi$_{0.93}$Sb$_{0.07}$ with different electron concentrations ($n_1$ = 8 $\times$ 10$^{15}$ cm$^{-3}$, $n_2$ = 1.2 $\times$ 10$^{17}$ cm$^{-3}$, and $n_3$ = 1.9 $\times$ 10$^{18}$ cm$^{-3}$), dependences of the electrical resistivity on magnetic fields up to 45 T parallel to the current and the bisector axis $(\mathbf{H}\parallel\mathbf{C}_1\parallel\mathbf{j})$ have been measured at temperatures of 1.5, 4.5, and 10 K. The obtained dependences $\rho_{22}(H)$ demonstrate quantum oscillations of the resistivity (Shubnikov–de Haas effect), and, in high magnetic fields, there is a resistivity maximum far away from other maxima. On assumption that this maximum is related to the spin-split Landau level N = 0$^-$ for electrons of the main ellipsoid, the spin-splitting parameters are calculated for electrons of the main ellipsoid: $\gamma_1$ = 0.87, $\gamma_2$ = 0.8, and $\gamma_3$ = 0.73. Using these values, the oscillation maxima can be reliably related to the numbers of split Landau levels for electrons of the main and secondary ellipsoids. The dependences of the resistivity $\rho_{11}$ and the Hall coefficient R 31.2 on magnetic field have been measured in a transverse magnetic field at $\mathbf{H}\parallel\mathbf{C}_1$ and $\mathbf{j}\parallel\mathbf{C}_2$ on the sample with the electron concentration $n_4$ = 1.4 $\times$ 10$^{17}$ cm$^{-3}$. Using similar analysis, the spin-splitting parameter is found to be $\gamma_4$ = 0.85, which is close to the value of $\gamma_2$ = 0.8 obtained for the sample with close electron concentration ($n_2$ = 1.2 $\times$ 10$^{17}$ cm$^{-3}$) during the measurements in a longitudinal magnetic field. The quantum oscillation maxima of Hall coefficient $R_{31.2}$ are shifted to the range of high magnetic fields as compared to the quantum oscillation maxima of resistivity $\rho_{11}$.