Magnetic susceptibility of (Bi$_{2-x}$Sb$_x$)Te$_3$ (0 $<x<$ 1) alloys in the temperature range 2 to 50 K

The superconducting quantum interferometer device with Josephson junctions (SQUID magnetometer) is used to study the temperature dependences of the magnetic susceptibility of (Bi$_{2-x}$Sb$_x$)Te$_3$ (0 $<x<$ 1) alloy crystals in the temperature range 2 to 50 K, at the magnetic field vector $\mathbf{H}$ orientations $C_3$ : $\mathbf{H}\parallel C_3$ and $\mathbf{H}\perp C_3$ with respect to the crystal trigonal axis $C_3$. It is found that the magnetic susceptibility of the ion core of the samples under study is $\chi^G$ = -0.35 $\times$ 10$^{-6}$ cm$^3$/g, the contribution of lattice defects to magnetic susceptibility can be disregarded, and the contribution of free carriers is of a diamagnetic nature in the entire studied temperature range. It is shown that the contribution of free carriers to the resulting magnetic susceptibility and its anisotropy can be described within the Pauli and Landau-Peierls approach. In calculating the magnetic susceptibility, taking into account the constant concentration of free carriers in the state of pronounced degeneracy, it is found that the temperature dependence of the anisotropic effective masses varies with crystal chemical composition. This is possibly associated with the complex structure of the valence band and its variation as the Sb$_2$Te$_3$ content in the alloy increases.