Magneto-optical transmission of Bi$_{2}$Se$_{3}$ at the fundamental absorption edge

Magneto-optical transmission spectroscopy of a series of n-type Bi$_{2}$Se$_{3}$ samples have been performed, around the fundamental absorption edge, up to 32 T. The absorption edge splits in two components related to the two spin polarization of the transmission. This spin splitting increases linearly with the magnetic field up to a critical value B$_{\mathrm{C}}$, depending on the carrier density, beyond which it remains constant. This corresponds to a complete spin polarization of the compound. The consequences of this specific property put some constrains on the parameters of the Hamiltonian describing the system.