Anisotropy of the electron $g$ factor in quantum wells based on cubic semiconductors

A new mechanism for the spin splitting of electron levels in asymmetric quantum wells based on GaAs-type semiconductors relative to rotations of the magnetic field in the well plane is suggested. It is demonstrated that the anisotropy of the Zeeman splitting (linear in a magnetic field) arises in asymmetric quantum wells due to the interface spin-orbit terms in the electron Hamiltonian. In the case of symmetric quantum wells, it is shown that the anisotropy of the Zeeman splitting is a cubic function of the magnitude of the magnetic field, depends on the direction of the magnetic field in the interface plane as the fourth-order harmonic, and is governed by the spin-orbit term of the fourth order by the kinematic momentum in the electron Hamiltonian of a bulk semiconductor.