Helical antiferromagnetic ordering in the lowest Landau level of a semiconductor superlattice

When subjected to a tilted magnetic field, the ground state of a semiconductor superlattice (SL) with two identical quantum wells per unit cell is shown to exhibit different magnetic configurations that are dependent on the strength and direction of the field and the SL characteristics. Intra- and interunit cell tunneling between the wells, assumed to be infinitely attractive, generate an energy miniband structure of the lowest Landau level that, in cooperation with the Zeeman splitting, creates, at certain points in the momentum space, an energy difference between opposite-spin single-particle states that can be overcome by the Coulomb interaction. Within the Hartree-Fock approximation, we show that the minimum free energy is reached in ground states with different magnetic characteristics: ferromagnetic, helical antiferromagnetic (HAFM) or paramagnetic, depending on the system parameters and the external field. The HAFM phase results from an antiferromagnetic coupling of opposite electron spins that are rotated in respect to the (z) over cap axis by an angle that varies continuously within the Brillouin zone between [0,pi/2]. As a result, a finite polarization is registered in real space. The self-consistent equation satisfied by the inclination angle is solved numerically at T = 0 K for an array of SL parameters. Its solutions demonstrate that a continuous driven transition between ferromagnetic, HAFM, and paramagnetic states can be realized by adjusting the parameters of the system.