Spin density waves in a semiconductor superlattice in a tilted magnetic field

The ground state of a semiconductor superlattice (SL) placed in a tilted magnetic field is shown to exhibit a spin-density wave structure when the energy spectrum favors crossings between opposite-spin Landau minibands. The SL is modeled as an array of infinitely attractive quantum wells, whose single energy level is broadened into a miniband of width Delta when weak interwell tunneling is considered. In the presence of the Coulomb interaction, by tailoring the relationship between Delta and the cyclotron and Zeeman energies, the system transitions between paramagnetic, ferromagnetic, spin-density wave (SDW), and ferromagnetic-paramagnetic stripe ordering. These results are obtained by solving numerically a spin-density-wave gap equation derived at T = 0 K in a self-consistent formalism. We find that for a given value of the difference between the Landau energy and the Zeeman splitting, the initial paramagnetic or ferromagnetic order becomes unstable with respect to the formation of a SDW for Delta within a certain range. At larger Delta, the system exhibits alternate ferromagnetic-paramagnetic stripes. In the SDW regime, the fractional polarization is up to the order of several tens of percent.