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

Abstract

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 $\ensuremath{\Delta}$ when weak interwell tunneling is considered. In the presence of the Coulomb interaction, by tailoring the relationship between $\ensuremath{\Delta}$ 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 $\ensuremath{\Delta}$ within a certain range. At larger $\ensuremath{\Delta}$, the system exhibits alternate ferromagnetic-paramagnetic stripes. In the SDW regime, the fractional polarization is up to the order of several tens of percent.