Hysteresis effect in the (formula presented) quantum Hall system under periodic electrostatic modulation

The effect of a one-dimensional periodic electrostatic modulation on quantum Hall systems with filling factor (formula presented) is studied. We propose that, either when the amplitude of the modulation potential or the tilt angle of the magnetic field is varied, the system can undergo a first-order phase transition from a fully spin-polarized homogeneous state to a partially spin-polarized charge-density-wave state, and show hysteresis behavior of the spin polarization. This is confirmed by our self-consistent numerical calculations within the Hartree-Fock approximation.