Hysteresis effect in \nu=1 quantum Hall system under periodic electrostatic modulation

The effect of a one-dimensional periodic electrostatic modulation on quantum Hall systems with filling factor \nu=1 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. Finally we suggest that the \nu=1/3 fractional quantum Hall state may also show similar hysteresis behavior in the presence of a periodic potential modulation.