  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.
