Spin Relaxation in Quantum Hall Systems

We study spin relaxation in an interacting two-dimensional electron gas in a strong magnetic field for the case where the electron density is close to filling just one Landau sublevel of one spin projection, i.e., for filling factor $\nu \simeq 1$. Assuming the relaxation to be caused by scattering with phonons, we derive the kinetic equations for the electrons' spin density which replace the Bloch equations in our case. These equations are nonlinear and their solution depends crucially on the filling factor $\nu$ and on the temperature $T$ of the phonon bath. In the limit of $T=0\mathrm{}$ and $\nu =1\mathrm{}$, the solution relaxes asymptotically with a power law inversely proportional to time, instead of following the conventional exponential behavior.