Electron/nuclear spin domain walls in quantum Hall systems

We propose experiments that can be done using both optically pumped NMR and the technique of all-optical NMR for creating spatially modulated nuclear-spin profiles. Due to the hyperfine coupling these would appear as spatially modulated Overhauser fields for the electrons that could have an amplitude large enough to cancel or even reverse the external Zeeman field at some places. We discuss two-dimensional electron-gas transport in the quantum Hall regime at filling factor $\nu =1\mathrm{}$ and demonstrate the existence of collective modes and topological excitations induced in the electron gas by various nuclear-spin patterns. We calculate the ${1/T}_1$ relaxation rate of the nuclear spins due to coupling with these low-lying collective modes and also discuss how transport and the low-energy modes would be affected by spin-orbit coupling in GaAs quantum wells grown in the $\left[001\right]$ and $\left[110\right]$ directions.