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We investigate nuclear spin effects in a two-dimensional electron gas in thequantum Hall regime modeled by a weakly coupled array of interacting quantumwires. We show that the presence of hyperfine interaction between electron andnuclear spins in such wires can induce a phase transition, ordering electronsand nuclear spins into a helix in each wire. Electron-electron interactioneffects, pronounced within the one-dimensional stripes, boost the transitiontemperature up to tens to hundreds of millikelvins in GaAs. We predict specificexperimental signatures of the existence of nuclear spin order, for instancefor the resistivity of the system at transitions between different quantum Hallplateaus.

Helical nuclear spin order in a strip of stripes in the Quantum Hall regime