Electrically Controlled Nuclear Spin Polarization and Relaxation by Quantum-Hall States

We study interactions between electrons and nuclear spins by using the resistance ([Formula presented]) peak which develops near the Landau-level filling factor [Formula presented] as a probe. Temporarily tuning [Formula presented] to a different value, [Formula presented], with a gate demonstrates that the [Formula presented] peak regenerates even after complete depletion ([Formula presented]), while it rapidly relaxes on either side of [Formula presented]. This indicates that the [Formula presented] domain morphology is memorized by the nuclear spins which can be rapidly depolarized by Skyrmions. An additional enhancement in the nuclear spin relaxation around [Formula presented] and [Formula presented] suggests a Fermi sea of partially polarized composite fermions.