Scanning microscopy of nuclear spin polarization via quantum Hall edge channels

Nuclear spin polarization is probed via hyperfine interaction with spin-split edge channels. By scanning the edge channels with a biased metal side gate, the local profile of nuclear spin polarization is imaged with a resolution of ~14 nm, determined by the extension of the edge-state wave function. Distribution of the nuclear spins dynamically polarized by the edge channels is found to be localized in a region as narrow as 35 nm at the lowest current (0.1 nA) but broadens with increasing current. The decay process is studied in detail with the same technique and the temporal dynamics of the nuclear polarization are interpreted in terms of the interplay of diffusion, electron-nuclear spin interaction, and spin-lattice relaxation.