Narrow Results

We develop a method for studying spatial distribution of the Knight shift using resistively-detected nuclear magnetic resonance (NMR) in an AlGaAs/GaAs quantum Hall device. By controlling the position of the dynamic nuclear polarization with the side-gate voltage, the spatial distribution of the NMR spectrum is investigated in a vicinity of quantum Hall edge channels. The value of Knight shift gradually changes in the region where the local Landau-level filling factor is between ν = 1 and ν = 2, implying that the change of the local electron spin polarization is detected in the edge channel.

In the low doping limit, a high T_c cuprate preserves a two band structure. O2p electrons are itinerant, Cu3d electrons are localized. Therefore the two component model is suitable to describe nuclear spin relaxation at copper sites. In addition to the Korringa process, the hyperfine interaction between nuclear spins and local electron spins is considered, which gives rise to the anomalous relaxation rate 1/T₁ = a + bT. The decrease of the susceptibility near T_c, as shown by the Knight shift measurements, can be attributed to the ordering of local spins and the pairing of the uncompensated spins created by holes at the oxygen sites.