All electrical probe of nuclear spin polarization and relaxation by spin phase transition peaks of the filling fraction ν = 2/3 quantum hall effect

We developed a sensitive spectroscopic tool to probe resistively as low as a few percent of an ensemble of nuclear spin polarizations in a GaAs quantum well. We take advantage of the spinphase-transition (SPT) peak of the filling fraction ν = 2/3 quantum Hall effect at which the electronic systems are energetically degenerate. The non-zero nuclear spin polarization incorporated in the system would be perceived as an effective magnetic field B _N that modifies the Zeeman energy exclusively. It would result in a change in the overall shape of the peak including the peak's position, width, and amplitude. The alteration of the shape of the overall peak provide essential information on the microscopic characteristics of nuclear spin polarization and its relation to the domain formations which was not well investigated in the previous reports.