Spin polarization measurement of the $\nu $ = 5/2 fractional quantum Hall state via NMR

The $\nu $ = 5/2 fractional quantum Hall state has attracted much interest due to its possible non-Abelian statistics, which are expected for the \textit{Pfaffian} state. While the \textit{Pfaffian} model assumes full spin polarization, recent optical experiments suggest a spin-unpolarized ground state at $\nu $ = 5/2 instead [1, 2], and have thus posed a new challenge for understanding the true nature of the 5/2 state. Here, we report a spin polarization measurement of the $\nu $ = 5/2 state using resistively-detected NMR and demonstrate its full polarization. The measurements were performed at $T$ = 10 mK on a gated 30-nm quantum well at 4.4 T. For the resistive read-out of the nuclear resonance frequencies, we used the $\nu $ = 2/3 spin transition by comparing its $R_{xx}$ prior to and after the application of an \textit{rf} pulse at $\nu $ = 5/2. The NMR spectrum at $\nu $ = 5/2 is shifted to lower frequencies from the one at $\nu $ = 2, where the system is unpolarized, indicating a nonzero polarization at $\nu $ = 5/2. Our analysis, which considers the changes of the sub-band wave function under a gate bias, indicates that the polarization at $\nu $ = 5/2 is very close to its maximal value. This, in turn, gives support for the Pfaffian state.\\[0pt] [1] T. D. Rhone, APS March Meeting 2010, Y2.00003 [2], M. Stern \textit{et al}., Phys. Rev. Lett. \textbf{105}, 096801 (2010).