NMR Evidence for Spin Canting in a Bilayer $\nu =2$ Quantum Hall System

We investigate the electron spin states in the bilayer quantum Hall system at total Landau level filling factor $\nu =2$ exploiting current-pumped and resistively detected NMR. The measured Knight shift, $K_S$, of ${}^{75}\mathrm{As}$ nuclei reveals continuous variation of the out-of-plane electronic spin polarization between nearly full and zero as a function of density imbalance. Nuclear spin relaxation measurements indicate a concurrent development of an in-plane spin component. These results provide direct information on the spin configuration in this system and comprise strong evidence for the spin canting suggested by previous experiments.

Figure 1

(a) Timing diagram of the current-pumped and resistively detected NMR. (b) Time evolution of $R_{xx}$ at $({\nu }_f,{\nu }_b)=(\sim 2/3,0)$, illustrating its response to rf irradiation during the short (70 ms) excursion to the bilayer $\nu =2$ state. (c) NMR spectra of ${}^{75}\mathrm{As}$ at depletion (solid circles) and for the $\nu =2$ state at $\delta =0.02$ (open circles). Lines are fits, from which $K_S=24.1\mathrm{kHz}$ is obtained. Traces are vertically offset for clarity.

Figure 2

(a) NMR spectra of ${}^{75}\mathrm{As}$ for several values of density imbalance $\delta$. For comparison, spectra at depletion (bottom) and for the single-layer $\nu =1$ state (top) are shown by closed circles. Solid lines represent the results of fitting (see text for details). Traces are vertically offset for clarity. (b) $K_S$ determined from the fitting plotted as a function of $\delta$. Inset shows $\Gamma$ vs $\delta$.

Figure 3

(a) Electron spin polarization $P_z$; (b) nuclear spin relaxation rate $1/T_1$ for several temperatures; and (c) charge excitation gap $\Delta$ as a function of $\delta$. Vertical dash-dotted lines represent the phase boundaries determined from the temperature dependence of $1/T_1$.