Spin polarization of theν=12/5fractional quantum Hall state

Abstract

We have carried out tilt magnetic field ($B$) studies of the $\ensuremath{\nu}=12/5$ fractional quantum Hall state in an ultrahigh-quality GaAs quantum well specimen. Its diagonal magnetoresistance ${R}_{xx}$ shows a nonmonotonic dependence on tilt angle (\ensuremath{\theta}). It first increases sharply with increasing \ensuremath{\theta}, reaches a maximal value of \ensuremath{\sim}70 \ensuremath{\Omega} at \ensuremath{\theta} \ensuremath{\approx} 14\ifmmode^\circ\else\textdegree\fi{}, and then decreases at higher tilt angles. Correlated with this dependence of ${R}_{xx}$ on \ensuremath{\theta}, the 12/5 activation energy (${\ensuremath{\Delta}}_{12/5}$) also shows a nonmonotonic tilt dependence. ${\ensuremath{\Delta}}_{12/5}$ first decreases with increasing \ensuremath{\theta}. Around $\ensuremath{\theta}={14}^{\ensuremath{\circ}}$, ${\ensuremath{\Delta}}_{12/5}$ disappears as ${R}_{xx}$ becomes nonactivated. With further increasing tilt angles, ${\ensuremath{\Delta}}_{12/5}$ reemerges and increases with \ensuremath{\theta}. This tilt $B$ dependence at $\ensuremath{\nu}=12/5$ is strikingly different from that of the well-documented 5/2 state and calls for more investigations on the nature of its ground state.