Tilt Magnetic Field Dependence of the 12/5 Fractional Quantum Hall State

The 12/5 state has attracted growing interest due to its superior potential in performing universal topological quantum computation. Up to date, except for the observation of a well developed quantum Hall plateau at this filling, much less experimental work has been carried out and there is no experimental evidence to support this state being a paraferminoic or non-Abelian state. Here, we present our tilt magnetic field dependence results in examining its spin-polarization. It was observed that the diagonal resistance R$_{xx}$ at $\nu $=12/5 shows a non-monotonic dependence on tilt angle ($\theta )$. It first increases sharply with increasing $\theta $, reaches a maximal value of $\sim $ 60 $\Omega $ around $\theta \sim $14$^{o}$, and then decreases with $\theta $ further increased. Correlated with this R$_{xx}$ dependence, the 12/5 activation energy gap ($\Delta _{12/5})$ also shows a non-monotonic $\theta $ dependence. $\Delta _{12/5 }$first decreases. Around 14$^{o}$, R$_{xx}$ becomes non-activated and a true activation energy gap is not obtainable. With further increasing $\theta $, R$_{xx}$ becomes activated again and $\Delta _{12/5 }$increases with $\theta $. This tilt dependence in R$_{xx}$ and $\Delta _{12/5 }$is similar to the composite fermion states at $\nu $=2/5 and 8/5 in the lowest Landau level, which was interpreted as a spin transition. Our results thus call for more investigations on the nature of the 12/5 ground state.