Activation energies for the $\nu $=5/2 Fractional Quantum Hall Effect at 10 Tesla

We reported on the low-temperature magnetotransport in a high-purity (mobility $\sim $ 1$\times $10$^{7}$cm$^{2}$/Vs) modulation-doped GaAs/AlGaAs quantum well with a high electron density (6$\times $10$^{11}$ cm$^{-2})$. A quantized $\nu $=5/2 Hall plateau is observed at B $\sim $ 10 T, with an activation gap $\Delta _{5/2} \sim $ 125$\pm $10 mK; the plateau can persist up to $\sim $ 25$^{o}$ tilt-field. We determined the activation energies $\Delta $ and quasi-gap energies $\Delta ^{quasi}$ for the $\nu $=5/2, 7/3, and 8/3 fractional quantum Hall states in tilted-magnetic field ($\theta )$. The $\Delta _{5/2} $, $\Delta _{7/3} $ and the $\Delta _{5/2}^{quasi} $, $\Delta _{7/3}^{quasi} $are found to decrease in $\theta $. We will present the systematic data and discuss their implications on the spin-polarization of $\nu $=5/2 states observed at 10 T.\\[4pt] [1] R. Willett, Phys. Rev. Lett. \textbf{59}, 1776 (1987).\\[0pt] [2] W. Pan et al, Solid State Commun. \textbf{119}, 641 (2001).