Thermodynamics and spin polarizations of the fractional quantum Hall states.

Abstract

The filling factor and temperature dependence of the electron spin polarization $〈{S}_{z}(T)〉$ of a two-dimensional electron system have been studied for various values of Zeeman coupling. At $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, there are sharp spin transitions for all the filling fractions considered here except $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{3}$. At low $T$, the appearance of a peak in $〈{S}_{z}(T)〉$ at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{2}{3}$ and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{2}{5}$ is interpreted as a manifestation of the reentrant behavior observed earlier. At $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{3}{5}$, one sees a gradual trasition from one spin state to another at low $T$. At large $T$, $〈{S}_{z}(T)〉$ generally decays as ${T}^{\ensuremath{-}1}$. These can be explored in the optically pumped nuclear magnetic resonance Knight shift measurements.