Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5

The residual interaction between composite fermions (CFs) can express itself through higher order fractional Hall effect. With the help of diagonalization in a truncated composite fermion basis of low-energy many-body states, we predict that quantum Hall effect with partial spin polarization is possible at several fractions between $\nu =1\mathrm{/}3$ and $\nu =2\mathrm{/}5$. The estimated excitation gaps are approximately two orders of magnitude smaller than the gap at $\nu =1\mathrm{/}3$, confirming that the inter-CF interaction is extremely weak in higher CF levels.