Partially spin-polarized quantum Hall effect in the filling factor range 1/3

The residual interaction between composite fermions (CF's) 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 $\ensuremath{\nu}=1/3$ and $\ensuremath{\nu}=2/5.$ The estimated excitation gaps are approximately two orders of magnitude smaller than the gap at $\ensuremath{\nu}=1/3,$ confirming that the inter-CF interaction is extremely weak in higher CF levels.