Partially spin-polarized quantum Hall effect in the filling factor range $1/3<\mathrm{}\nu <2/5\mathrm{}$

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