We have studied the partially spin polarized fractional quantum Hall states using Chern Simon's theory and plasma picture proposed by Halperin. Using these theoretical techniques we have tried to find the stable polarized states of different filling fractions observed in experiments. We have calculated the ground state energies of those states and also pair correlation function. We have described the nature of the states by the behavior of this quantity. In our study, we have seen that the partially polarized states, which do not fit with Jain's composite fermion description are basically the mixed state of up-spin liquid phase and down-spin solid phase.

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We have calculated the energy spectra for almost all the filling fraction in the Jain series, low energy fundamental mode as well as higher energy modes using CF theory. The nature of low energy mode and higher energy mode is nearly identical roton mode. We have observed that, these series of filling fractions ν = n 2pn+1 posses n number of roton minima in their higher energy mode.

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