Motivated by the discovery of extremely low-energy collective modes in the fractional quantum Hall effect [Kang, Pinczuk et al., Phys. Rev. Lett. 84, 546 (2000)], with energies below the Zeeman energy, we study theoretically thr spin-reversed excitations for fractional quantum Hall states at v= 2/5 and 3/7 and find qualitatively different behavior than for v= 1/3. We find that a low-energy, charge-neutral ''spin roton, associated with spin-reversed excitations that involve a change in the composite-fermion Landau level index, has energy in reasonable agreement with experiment.
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