This work provides a theory of the general structure of mixed-spin fractional quantum Hall states, which are relevant at low magnetic fields. This, in particular, leads to a microscopic description of the experimentally observed mixed-spin states at v -j, j, and j. Antiparallel-flux-attachment transformation of the composite fermion theory plays an important role in explaining the mixed-spin states in the filling factor range \ > v > j.PACS numbers: 73.40.Hm, 73.20.Dx, 73.50.JtThe fractional quantum Hall state is characterized by quantized Hall resistance and vanishing longitudinal resistance [1], In the limit of infinitely large magnetic field, B, the Zeeman splitting is infinitely large, the spin degrees of freedom are frozen out, and electrons can be taken to be spinless. An intuitively simple and microscopically accurate understanding of the fractional quantum Hall effect state in this limit is provided by the composite fermion (CF) theory [21. This theory relates, through a flux-attachment transformation, the complicated problem of highly correlated electrons in the fractional quantum Hall effect (FQHE) regime to the simple problem of weakly interacting electrons in the integer QHE (IQHE) regime. In this paper, we use this approach to investigate odd-denominator FQHE in the low-field limit.
It was realized by Halperin [3] that Zeeman splitting is quite small in GaAs (approximately ^ of the cyclotron energy), so, at relatively low B, it may be possible that the ground state of interacting electrons is not fully spin polarized. There is good experimental evidence that the FQHE states at v™ j, f, y, and f are not fully spin polarized at low magnetic fields. A transition from the high-/? maximally polarized FQHE states to mixed-spin states has been observed at these filling factors as the Zeeman energy is lowered in several beautiful experiments [4-7].There is no satisfactory understanding of the general structure of the FQHE states in the low-field limit. Theoretical studies investigating FQHE in the low-field limit set the Zeeman splitting to zero, while still keeping the Landau level (LL) separation large, so that only the lowest LL is retained in the calculations. This will be referred to as the vanishing-Zeeman-splitting (VZS) limit. There have been several exact diagonalization studies in the VZS limit [8,9]. The calculations of Ref.[8] show that, in this limit, the incompressible ground states at filling factors v""2/(2/i + l) are spin singlet in the thermodynamic limit, while those at v*=l/(2n + 1) are maximally polarized. The state at v =-f was found to be partially polarized [9]. The fully polarized states at v^l/ (2n +1) are, of course, the celebrated Laughlin states [10]. There is also a good microscopic understanding for filling factors v^l/iAn + 1) " j, \,. . . (and their par-