Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, gμ_BB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in ν for the R_xx minimum, e.g., from ν  = 11/7 to ν  = 8/5, and a corresponding change in the R_xy, e.g., from R_xy/R_K = (11/7)^-1 to R_xy/R_K = (8/5)^-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the ν  = 4/3 and ν  = 7/5 resistance minima, including "avoided crossing" type lineshape characteristics, and observable shifts of R_xy at the R_xx minima- the latter occurring for ν = 4/3, 7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same ν and R_xy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.[1]

[1] Wijewardena, U.K.,  et al. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields. Sci Rep 12, 19204 (2022). https://doi.org/10.1038/s41598-022-22812-x