  A recent study has demonstrated that a fermionic two-leg ladder model,
threaded by a flux and characterized by a spatially varying interleg hopping
term, gives rise to a quasiflat low-energy band. This band exhibits an unusual
ground state at half filling in the presence of interaction -- a ferromagnetic
Mott insulator. In this paper, we extend the study of this model to other
fillings of the quasiflat band and explore the magnetic properties of the
ground state at these fillings. In particular, we study four fillings:
one-quarter, three-quarters, slightly above half filling (half filling plus two
electrons), and slightly below half-filling (half filling minus two electrons).
Incorporating interaction within the Hubbard model and using the Density Matrix
Renormalization Group method to find the ground states, we find that the
spin-spin correlation is ferromagnetic at fillings less than half, similar to
that observed at half filling, but is antiferromagnetic beyond half filling.
Interestingly, these results hold only when mixing between the lowest quasiflat
band and the next-to-lowest dispersive band is negligible; once mixing between
the two bands is facilitated by increasing the interaction strength, the
correlation becomes ferromagnetic above half filling as well. Additionally, by
reducing the strength of the interaction in comparison to the bandwidth, a
transition from the ferromagnetic to the antiferromagnetic state is observed in
all the cases.
