  We study the magnetic response of buckled honeycomb-lattice materials. The
buckling breaks the sublattice symmetry, enhances the spin-orbit coupling, and
allows the tuning of a topological quantum phase transition. As a result, there
are two doubly degenerate spin-valley coupled massive Dirac bands, which
exhibit an unconventional Hall plateau sequence under strong magnetic fields.
We show how to externally control the splitting of anomalous zeroth Landau
levels, the prominent Landau level crossing effects, and the polarizations of
spin, valley, and sublattice degrees of freedom. In particular, we reveal that
in a p-n junction, spin-resolved fractionally quantized conductance appears in
a two-terminal measurement with a spin-polarized current propagating along the
interface. In the low-field regime where the Landau quantization is not
applicable, we provide a semiclassical description for the anomalous Hall
transport. We comment briefly on the effects of electron-electron interactions
and Zeeman couplings to electron spins and to atomic orbitals.
