  Combining tight-binding models and first principles calculations, we
investigate the quantum anomalous Hall (QAH) effect induced by intrinsic
spin-orbit coupling (SOC) in buckled honeycomb lattice with sp orbitals in an
external exchange field. Detailed analysis reveals that nontrivial topological
properties can arise utilizing not only spin but also orbital degrees of
freedom in the strong SOC limit, when the bands acquire non-zero Chern numbers
upon undergoing the so-called orbital purification. As a prototype of a buckled
honeycomb lattice with strong SOC we choose the Bi(111) bilayer, analyzing its
topological properties in detail. In particular, we show the emergence of
several QAH phases upon spin exchange of the Chern numbers as a function of SOC
strength and magnitude of the exchange field. Interestingly, we observe that in
one of such phases, namely, in the quantum spin Chern insulator phase, the
quantized charge and spin Hall conductivities co-exist. We consider the
possibility of tuning the SOC strength in Bi bilayer via alloying with
isoelectronic Sb, and speculate that exotic properties could be expected in
such an alloyed system owing to the competition of the topological properties
of its constituents. Finally, we demonstrate that 3d dopants can be used to
induce a sizeable exchange field in Bi(111) bilayer, resulting in non-trivial
Chern insulator properties.
