  Two-dimensional (2D) magnetic materials empowered with nontrivial band
topology may lead to the emergence of exotic quantum states with significant
application potentials. Here we predict a family tree of 2D magnetic materials
with tunable topological properties, starting from the parental materials of
CrI3 and CrBr3. The underlying design principle is that, by substituting the
alternating sites of the Cr honeycomb lattice sandwiched between the halogen
layers with V or Mn, the parental materials of trivial ferromagnetic insulators
are ripe to be converted into topological systems. Specifically, our
first-principles calculations show that, due to the elegant interplay between
bandgap narrowing and spin-orbital coupling, CrI3 branches into
high-temperature quantum anomalous Hall insulators of CrVI6 and CrMnI6 with
different topological invariants, while CrBr3 branches into topological
half-metals of CrVBr6 and CrMnBr6. Those novel 2D magnets are also shown to be
easily exfoliated from their bulk counterparts. The present study is thus
geared to advance the field of 2D magnetic materials into the topologically
nontrivial realm.
