Two-dimensional magnetic materials with tunable topological properties

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 $\mathrm{Cr}{\mathrm{I}}_{3}\phantom{\rule{0.16em}{0ex}}$ and $\mathrm{CrB}{\mathrm{r}}_{3}$. 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 band-gap narrowing and spin-orbital coupling, $\mathrm{Cr}{\mathrm{I}}_{3}\phantom{\rule{0.16em}{0ex}}$ branches into high-temperature quantum anomalous Hall insulators of $\mathrm{CrV}{\mathrm{I}}_{6}$ and $\mathrm{CrMn}{\mathrm{I}}_{6}\phantom{\rule{0.16em}{0ex}}$ with different topological invariants, while $\mathrm{CrB}{\mathrm{r}}_{3}$ branches into topological half metals of $\mathrm{CrVB}{\mathrm{r}}_{6}$ and $\mathrm{CrMnB}{\mathrm{r}}_{6}$. Those 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.