  We present a density functional theory (DFT) based study of a two-dimensional
phase of chromium bismuthate (CrBi), previously unknown material with
exceptional magnetic and magnetooptical characteristics. Monolayer CrBi is a
ferromagnetic metal with strong spin-orbit coupling induced by the heavy
bismuth atoms, resulting in a strongly anisotropic Ising-type magnetic ordering
with the Curie temperature estimated to be higher than 300 K. The electronic
structure of the system is topologically nontrivial, giving rise to a nonzero
Berry curvature in the ground magnetic state, leading to the anomalous Hall
effect with the conductivity plateau of $\sim$1.5 $e^2/h$ at the Fermi level.
Remarkably, the Hall conductivity and the magnetooptical constant are found to
be strongly dependent on the direction of magnetization. Besides, monolayer
CrBi demonstrates the polar magnetooptical Kerr effect in the visible and
near-ultraviolet spectral ranges with the maximum rotation angles of up to 10
mrad. Our findinds suggest that monolayer CrBi is a promising system for
practical applications in magnetooptical and spintronic devices.
