  Reflecting the fundamental interactions of polarized light with magnetic
matter, magneto-optical effects are well known since more than a century. The
emergence of these phenomena is commonly attributed to the interplay between
exchange splitting and spin-orbit coupling in the electronic structure of
magnets. Using theoretical arguments, we demonstrate that topological
magneto-optical effects can arise in noncoplanar antiferromagnets due to the
finite scalar spin chirality, without any reference to exchange splitting or
spin-orbit coupling. We propose spectral integrals of certain magneto-optical
quantities that uncover the unique topological nature of the discovered effect.
We also find that the Kerr and Faraday rotation angles can be quantized in
insulating topological antiferromagnets in the low-frequency limit, owing to
nontrivial global properties that manifest in quantum topological
magneto-optical effects. Although the predicted topological and quantum
topological magneto-optical effects are fundamentally distinct from
conventional light-matter interactions, they can be measured by readily
available experimental techniques.
