  Magnetoelectrics with ultra-low symmetry and spin-orbit coupling are well
known to display a number of remarkable properties including nonreciprocal
directional dichroism. As a polar and chiral magnet, Ni$_3$TeO$_6$ is predicted
to host this effect in three fundamentally different configurations, although
only two have been experimentally verified. Inspired by the opportunity to
unravel the structure-property relations of such a unique light-matter
interaction, we combined magneto-optical spectroscopy and first-principles
calculations to reveal nonreciprocity in the toroidal geometry and compared our
findings with the chiral configurations. We find that formation of Ni toroidal
moments is responsible for the largest effects near 1.1 eV - a tendency that is
captured by our microscopic model and computational implementation. At the same
time, we demonstrate deterministic control of nonreciprocal directional
dichroism in Ni$_3$TeO$_6$ across the entire telecom wavelength range. This
discovery will accelerate the development of photonics applications that take
advantage of unusual symmetry characteristics.
