  Magneto-optical Kerr effect, normally found in magnetic materials with
nonzero magnetization such as ferromagnets and ferrimagnets, has been known for
more than a century. Here, using first-principles density functional theory, we
demonstrate large magneto-optical Kerr effect in high temperature noncollinear
antiferromagnets Mn$_{3}X$ ($X$ = Rh, Ir, or Pt), in contrast to usual wisdom.
The calculated Kerr rotation angles are large, being comparable to that of
transition metal magnets such as bcc Fe. The large Kerr rotation angles and
ellipticities are found to originate from the lifting of the band
double-degeneracy due to the absence of spatial symmetry in the Mn$_{3}X$
noncollinear antiferromagnets which together with the time-reversal symmetry
would preserve the Kramers theorem. Our results indicate that Mn$_{3}X$ would
provide a rare material platform for exploration of subtle magneto-optical
phenomena in noncollinear magnetic materials without net magnetization.
