  Materials with optical activity can rotate the polarization plane of
transmitted light. The most typical example is the natural optical activity,
which has the symmetry property of changing sign after space inversion but
being invariant to time inversion. Faraday rotation exhibits the opposite: it
is invariant to space inversion but changes sign after time reversal. Here, we
demonstrate that in a magnetoelectric material, another type of polarization
rotation is possible. This effect is investigated in magnetoelectric
YbAl3(BO3)4 under the viewpoint of time and space inversion symmetry arguments.
We observe the sign change of the rotation sense under either time or space
reversal. This investigation proves that the polarization rotation in
YbAl3(BO3)4 must be classified as gyrotropic birefringence, which has been
discussed within the idea of time-reversal breaking in underdoped cuprates. The
diagonal terms in the magnetoelectric susceptibility are responsible for the
observed signal of gyrotropic birefringence. Further analysis of the
experimental spectra reveals a substantial contribution of the natural optical
activity to the polarization rotation. We also demonstrate that the observed
activity originates from the magnetoelectric susceptibility.
