Non-reciprocal circular dichroism of ferro-rotational phonons in MnTiO$_{3}$

Abstract: X-ray circular dichroism (XCD), defined as the difference in absorption or scattering intensity between X-rays of opposite polarizations, arises from the breaking of spatial inversion or time-reversal symmetry and is thus sensitive to chirality, magnetism, and their interplay. Non-reciprocal XCD, in which the dichroic response changes upon reversing the propagation direction of the probe, is generally forbidden in systems with both symmetries. Using resonant inelastic X-ray scattering, we identify circularly polarized phonons in ferro-rotational MnTiO$_3$, which we term ferro-rotational phonons. Their excitations provide a direct demonstration of non-reciprocal XCD in a system that globally preserves inversion and time-reversal symmetries. We propose that a condensate of these phonons, manifested as standing waves, underlies the ferro-rotational order in MnTiO$_3$. The interplay among photon helicity, phonon polarization, and the axial ferro-rotational order gives rise to the observed non-reciprocal circular dichroism.