Non-reciprocal circular dichroism of axial phonons coupled to ferro-rotational order
Circular dichroism (CD) in X-ray absorption, defined as the difference in absorption between opposite circular polarizations, is fundamentally enabled by the breaking of time-reversal symmetry or inversion symmetry. It is therefore sensitive to magnetism, chirality, and their interplay. In contrast, the sample symmetry alone is insufficient to determine whether CD in resonant inelastic X-ray scattering (RIXS) is allowed. Rather, RIXS-CD is governed by both the sample symmetry and the scattering geometry. Here, using RIXS, we identify circularly polarized phonons coupled to ferro-rotational order in MnTiO$_3$, which we refer to as ferro-axial phonons. Their excitations provide a direct demonstration of non-reciprocal RIXS-CD, in which the dichroic response changes upon reversing the propagation direction of the incident X-rays, although the system globally preserves both 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 observed non-reciprocal CD reflects the interplay among photon helicity, phonon polarization, and ferro-rotational order.