Origin of circular dichroism in resonant elastic X-ray scattering from magnetic and polar chiral structures

Circular dichroism in resonant elastic X-ray scattering (CD-REXS) has recently been observed in chiral structures composed of multiferroic materials as well as magnetic moments or electric polarization vectors. In order to comprehensively understand the experimental results of these previous studies, we present here in detail the analytical formulation of CD-REXS for one-dimensional helices composed of magnetic moments and electric polarization vectors, respectively. In particular, by comparing CD-REXS for a proper-screw-shaped Bloch-type helix and cycloid-shaped Néel-type helix, we found that CD-REXS for both magnetic and polar helices can discriminate between both types of helices. We also found that the X-ray polarization factor depending on the scattering geometry is a significant factor in determining the characteristics of CD-REXS for chiral structures. The results obtained from the detailed formulas can be intuitively understood using the concept of mirror reflection. In particular, in this way it can be understood that Bloch-and Néel-type helices correspond to truly chiral and achiral structures, respectively, and why CD-REXS is able to distinguish between these two types of helices.