-------------------------------------------------------------------------------- ### Revealing hidden magneto-electric multipoles using Compton scattering -------------------------------------------------------------------------------- Sayantika Bhowal and Nicola A. Spaldin -------------------------------------------------------------------------------- #### Abstract: Magneto-electric multipoles, which are odd under both space-inversion $\cal I$ and time-reversal $\cal T$ symmetries, are fundamental in understanding and characterizing magneto-electric materials. However, the detection of these magneto-electric multipoles is often not straightforward as they remain ``hidden" in conventional experiments in part since many magneto-electrics exhibit combined $\cal IT$ symmetry. In the present work, we show that the anti-symmetric Compton profile is a unique signature for all the magneto-electric multipoles, since the asymmetric magnetization density of the magneto-electric multipoles couples to space via spin-orbit coupling, resulting in an anti-symmetric Compton profile. We develop the key physics of the anti-symmetric Compton scattering using symmetry analysis and demonstrate it using explicit first-principles calculations for two well-known representative materials with magneto-electric multipoles, insulating LiNiPO$_4$ and metallic Mn$_2$Au. Our work emphasizes the crucial roles of the orientation of the spin moments, the spin-orbit coupling, and the band structure in generating the anti-symmetric Compton profile in magneto-electric materials. -------------------------------------------------------------------------------- All calculations were performed using the Elk code. The main folder contains two separate folders: (a) cal and (b) data-file. The subfolders of "cal" contains input and the most relevant output files for the Compton scattering calculations. The subfolders of "data-file" contains the data files corresponding to the figures, presented in the paper.