Revealing hidden magnetoelectric multipoles using Compton scattering

Magneto-electric multipoles, which are odd under both space-inversion $\cal I$ and time-reversal T$ symmetries, fundamental in understanding characterizing magneto-electric materials. However, the detection of these multipoles is often not straightforward as they remain "hidden" conventional experiments part since many magneto-electrics exhibit combined IT$ symmetry. In present work, we show that anti-symmetric Compton profile a unique signature for all asymmetric magnetization density couples to space via spin-orbit coupling, resulting an profile. We develop key physics scattering using symmetry analysis demonstrate it explicit first-principles calculations two well-known representative materials with insulating LiNiPO$_4$ metallic Mn$_2$Au. Our work emphasizes crucial roles orientation spin moments, band structure generating