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.
Highlights
Multipoles provide a convenient basis for describing properties as diverse as electric charge densities and gravitational fields and are widely used in many areas of physics, such as classical electromagnetism, metamaterials, and nuclear and particle physics [1,2,3,4,5]
We have shown that the antisymmetric Compton profile is a signature of parity-odd, time-odd ME multipoles
The ME multipoles, which break both space-inversion and time-reversal symmetries, generate an asymmetry in the magnetization density, the details of which are governed by the specific components of the ME multipoles that occur
Summary
Multipoles provide a convenient basis for describing properties as diverse as electric charge densities and gravitational fields and are widely used in many areas of physics, such as classical electromagnetism, metamaterials, and nuclear and particle physics [1,2,3,4,5] They are useful in condensed matter systems for characterizing the charge and spin and orbital magnetic moments of electrons in a unified way and have enabled understanding as well as prediction of various cross couplings and transport properties [6,7,8,9]. An additional possibility, Compton scattering, which measures the electron density as a function of momentum, was proposed as a candidate probe for the toroidal moment based on symmetry arguments relating a nonzero toroidal moment to an antisymmetric Compton profile [21]. In addition to the Compton scattering explored here, this observation implicates other momentum-space k-resolved but spin-insensitive probes, such as angle-resolved photoemission spectroscopy (ARPES), as suitable for direct observation of magnetoelectric multipoles
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