Related Experiment Video
Updated: Sep 17, 2025

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
Published on: November 21, 2019
Sum rules for X-ray circular and linear dichroism based on complete magnetic multipole basis
Y Yamasaki1,2,3, Y Ishii1, N Sasabe1
1Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba, Japan.
Abstract:
X-ray magnetic circular dichroism (XMCD) and X-ray magnetic linear dichroism (XMLD) are powerful spectroscopic techniques for probing magnetic properties in solids. In this study, we revisit the XMCD and XMLD sum rules within a complete magnetic multipole basis that incorporates both spinless and spinful multipoles. We demonstrate that these multipoles can be clearly distinguished and individually detected through the sum-rule formalism. Within this framework, the anisotropic magnetic dipole term is naturally derived in XMCD, offering a microscopic origin for ferromagnetic-like behavior in antiferromagnets. Furthermore, we derive the sum rules for out-of-plane and in-plane XMLD regarding electric quadrupole contributions defined based on the complete multipole basis. Our theoretical approach provides a unified, symmetry-consistent framework for analyzing dichroic signals in various magnetic materials. These findings deepen the understanding of XMCD and XMLD and open pathways to exploring complex magnetic structures and spin-orbit coupling effects in emergent magnetic materials.
Related Concept Videos
¹H NMR: Complex Splitting
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
Atomic Nuclei: Magnetic Resonance
¹H NMR Signal Multiplicity: Splitting Patterns
Spin–Spin Coupling Constant: Overview
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
Atomic Nuclei: Nuclear Relaxation Processes

