Related Experiment Video
Updated: Sep 17, 2025
08:01
Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
Published on: November 21, 2019
7.2K
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.
Science and Technology of Advanced Materials
|July 2, 2025
Summary
This study refines X-ray magnetic circular dichroism (XMCD) and X-ray magnetic linear dichroism (XMLD) sum rules using a complete multipole basis. It enables distinguishing spinless and spinful multipoles, clarifying magnetic behavior in materials.
Area of Science:
- Solid-state physics
- Spectroscopy
- Materials science
Background:
- X-ray magnetic circular dichroism (XMCD) and X-ray magnetic linear dichroism (XMLD) are key techniques for studying magnetism in solids.
- Existing sum rules require refinement for a comprehensive understanding of magnetic properties.
Purpose of the Study:
- To revisit and extend XMCD and XMLD sum rules within a complete magnetic multipole framework.
- To provide a unified and symmetry-consistent theoretical approach for analyzing magnetic dichroic signals.
- To offer new insights into the microscopic origins of magnetic behavior.
Main Methods:
- Development of a theoretical framework based on a complete magnetic multipole basis (including spinless and spinful multipoles).
- Application of sum-rule formalism to distinguish and detect individual multipoles.
- Derivation of sum rules for XMCD and XMLD, including anisotropic magnetic dipole and electric quadrupole contributions.
Main Results:
- Demonstration that spinless and spinful multipoles can be individually resolved using the sum-rule formalism.
- Microscopic origin of ferromagnetic-like behavior in antiferromagnets identified through the anisotropic magnetic dipole term in XMCD.
- Derivation of new sum rules for out-of-plane and in-plane XMLD, incorporating electric quadrupole effects.
Conclusions:
- The complete multipole basis provides a unified framework for analyzing XMCD and XMLD signals.
- This approach deepens the understanding of magnetic properties and spin-orbit coupling in magnetic materials.
- Opens new avenues for investigating complex magnetic structures and emergent magnetic phenomena.
Related Concept Videos
01:13¹H NMR: Complex Splitting
1.4K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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...
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...
1.4K
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
1.4K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.4K
01:05Atomic Nuclei: Magnetic Resonance
764
The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
764
01:13¹H NMR Signal Multiplicity: Splitting Patterns
5.3K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
5.3K
01:08Spin–Spin Coupling Constant: Overview
1.0K
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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...
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...
1.0K
01:23Atomic Nuclei: Nuclear Relaxation Processes
728
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
728