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Spin–Spin Coupling Constant: Overview

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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.
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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.

Paramagnetism

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Diamagnetism

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Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
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Related Experiment Video

Updated: Sep 5, 2025

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

Spin-phonon dispersion in magnetic materials.

Mingqiang Gu¹, Y H Bai², G P Zhang³

¹Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|July 6, 2022

Summary

We introduce spin-phonon dispersion to map electron spin changes with lattice vibrations. This new concept reveals distinct spin enhancement and reduction branches, advancing our understanding of magnetic materials.

Keywords:

Elliot-Yafet dispersion force matrix magnetism phonon spin

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

Microscopic spin-phonon coupling drives exotic properties in magnetic and non-magnetic materials.
Traditional spin-phonon coupling constants inadequately describe complex electromagnetic behaviors.

Purpose of the Study:

Introduce and define spin-phonon dispersion for comprehensive spin moment analysis.
Map the entire spin change along phonon crystal momentum.
Extend the Elliott-Yafet theory to magnetic materials.

Main Methods:

Developed the concept of spin-phonon dispersion.
Analyzed spin moment changes along phonon crystal momentum.
Studied bcc Fe and hcp Co using spin force matrix analysis.

Main Results:

Spin-phonon dispersion exhibits positive (enhancement) and negative (reduction) frequency branches.
The spin force matrix in Fe and Co shows smaller diagonal elements compared to off-diagonal ones.
This asymmetry results in distinctive spin-phonon dispersion patterns.

Conclusions:

Spin-phonon dispersion provides a more complete picture of spin-lattice interactions than traditional methods.
This framework enables the study of excited states in magnetic materials like CoF2 and NiO.
The findings open new avenues for exploring THz-regime spin-lattice coupling.