Electron Magnetic Resonance: The Modified Bloch Equation

TL;DR

This paper derives a modified Bloch equation for electronic magnetic moments that include diamagnetic effects, revealing how these moments oscillate and absorb energy in magnetic fields, with explicit analysis for p-state electrons.

Contribution

It introduces a modified Bloch equation incorporating diamagnetic contributions and couples it with equations of motion, advancing understanding of magnetic resonance phenomena.

Findings

Magnetic moments oscillate out of phase with magnetic fields.

Power absorption occurs without environmental coupling.

Spectrum and absorption are explicitly calculated for p-state electrons.

Abstract

We find a modified Bloch equation for the electronic magnetic moment when the magnetic moment explicitly contains a diamagnetic contribution (a magnetic field induced magnetic moment arising from the electronic orbital angular momentum) in addition to the intrinsic magnetic moment of the electron. The modified Bloch is coupled to equations of motion for the position and momentum operators. In the presence of static and time varying magnetic field components, the magnetic moment oscillates out of phase with the magnetic field and power is absorbed by virtue of the magnetic field induced magnetic moment, even in the absence of coupling to the environment. We explicitly work out the spectrum and absorption for the case of a $p$ state electron.