Spin relaxation and linear-in-electric-field frequency shift in an arbitrary, time-independent magnetic field

TL;DR

This paper introduces a method to calculate spin relaxation times and electric-field-induced frequency shifts in arbitrary magnetic fields within a rectangular cell, using a diffusion approximation and spatial cosine-transform components.

Contribution

It provides a general analytical approach for determining T1, T2, and frequency shifts in non-uniform magnetic fields for confined spins.

Findings

Derived formulas for T1, T2, and frequency shift in terms of magnetic field components.

Applicable to arbitrary, time-independent magnetic fields in rectangular geometries.

Facilitates analysis of spin dynamics in complex magnetic environments.

Abstract

A method is presented to calculate the spin relaxation times T1, T2 due to a non-uniform magnetic field, and the linear-in-electric-field precession frequency shift {\delta}{\omega}E when an electric field is present, in the diffusion approximation for spins confined to a rectangular cell. It is found that the rectangular cell geometry admits of a general result for T1, T2, and {\delta}{\omega}E in terms of the spatial cosine-transform components of the magnetic field.