Spin Echo Decay in a Stochastic Field Environment

TL;DR

This paper develops a formalism to analyze spin echo decay in stochastic environments, revealing different decay behaviors depending on the field distribution, including exponential and stretched exponential forms.

Contribution

It introduces a general model based on strong collisions to derive spin echo decay in various stochastic field scenarios.

Findings

Identifies T2 minimum effect in certain field distributions.

Shows exponential decay in time cubed for short times in specific cases.

Demonstrates stretched exponential decay for Lorentzian distributions.

Abstract

We derive a general formalism with which it is possible to obtain the time dependence of the echo size for a spin in a stochastic field environment. Our model is based on ``strong collisions''. We examine in detail three cases where: (I) the local field is Ising-like, (II) the field distribution is continuous and has a finite second moment, and (III) the distribution is Lorentzian. The first two cases show a T2 minimum effect and are exponential in time cubed for short times. The last case can be approximated by a phenomenological stretched exponential.