Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

TL;DR

This paper introduces a new mathematical model for analyzing the time evolution of dynamic nuclear polarization in the thermal mixing regime, accounting for electron and nuclear spin interactions without assuming predefined electron polarization forms.

Contribution

It provides a quantitative framework that recovers known thermodynamic predictions and explains deviations observed in experiments by relaxing certain assumptions.

Findings

The model recovers Borghini's thermodynamic prediction under fast electron-nuclei transition rates.

Deviations from the prediction occur when transition rates are slower and nuclear leakage is present.

Numerical results match various dynamical behaviors observed in DNP experiments.

Abstract

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that recovers the well known Borghini prediction based on thermodynamics arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows to calculate nuclear polarization and relaxation times, once specified the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species. Numerical results are shown to account for the manifold dynamical behaviours of typical DNP samples.