Sub-picosecond molecular dynamics modulate the energies of spin states for hundreds of nanoseconds

TL;DR

This study demonstrates how molecular vibrations on sub-picosecond timescales can cause rapid fluctuations in spin energy levels, but these effects average out over longer periods, impacting the understanding of spin dynamics in molecular magnets.

Contribution

The paper introduces a cost-effective method combining molecular dynamics and crystal field analysis to dynamically model spin energy level fluctuations over hundreds of nanoseconds.

Findings

Spin energy levels oscillate with amplitudes up to tens of cm-1 on femtosecond timescales.

Oscillations diminish and average out over longer timescales, reducing long-term modulation effects.

Long-wavelength phonons do not significantly modulate spin energy levels at longer timescales.

Abstract

Molecular vibrations are increasingly seen as a key factor for spin dynamics in single-ion magnets and molecular spin qubits. Herein we show how an inexpensive combination of molecular dynamics calculations and a crystal field analysis can be employed to obtain a dynamical picture of the crystal field splitting. We present the time evolution during 500ns of the spin energy levels in a terbium complex. Our calculations evidence an amplitude of up to tens of cm-1 for the oscillations of the spin energy levels in the fs time scale. Crucially, we also see that the oscillations average out and practically disappear at longer time scales, thus ruling out the modulation of spin energy levels by phonons of long wavelength $\lambda$ (up to $\lambda$ = 40 $\AA$). Our results are compatible with the common approximation of focusing on local vibrations, but at the same time highlight the risks of assuming that the spin energy levels are time- and temperature-independent.