Theory of non-Markovian relaxation of single triplet electron spins using time- and frequency-domain magnetic resonance spectroscopy measured via optical fluorescence: Application to single pentacene molecules in crystallinep-terphenyl

Abstract

Fluorescence-detected magnetic resonance (FDMR) allows one to monitor magnetic resonance phenomena via fluorescence. Experimental FDMR data obtained using single triplet-state chromophore guest molecules in a low-temperature organic host matrix are analyzed using a stochastic approach to describe triplet electron spin dephasing resulting from frequency fluctuations ${U}^{t}$ induced by host-matrix proton spin dynamics. Modeling the fluctuations ${U}^{t}$ by a sum of N independent random telegraph processes with the same jump rate $\ensuremath{\nu}$ but different variances ${\ensuremath{\sigma}}_{k}$ we construct an exact set of equations for the density matrix of a five-level molecule averaged over fluctuation histories ${U}^{t}.$ These equations provide a basis to study non-Markovian effects of microwave- (MW-) field-dependent dephasing in the FDMR response of a molecule undergoing slow fluctuations ${U}^{t} ({\ensuremath{\sigma}}^{2}/{\ensuremath{\nu}}^{2}>~1, {\ensuremath{\sigma}}^{2}=\ensuremath{\sum}{\ensuremath{\sigma}}_{k}^{2})$ to a MW field that is resonant with a transition between triplet spin substates. Both frequency- and time-domain FDMR phenomena such as (i) power-broadened FDMR line shapes, (ii) FDMR Hahn echo signals, and (iii) FDMR free induction decay are studied. Analytical expressions for the FDMR response are obtained in the case $\ensuremath{\nu}\ensuremath{\gg}{k}_{j}^{i}$ where ${k}_{j}^{i}$ is an intersystem crossing rate. Experimental data on power-broadened line shapes for a pentacene+p-terphenyl pair which demonstrate a pronounced effect of MW-field-suppressed dephasing are explained in the context of the theory.