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

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 $\nu$ but different variances ${\sigma }_k$ 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 $U^t\hspace{0.5em}({\sigma }^2/{\nu }^2>~1,\hspace{0.5em}{\sigma }^2=\sum {\sigma }_k^2)$ 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 $\nu \gg k_j^i$ 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.