Anomalous pulse angle dependence of the single and double quantum echoes in a photoinduced spin-correlated coupled radical pair

In this work the response of a spin-correlated coupled radical pair to the sequence flash-t-P _ζ-τ-P _2ζ-T is investigated. For the theoretical analysis, the density operator formalism is used. Analytical expressions are derived for the electron spin single (SQ ESE) and double-quantum echoes (DQ ESE) as a function of pulse flip angle and singlet-triplet mixing angle. To illustrate the theoretical results, computer simulations are presented. In the limit of weak coupling, the “out-of-phase” SQ ESE is shown to be of a pure two-spin order having the maximal amplitude for the flip angle of 65.9°. The echo following the Hahn sequence vanishes in the same limit. This confirms the theoretical result already presented in the literature. However, the more general analysis shows that outside the weak coupling approximation the Hahn echo is of purely one-spin order, whereas the echo following the flash-t-P _ζ-τ-P _2ζ-t sequence has its maximal amplitude for the flip angle of 75° and the singlet-triplet mixing angle of 27°. The “in-phase” single- and double-quantum echoes are shown to vanish due to averaging out, within the electron spin resonance spectrometer deadtime, of contributions modulated with the sum and difference of the zero-quantum beat frequency and the frequency due to the spin-spin interaction within the pair. The calculated out-of-phase DQ ESE signal is inverted with respect to the out-of-phase SQ ESE and has only the half of its amplitude. The DQ ESE vanishes for the Hahn sequence. The echo has maximal amplitude in the weak-coupling limit for the flip angle of 65.9°. In contradiction to the analytical result previously published, the out-of-phase DQ ESE does not vanish for long τ and large zero-quantum-beat frequency.