Relaxation and modulation interference effects in two-pulse electron spin echo envelope modulation (ESEEM).

Two-pulse electron spin echo envelope modulation (ESEEM) line widths are influenced by transverse electron spin relaxation, which is in turn induced by local field fluctuations. Simultaneous analysis of the decays of the unmodulated and modulated parts of the ESEEM signal provides deeper insight into the relaxation of a spin system consisting of an electron spin 1/2 coupled to N(I) nuclei with spin 1/2. Standard two-pulse ESEEM formulas either do not account for relaxation or assume uniform relaxation for all lines. In general, the relaxation rates on allowed and forbidden transitions may not be the same. Experimental results obtained on a single crystal of Cu(II)-doped L-histidine suggest that such a difference exists. Theoretical considerations show that in such a case the product rule for two-pulse ESEEM does not extend to expressions including relaxation. Product rules in general do not properly account for relaxation in three-pulse ESEEM and HYSCORE experiments. Decay of the apparently non-oscillatory part of the two-pulse echo may be strongly affected by modulation interference. Such interference of difference frequencies of matrix nuclei may cause a rather flat initial feature, which was previously attributed solely to non-exponential phase relaxation of electron spin transitions due to spin diffusion of the matrix nuclei. In addition, the sometimes observed drastic initial decay of the time domain signal is related to modulation interference of multiple-quantum coherences that arise from a strong cross-suppression effect.