Continuous wave multiquantum electron paramagnetic resonance spectroscopy. IV. Multiquantum electron–nuclear double resonance

Abstract

We report a theoretical and experimental investigation of the interaction of a coupled electron–nuclear spin system with three electromagnetic fields: two equally intense microwave fields resonant with the electron spin, and one radio-frequency field resonant with the nuclear spin. This is an electron–nuclear double-resonance experiment where the effect of the nuclear transition is detected via changes of the electron multiple photon transitions (MQ-EPR) rather than steady-state saturation and, therefore, is called multiquantum electron–nuclear double resonance (MQ-ENDOR). The theoretical framework previously developed for the description of multiple photon phenomena in a two level system is extended to the case of a four level system. The equation of motion of the density matrix is solved in the presence of three fields, which results in five master equations relating various populations and coherences. A ten photon approximation is used to study the functional dependence on spectral parameters and determine the sensitivity of this technique to spin relaxation rates. The experimental investigation is carried out on a sample of tri-t-butyl phenoxyl radical dissolved in mineral oil. At low values of the electron saturation factor Se, the rf-swept MQ-ENDOR is a de-enhancement of the 3Q-EPR signal (i.e., the first intermodulation sidebands). As the microwave field strength increases, the MQ-ENDOR signal changes phase by 180° due to dominance of generalized saturation. Higher order MQ-EPR signals (i.e., higher order sidebands) have larger negative enhancement and tend to display smaller positive enhancement. Line splitting results if the microwave frequency difference or field strength is increased. The dependence of MQ-ENDOR displays on various spectral parameters was found to be consistent with the general trends predicted by the theory. These displays provide a convenient way to estimate electron and nuclear relaxation rates.