The electron spin echo envelope modulation (ESEEM) effect is the key element of many powerful pulsed EPR techniques that are used to determine weak hyperfine and nuclear quadrupole interactions in solids. These include methods that are based on electron spin coherence like the primary two-pulse and refocused primary echo sequences, or schemes that are based on evolution of nuclear spin coherence like three-pulse, four-pulse, hyperfine sublevel correlation (HYSCORE) and double nuclear coherence transfer (DONUT)-HYSCORE. While some of these methods provide optimum resolution for given paramagnetic systems, they may suffer from poor sensitivity due to small modulation depths, low abundances of magnetic nuclei and/or additional multinuclear suppression effects. For this reason, the development of methods with improved sensitivity or towards resolution enhancement is an important field of modern EPR spectroscopy.

• Measurement of reliable electron spin coherence times with dynamical decoupling methods

With increasing interest in spin-based quantum computing and the quest for paramagnetic systems with long relaxation times, the measurement of reliable electron spin coherence times has become of paramount importance. Dynamical decoupling pulse EPR methods such as Carr-Purcell-Meiboom-Gill (CPMG) or XY4- and XY8-based sequences play a key role in this effort, as they help to disentangle different sources of decoherence and potentially reveal the intrinsic T₂ value, while they also provide a means to probe the noise spectrum of the paramagnetic system under study. Although these methods are mainly evaluated for their robustness and ability to mitigate pulse imperfections, to date little attention has been paid to the selectivity of the microwave (mw) pulses, despite the fact that they are consistently applied to paramagnetic systems having a wide range of line widths relative to the pulse excitation bandwidth.

As partial excitation of the spectrum of metal complexes is the norm in pulsed EPR spectroscopy, this factor can hinder the reliable determination of T₂ in two ways: first, unwanted stimulated echoes, which decay with T₁, overlap with desired refocused echoes, resulting in overestimated values of T₂. Second, under selective mw excitation, the amplitude of the different refocused echoes shows additional time decay even in the absence of relaxation processes.

Due to the complexity of the problem, one cannot predict the contribution of unwanted stimulated echoes to the reliable determination of T₂ in a straightforward way. Here, we investigate the characteristics of CPMG, XY4 and XY8-based sequences by performing numerical simulations for a two-level spin system. We show that our numerical calculations reproduce well all the features of the experimental echoes and allow for the accurate determination of T₂ times without the need to perform tedious phase-cycle protocols to eliminate unwanted signals.

• Modulation depth enhancement using pulse trains

In the present work we study a new way to increase the modulation amplitude of ESEEM experiments by applying multiple refocusing π-pulses on the electron spin coherence created initially by a π/2-pulse. Each one of these pulses redistributes the electron spin coherence among allowed and forbidden EPR transitions and this in turn leads to a significant enhancement of the ESEEM effect, depending on the strength of the hyperfine interaction and the number of applied pulses, N. We derive analytical expressions for a general two-dimensional (2D) scheme and we explore the expected modulation enhancement of various correlation peaks as a function of k (modulation depth parameter) and N. Our study shows that these methods are particularly useful for detecting weak hyperfine couplings of magnetic nuclei having small g_n factors and low natural abundances like ¹³C and ²⁹Si.

Reference

1. Measuring reliable electron spin coherence times with dynamical decoupling sequences that use selective mw pulses, George Mitrikas, Rania Giourtsidou, J. Magn. Reson. 381, 107981 (2025) DOI: 10.1016/j.jmr.2025.107981
2. Modulation depth enhancement of ESEEM experiments using pulse trains, G. Mitrikas, G. Prokopiou, J. Magn. Reson. 254, 75-85 (2015) DOI: 10.1016/j.jmr.2015.03.002