Cross peak intensities in two-dimensional four-pulse electron spin echo modulation spectra of deuteriums in single crystals

Abstract

The intensities of the cross peaks in two-dimensional deuterium four-pulse electron spin echo envelope modulation spectra of single crystals have been calculated by a first order approximation for two limiting cases where the deuterium hyperfine interactions is small or large with respect to the deuterium nuclear Larmor frequency. The analysis shows that four out of the eight possible cross peaks of the single quantum transitions have intensities linearly proportional to the modulation depth parameter in both limits. The intensities of the other four cross peaks together with the cross peaks of the double quantum transitions are proportional to higher order in the modulation depth parameter. Therefore, only four deuterium peaks will be observed in many experimental cases leading to a simplification of the two-dimensional four-pulse electron spin echo envelope modulation spectra. The presented analysis is supported by experimental spectra of two different single crystals and by simulations based on an exact diagonalization of the spin Hamiltonian. The impact of the simplification of the deuterium spectra on investigations in disordered systems is briefly outlined.