Determination of hyperfine interactions from the magnetic field dependence of nuclear modulation frequencies: An electron spin echo envelope modulation study of protons in γ-irrradiated potassium dihydrogen arsenate

Abstract

A study is presented of the field dependence of proton ESEEM (electron spin echo envelope modulation) of the AsO4−4 center in γ-irradiated single crystals of KDA (potassium dihydrogen arsenate). Modulation patterns and corresponding spectra were registered over the range of external field strengths spanned by the nominally allowed EPR transitions (∼3.5 kG) with the field orientation selected along the crystallographic c axis. By tracking the external field dependence of the ESEEM frequencies of the protons attached and hydrogen-bonded to the AsO4−4 center, the absolute value of both the secular and nonsecular portions of their hyperfine interactions, as well as the sign of the secular component, are determined. The results are compared with those obtained by ENDOR (electron-nuclear double resonance) spectroscopy. The implications of this work for the determination of the magnitudes and signs of the elements, principal values, and direction cosines of the principal axes of hyperfine interaction matrices in orientationally disordered solids are discussed in detail. The large hyperfine coupling to the 75As nucleus has important ramifications upon the ESEEM spectroscopy and its analysis. In general, such couplings increase the breadth of the EPR spectrum and thereby facilitate the survey of ESEEM field dependences; they can also seriously complicate the analysis of the ESEEM results by precipitating significant deviations between the magnitude of the expectation value of the electron spin angular momentum and its nominal value, MS: ESEEM frequency expressions in which these two quantities are implicitly equated are not generally applicable. This issue is commented on in detail. Expressions are derived and discussed that elucidate the effect of a large hyperfine coupling on the magnitude of the expectation value of the electron spin, its deviations from MS, and the consequent shifts in ESEEM frequencies. Experimental situations in which these deviations and shifts are negligible are delineated. These effects are illustrated with the results of our 1H ESEEM study of the AsO4−4 center in KDA.