Effect of electric field on NMR spectra in centroantisymmetric antiferromagnets

A symmetry approach is used to study the influence of electric field E on the NMR frequency spectrum of antiferromagnets of the rhombohedral (Cr2O3) and tetragonal (e.g., the Fe2TeO6 trirutiles) systems exhibiting a linear magnetoelectric (ME) effect. The latter originates from the presence in their magnetic structure of an antisymmetry center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar 1'$$ \end{document}. It is shown that besides the trivial effect of E on the NMR frequency through the total magnetization induced by the ME phenomenon, there also exists an independent mechanism of a direct action of electric field on the local field at the nuclei, which can, in particular, produce an additional NMR frequency splitting. The dependence of this effect on the exchange magnetic structure and orientational state is considered.