Theory of Line Narrowing by Double-Frequency Irradiation

Abstract

Starting from the general equation for the distribution matrix, magnetic resonance absorption in crystals is treated by introducing the Fourier transform of the resonance line which is shown to have the convenient form of a simple trace. The method is first applied to rederive some earlier results of Van Vleck, concerning the moments of the line. It is then extended to include the case of the following experimental paper, where resonance absorption of one magnetic ingredient is observed while another magnetic ingredient is at the same time subjected to a strong resonant rf field. It is shown that the absorption line exhibits a center line and faint sidebands, and formulas for the intensity and shape of these lines are developed. In particular, it is shown that the total second moment of the absorption is unaltered by irradiation of the other ingredient. A quantitative measure for the observed narrowing of the center line is found through the reduction of its second moment, which is compensated by the contribution of the sidebands to the total second moment.