Integrated-Magnetic-Resonance-Absorption Dependence on the Resonance Frequency and Spin-Hamiltonian Parameters for a Non-Kramers Doublet

Abstract

A model is derived for the frequency dependence of the magnetic-resonance integrated absorption for non-Kramers doublets. The integrated electron-paramagnetic-resonance absorption is shown to be independent of the resonance frequency through second order in the crystal field perturbation for transitions within a non-Kramers doublet. This in in large contrast with the frequency-squared dependence in first order for the acoustical-paramagnetic-resonance and the paraelectric-resonance integrated intensities. For the cases of the acoustical-paramagnetic-resonance and paraelectric-resonance integrated absorptions as functions of the resonance frequency squared, the intercept is shown to depend explicitly upon the zero-field splitting of the states of the doublet. The slopes determine the relative strengths of the acoustical-paramagnetic-resonance and paraelectric-resonance absorptions. A transformation is derived from the spin Hamiltonian which transforms the absorption line shape from that in field variation ($H$) to that in frequency variation ($\ensuremath{\nu}$). The transformation shows that the line shapes in the two cases are basically different when the absorption line is broadened by crystal field perturbations. The model predicts that the integrated intensity in frequency variation is greater than that in field variation by a term proportional to the average value of the square of the crystal field perturbations.