Frequency dependent faraday rotation in paramagnetic crystals

Abstract

The plane of polarization of a light beam traversing a diamagnetic CaF2 crystal doped with paramagnetic Eu++ and subjected to simultaneous ac and dc magnetic fields is modulated by Faraday rotation. The Faraday rotation is proportional to the magnetization of the crystal, which consists of the sum of paramagnetic ,and diamagnetic parts. The relative amount of Eu++ present in each crystal is calculated from static rotation data and confirmed by data taken with a Cary 14 spectrophotometer. The frequency of the ac magnetic field is varied from 2 to 200 Hz. Diamagnetic relaxation times are of the order of 10^-12 seconds; therefore the diamagnetic rotation is effectively in phase with the ac magnetic field. Since the paramagnetic relaxation times, tau, are of the order of 10^-3 seconds, the phase and the amplitude of the resulting light signal are each modulated by the paramagnetic rotation by a measureable amount. Theory is developed to correlate tau with the dynamic Faraday rotation. The phase and the amplitude data are each analyzed to determine values of tau, and the values obtained by the two different calculations are shown to be in agreement. The range of agreement between theory and phase data shown in previous work is extended, and agreement between theory and amplitude data is shown for the first time. The values of tau are found to be independent of the concentration of Eu++ present in the crystal over the range of values used, and inversely dependent upon temperature between 11.2ºK, where tau equals 0.01 seconds, and 3.2ºK, where L equals 0.08 seconds, when the de magnetic field is 5800 Gauss. The magnetic field dependence of tau is approximately linear for small fields, but begins to saturate above fields of 3000 Gauss.