Theory of microwave eddy currents and paramagnetic resonance in materials of intermediate conductivity

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Abstract
An analysis has been made of the eddy currents in a conducting solid in the shape of a long rectangular prism, with the applied rf magnetic field perpendicular to the length. The results are expressed in terms of a complex susceptibility. This, in turn, is related to the changes in resonant frequency and quality factor of a microwave cavity when the sample is introduced at the site of a magnetic field antinode. The calculations are performed for conductivities in the range of values for which the skin depth is comparable to the transverse dimensions of the sample. Solution is by the Rayleigh-Ritz method applied to a variational expression for the dipole moment of the sample. Several representative rectangular cross sections are treated. Also, the results for the cylinder in a transverse field are presented in closed form. In addition to the eddy-current loss and resonant-frequency shift, results are given for the modulation of the loss by paramagnetic resonance. The integrated resonance absorption intensity and the line shape anisotropy for Lorentzian lines are presented. The results are applied to the case of tetrathiafulvalinium-tetracyanoquinodimethane (TTF-TCNQ).