Some Aspects of Paramagnetic Relaxation

Abstract

This paper concerns the effect of interactions inside the spin system in giving a finite line width to the energy absorption lines in an oscillating magnetic field. The principal calculations are of absorption coefficients at low frequencies for copper salts. These absorption coefficients refer in most cases to the aperiodic line near zero frequency and not to the Larmor line. The first step is a discussion of the general procedure for reconstructing a shape function $f\left(\nu \right)$ from its moments. The special case in which the zeroth, second, and fourth moments are known arises in the absence of a constant magnetic field, and at the Larmor frequency in a constant magnetic field perpendicular to the oscillating field. These cases are discussed and compared with experiment in Section III; extensive calculations have already been made by Van Vleck in the second case. The magnitude of the exchange coupling is the decisive factor, as pointed out by Gorter and Van Vleck; and various methods of calculating this magnitude from experimental data are given. Low frequency absorption in a perpendicular field is discussed on the basis of a Gaussian approximation in Section IV, and the agreement with the experiments of Volger, Vrijer, and Gorter is good. In Section V it is shown that quantitative calculations only emphasize the discrepancy, pointed out by Broer, between theory and experiment for low frequency absorption in a parallel constant field. An explanation of the discrepancy is given in terms of the difficulty in resolving out the different lines in this case, due to the exchange broadening of the Larmor line, in contrast to the exchange narrowing of the Larmor line in a perpendicular field. In Section VI a calculation of the isolated susceptibility of a spin system is given for strong fields; it is found to be 0.80 of the thermodynamic or adiabatic susceptibility of Casimir and du Pré, even in the absence of exchange.