Low-temperature exchange narrowing of the ESR line

The relaxation function method (Kubo–Tomita theory) is generalized to arbitrary temperatures on the basis of the admissibility of a semiinvariant representation for the correlation functions. The given generalization is used to investigate the exchange-narrowing effect at low temperatures, for which the odd-order moments of the magnetic resonance line are nonvanishing. On the assumption of a Gaussian distribution function for the local field, expressions are derived for calculating the shift and width of the resonance line. It is shown that the shift is nonzero even when the first moment of the line is zero. It is suggested that the isotropic exchange-coupling parameter between identical spins can be determined from measurements of the shift of the resonance line.