The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency

We investigate the high-temperature relaxation function of a spin system with quadratic coupling of the resonance frequency to the Gaussian random process. In the general case, this function is expressed as an integral of an infinite auxiliary series. For the $N$-exponential Gauss–Markov process, the problem is reduced to solving a system of $2N$ linear equations. For brevity, we analyze the effect of fluctuations on the form of the magnetic resonance line (the Fourier image of the relaxation function). For both the one- and multiexponential processes in a crystal with dynamics of a relaxation type in the continuous phase transition domain, we find a nonmonotonic dependence of the asymmetrical homogeneously widened resonance line on the rate of fluctuations.