Spin-Wave Model of Free Induction Decay in Ring Spin Cluster

The study presents an analysis of free induction decay (FID) in the ensemble of ring spin clusters using the formalism of collective modes similar to the spin waves. A dispersion relation for the waves is obtained. FID from a spin cluster is estimated and averaged over system parameters to simulate the signal given by a spherical structure or by an ensemble of rings withrandom orientation. There exists a fast relaxation according to the Gaussian law in the initial time interval. After T2, the signal decays as a power function which matches the direct numerical simulations of the signal from the ring clusters.