Dynamic spin susceptibility in the $t$–$J$ model

The dynamic spin susceptibility is calculated for the $t$–$J$ model in the paramagnetic phase using the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained in the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. The spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.