Schwinger bosons and hydrodynamics of two-dimensional magnets

Motivated by the strong experimental evidence in favor of the crucial role of antiferromagnetic fluctuations in copper oxide superconductors, I considered low-temperature properties of the disordered two-dimensional ferromagnets and antiferromagnets by means of the now-familiar Schwinger boson approach. The main aim of the paper was to go beyond the mean-field approximation and to derive an expression for the dynamical susceptibility (q,) in the hydrodynamic region where the energies of physical excitations, which are collective modes in Schwinger boson approach, are small in comparison with the characteristic damping rate of single-particle excitations. In ferromagnets, the order parameter (magnetization) is a conserved quantity and the pole of (q,) near q=0 describes a diffusion mode with =-iDq2. In antiferromagnets, the low-energy part of the spectrum involves the fluctuations of the (conserved) uniform magnetization and (nonconserved) antiferromagnetic order parameter. Correspondingly, a dynamical susceptibility near q=0 also has a pole for a diffusion mode, =-iDq2, while that near q=(,) descibes a relaxation mode with a finite gap. The temperature variations of D and as well as of the antiferromagnetic part of spin-lattice relaxation rate are calculated and a comparison is made with the experimental data and with the works of other authors.