Rotons and spin transport in square lattice antiferromagnets in magnetic fields

We investigate the excitation spectrum and spin conductivity in square lattice antiferromagnets by nonlinear spin-wave theory. We have found that the excitation spectrum have a rotonlike minimum at about 3/4 of the saturation field. The «roton» appears and softens rapidly to zero as a function of the magnetic field as a result of the especially strong three-magnon interactions. For the spin conductivity, it becomes clear that a two-magnon sideband appears for sufficiently strong three-magnon interactions.