Calculation of the out-of-plane dynamical correlation for two-dimensional magnetic systems

The out-of-plane dynamical correlation functionsS ^zz (q, ) for two-dimensional easy-plane ferro- and antiferromagnets are calculated using a diagrammatic expansion for the temperature dependent Green function. Vortex-magnon interference effects on the multimagnon and vortex contribution toS ^zz (q, ) are also analised, in a classical context, for ferromagnets. Our calculations show that we cannot expect multimagnon processes to contribute to a central peak (=0) that has been observed in these systems for temperaturesT>T _c , whereT _c is the temperature at which a topological phase transition is predicted to occur. However, vortex-magnon interactions considerably reduce the intensity of the vortex induced central peak.