TIME-DEPENDENCE OF SPIN-WAVE DAMPING IN SHORT PULSES

The influence of thermal magnons on evolution of a spin-wave packet is studied. For a short packet, if its length is shorter than the time of phase mixing the damping is small and proportional to the length. If the length of the packet is greater than the time of phase mixing the magnon damping can be obtained from the kinetic equation. The evolution equation for a packet with an arbitrary length is derived. In particular, if the packet arises instantly, one should replace delta(DELTA-omega-k) --> sin(DELTA-omega-k(t))/DELTA-omega-k in the energy conservation condition in the kinetic equation to allow for the time dependence of the damping. The characteristic time of phase mixing tau-ph is of the order of 1/DELTA-omega-k. As a rule DELTA-omega-k approximately omega-k, so the time tau-ph is of the order of the spin-wave period. If the thermal magnon dispersion is small, the damping grows slowly. This occurs when a nuclear spin wave with a large wave vector is excited. A slow growth of damping can occur in a quasi-one-dimensional antiferromagnet also.