The coupling of spin waves in a finite Heisenberg system

Abstract

The coupling of spin waves for a Heisenberg system with a finite size is studied. It is found that the final results are boundary condition dependent. For a periodic system, the finite-size effect weakens the coupling of spin waves and an additional term proportional to -T72//N appears with N, the system's size, in the expression for the number density of spin waves at temperature T. The free boundary greatly complicates the coupling of spin waves. There are three new kinds of scattering process: between spin waves parallel to the free surfaces of the system, between spin waves parallel to the surface and other waves, and between spin waves with the same components in the direction perpendicular to the free surface of the system. Unlike the others, the last effective interaction tends to depress the excitation of spin waves at low temperatures.