Two spin deviations in two and three dimensions with next nearest neighbour interactions

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Abstract
The problem of one and two spin deviations from the fully aligned state is studied for regular solids in two and three dimensions for the Hamiltonian (J(i,j)>0) H=-1/2 Sigma (nn)J(i,j)Si.Sj-1/2 alpha Sigma (nnn)J(i,j)Si.Sj where (nn) and (nnn) mean nearest and next nearest neighbour interactions, respectively, using a Green function technique. It is shown that for S=1/2 the two spin wave bound states are somewhat sensitive functions of alpha . As alpha increases they tend to go into the continuum. On the boundary of the Brillouin zone Kx=Ky= pi in two dimensions, and Kx=Ky=Kz= pi in three dimensions, the critical values of alpha for merging into the continuum are l/ pi and 0.093 respectively.

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