Evaluation of the spin wave Green's functions for rutile structure Heisenberg antiferromagnets with exchange between ions both on the same and opposite sublattices

A straightforward method is presented for the evaluation of the spin wave Green's function appropriate to the Raman scattering in the xy and xz geometry in rutile structure Heisenberg antiferromagnets with exchange between ions both on the same and on opposite sublattices and arbitrary local anisotropy. The analytical asymptotic behaviour of the Green's functions near the singularities is explicitly given and the problem of the numerical evaluation of their real and imaginary parts is discussed. Tables of the imaginary parts, calculated at the points corresponding to a Gaussian quadrature procedure in the appropriate interval, are supplied on request.