Spin-wave impurity states in antiferromagnets

The case of a single impurity substituted in an otherwise ordered antiferromagnetic crystal is considered. The effect of the impurity is treated as a perturbation on the Hamiltonian of the perfect lattice. In order to write down the spin-wave eigenvector for the anti-ferromagnetic case, a factor φλ is introduced as the unknown phase difference between the spin deviations of the two sublattices. The matrix of the perturbation V is obtained explicitly in the site representation. The perturbed Green's function is related to V by the Dyson's equation and the conditions for the existence of new states are obtained by making use of the cubic symmetry of the lattice. It is seen that the new states may lie either inside or outside the continuum of spin-wave energies. States lying outside the band are localized states characterized by infinite lifetime. For the states which lie inside the spin-wave band, the line width is calculated