Two-Spin Light Scattering in Heisenberg Antiferromagnets

Abstract

Since its first experimental observations¹ two-spin Raman scattering in antiferromangets has proved to be a very useful tool to study the high-wavevector magnetic excitations in these systems. The scattering cross section turns out² to be proportional to the Fourier transform of <M(O)N(t)> where the Raman transition operator is given by

$$M = \sum\nolimits_{\vec k} {{\Phi _k}\left( {{{\vec S}_{\vec k}} \cdot {{\vec S}_{ - \vec k}}} \right)}$$

((1))

Here ${\vec S_k}$ is the space Fourier transform of the site spin operators and Φ_k is a weighting factor determined by the field polarizations and by crystal symmetry. In the following we shall explicitly refer to three-dimensional cubic antiferromagnets like RbMnF₃ and KNiF₃, which are well described by a Heisenberg Hamiltonian with exchange J limited to the z nearest neighbours of a given spin.