Vertex functions, spectral weights, and anisotropy in phonon-assisted multimagnon optical absorption

We discuss the general vertex function coupling light with phonon-assisted multimagnon excitations in perovskitelike antiferromagnets. We make a symmetry analysis and use exact diagonalization of a multiband Peierls-Hubbard Hamiltonian in a small cluster to propose a simple parametrization of the vertex. The parameters obtained determine the strength of the spectral weight, the optical anisotropy, and the momentum dependence of the vertex. The nonperturbative results are compared with perturbation theories in the hybridization. We find that although the momentum dependence of the vertex is similar to the one obtained in perturbation the absolute values renormalize strongly and the anisotropy in lamellar compounds changes in two orders of magnitude. This explains the success of the perturbative computation in getting the correct line shape for phonon-assisted multimagnon absorption [J. Lorenzana and G. A. Sawatzky, Phys. Rev. Lett. 74, 1867 (1995)] but the poor results for the strength of the optical anisotropy. Our calculated values of the anisotropy are in good agreement with experiments.