Theory of phonon-assisted multimagnon optical absorption and bimagnon states in quantum antiferromagnets

We calculate the effective charge for multimagnon infrared absorption assisted by phonons in a perovskitelike antiferromagnet and we compute the spectra for two-magnon absorption using interacting spin-wave theory. The full set of equations for the interacting two-magnon problem is presented in the random-phase approximation for arbitrary total momentum of the magnon pair. The spin-wave theory results fit very well the primary peak of recent measured bands in the parent insulating compounds of cuprate superconductors. The line shape is explained as being due to the absorption of one phonon plus a new quasiparticle excitation of the Heisenberg Hamiltonian that consists of a long-lived virtual bound state of two magnons (bimagnon). The bimagnon states have well-defined energy and momentum in a substantial portion of the Brillouin zone. The higher-energy bands are explained as one phonon plus higher multimagnon absorption processes. Other possible experiments for observing bimagnons are proposed. In addition we predict the line shape for the spin-1 system ${\mathrm{La}}_2$ ${\mathrm{NiO}}_4$.