Two-magnon excitations in resonant inelastic x-ray scattering from quantum Heisenberg antiferromagnets

We study two-magnon spectra in resonant inelastic x-ray scattering (RIXS) from the Heisenberg antiferromanets by extending the formula of Nomura andIgarashi (Phys. Rev. B 71, 035110 (2005)). The core-hole potential in the intermediate state of RIXS gives rise to a change in the exchange coupling between 3d electrons, leading to an effective interaction between the core hole and spins of 3d electrons. We derive a formula suitable to calculate the two-magnon RIXS intensities, replacing the bare core-hole potential responsible to charge excitations by this effective interaction creating two magnons in our previous formula. It consists of two factors, one of which determines the incident-photon-energy dependence and another is the two-magnon correlation function. We evaluate the former factor for La_{2}CuO_{4} in terms of the density of states of the 4p states obtained by the band calculation. We also calculate the two-magnon correlation function as a function of energy loss \omega and momentum transfer \textbf{q} of the Heisenberg model on a square lattice,by summing up the ladder diagrams after transforming the magnon-magnon interaction into a separable form. The calculated spectra form a broad peak around \omega=3J for S=1/2 on the magnetic Brillouin zone boundary and vanish at \textbf{q}=(0,0) and (\pi,\pi). Such momentum dependence of the RIXS spectra could provide an excellent opportunity to study the dynamics in the Heisenberg model.