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 Heisenberg antiferromagnets by extending the formula of Nomura and Igarashi [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 for 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 while the other is a two-magnon correlation function. We evaluate the former factor for La₂CuO₄ in terms of the density of states of the $4p$ states obtained by a band calculation. We also calculate the two-magnon correlation function as a function of energy loss ω and momentum transfer 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 ω=3J for $S=1∕2$ on the magnetic Brillouin zone boundary and vanish at q=(0,0) and (π,π). Such momentum dependence of the RIXS spectra could provide an excellent opportunity to study the dynamics in the Heisenberg model.