  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.
