Magnetic nature of the 500 meV peak in $rm La_{2-x}Sr_{x}CuO_4$ observed with resonant inelastic x-ray scattering at the Cu $K$-edge

We present a comprehensive study of the temperature and doping dependence of the 500 meV peak observed at ${bf q}=(pi,0)$ in resonant inelastic x-ray scattering (RIXS) experiments on $rm La_2CuO_4$. The intensity of this peak persists above the Neel temperature (T$_{N}$=320 K), but decreases gradually with increasing temperature, reaching zero at around T=500 K. The peak energy decreases with temperature in close quantitative accord with the behavior of the two-magnon $rm B_{1g}$ Raman peak in $rm La_2CuO_4$, and with suitable rescaling, agrees with the Raman peak shifts in $rm EuBa_2Cu_3O_6$ and $rm K_2NiF_4$. The overall dispersion of this excitation in the Brillouin zone is found to be in agreement with theoretical calculations for a two-magnon excitation. Upon doping, the peak intensity decreases analogous to the Raman mode intensity and appears to track the doping dependence of the spin correlation length. Taken together, these observations strongly suggest that the 500 meV mode is magnetic in character and is likely a two-magnon excitation.