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We present a comprehensive study of the temperature and doping dependence ofthe 500 meV peak observed at ${\bf q}=(\pi,0)$ in resonant inelastic x-rayscattering (RIXS) experiments on $\rm La_2CuO_4$. The intensity of this peakpersists above the N\'eel temperature (T$_{N}$=320 K), but decreases graduallywith increasing temperature, reaching zero at around T=500 K. The peak energydecreases with temperature in close quantitative accord with the behavior ofthe two-magnon $\rm B_{1g}$ Raman peak in $\rm La_2CuO_4$, and with suitablerescaling, agrees with the Raman peak shifts in $\rm EuBa_2Cu_3O_6$ and $\rmK_2NiF_4$. The overall dispersion of this excitation in the Brillouin zone isfound to be in agreement with theoretical calculations for a two-magnonexcitation. Upon doping, the peak intensity decreases analogous to the Ramanmode intensity and appears to track the doping dependence of the spincorrelation length. Taken together, these observations strongly suggest thatthe 500 meV mode is magnetic in character and is likely a two-magnonexcitation.

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