By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we measured the spin wave dispersion along $langle$100$rangle$ and $langle$110$rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data yields a reliable estimate of the superexchange parameter $J$ = 135 $pm$ 4 meV using a classical spin-1/2 2D Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2,,0) and (1/4,,1/4) indicates that next-nearest neighbor interactions in this compound are intermediate between the values found in La$_{2}$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Owing to the low-$Z$ elements composing Ca$_2$CuO$_2$Cl$_2$, the present results may enable a reliable comparison with the predictions of quantum many-body calculations, which would improve our understanding of the role of magnetic excitations and of electronic correlations in cuprates.
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