High-Energy Magnon Dispersion and Multimagnon Continuum in La$_2$CuO$_4$

We report high-energy neutron scattering measurements of the magnetic excitations in the S=1/2 antiferromagnet La$_2$CuO$_4$. Measurements were made using the MAPS time-of-flight spectrometer at the ISIS spallation source. Previous measurements found evidence for higher order (cyclic) exchange couplings. We find evidence for significant corrections to linear spin-wave (SW) theory including these higher-order exchange constants. In particular, the intensity of the spin wave pole deviates strongly from that predicted by SW theory near the $\mathbf{Q}=(1/2,0)$ position. We also find evidence for a multi-magnon continuum.