Anomalous High-Energy Spin Excitations in the High-$T_c$ Superconductor Parent Antiferromagnet La$_2$CuO$_4$

Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor parent antiferromagnet La$_2$CuO$_4$. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the (1/2,0) position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs. The spinon dispersion that can explain the observed spin-wave damping in our experiments has the same form as the pseudogap dispersion observed in superconducting cuprates, with a minimum at (1/4,1/4).