Spin Waves and Electronic Interactions in ${\mathrm{La}}_2{\mathrm{CuO}}_4$

The magnetic excitations of the square-lattice spin-1/2 antiferromagnet and high- $T_c$ parent compound ${\mathrm{La}}_2{\mathrm{CuO}}_4$ are determined using high-resolution inelastic neutron scattering. Sharp spin waves with absolute intensities in agreement with theory including quantum corrections are found throughout the Brillouin zone. The observed dispersion relation shows evidence for substantial interactions beyond the nearest-neighbor Heisenberg term which can be understood in terms of a cyclic or ring exchange due to the strong hybridization path around the ${\mathrm{Cu}}_4{\mathrm{O}}_4$ square plaquettes.