Universal Dispersive Excitations in the High-Temperature Superconductors
High-resolution neutron scattering experiments on optimally doped La$_{2-x}$Sr$_x$CuO$_4$ have been performed which reveal that the magnetic excitations are dispersive. The dispersion is found to be the same as in the YBa$_2$Cu$_3$O$_{6+x}$ family, and is quantitatively related to that observed with charge sensitive probes. The excitations are also found to broaden rapidly with increasing energy, forming a continuum at higher energy, and bear a remarkable resemblance to multi-particle excitations observed in low-dimensional antiferromagnets and some magnetic metals. The magnetic correlations are two dimensional, and so rule out the simplest scenarios where the copper oxide planes are subdivided into weakly interacting one-dimensional magnets.