High-resolution neutron scattering experiments on optimally doped ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_4$ ($x=0.16$) reveal that the magnetic excitations are dispersive. The dispersion is the same as in ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.85}$, and is quantitatively related to that observed with charge sensitive probes. The associated velocity in ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_4$ is only weakly dependent on doping with a value close to the spin-wave velocity of the insulating ($x=0$) parent compound. In contrast with the insulator, the excitations broaden rapidly with increasing energy, forming a continuum at higher energy and bear a remarkable resemblance to multiparticle excitations observed in 1D $S=1/2$ antiferromagnets. The magnetic correlations are 2D, and so rule out the simplest scenarios where the copper oxide planes are subdivided into weakly interacting 1D magnets.

• Received 17 March 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.147002