Magnetic and Charge Fluctuations in High-$T_c$ Superconductors

Neutron scattering has been used to study the spin fluctuations in the YBa${}_2$Cu${}_3$O${}_{7-x}$ and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ materials. Evidence is found for both incommensurate fluctuations and a commensurate resonance excitation. Measurements on the lattice dynamics for YBa${}_2$Cu${}_3$O${}_{6.6}$ show incommensurate structure that appears to stem from charge fluctuations that are associated with the spin fluctuations.