Resonant Spin Excitation in an Overdoped High Temperature Superconductor

An inelastic neutron scattering study of overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ ( $T_c=83\mathrm{K}$) has revealed a resonant spin excitation in the superconducting state. The mode energy is $E_{\mathrm{res}}=38.0\mathrm{meV}$, significantly lower than in optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ ( $T_c=91\mathrm{K}$, $E_{\mathrm{res}}=42.4\mathrm{meV}$). This observation, which indicates a constant ratio $E_{\mathrm{res}}/k_B{T}_c\sim 5.4$, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high temperature superconductors.