  An inelastic neutron scattering study of overdoped Bi_2Sr_2CaCu_2O_{8+\delta}
$ (T_c = 83 K) has revealed a resonant spin excitation in the superconducting
state. The mode energy is E_res=38 meV, significantly lower than in optimally
doped Bi_2Sr_2CaCu_2O_{8+\delta} (T_c = 91 K, E_ res =43 meV). This
observation, which indicates a constant ratio E_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.
