Coupling to spin fluctuations from conductivity scattering rates

A recent analysis of optical conductivity data which has provided evidence for coupling of the charge carriers to the 41-meV spin resonance seen in the superconducting state of optimally doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.95}$ (Y123) is extended to other systems. We find that the corresponding spin resonance is considerably broader in ${\mathrm{Tl}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_{8+\delta }$ (Tl2201) and ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ (Y124) than it is in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) and there is no resonance in overdoped Tl2201 with $T_c=23\mathrm{}\mathrm{K}.$ The effective charge-spin spectral density is temperature dependent and contains feedback effects that further stabilize superconductivity as T is reduced.