The bosonic peak in Bi-2212: Is it caused by phonons or the 41 meV magnetic resonance?

The infrared spectra of the high temperature superconductors are dominated by two features, a broad continuous background absorption extending to $\approx$ 1 eV and a sharp onset at $\hbar\omega \approx 8 k_BT_c$. Dispersion curves of the free carriers in the same materials measured by angle resolved photo emission (ARPES) display strong curvature (termed the ``kink'') in the same spectral region suggesting that the IR absorption features are spectroscopic signatures of the bosonic excitations that scatter the carriers. The feature at $8 k_BT$ has been attributed to the neutron scattering resonance, seen at $(\pi,\pi)$ momentum transfer. We test this notion by tracking the IR mode as a function of doping level in Bi$_2$Sr$_2$CaCu$_2$O$_8$ and compare our data with ARPES dispersion. We also show new data on the temperature dependence of the mode strength in YBa$_2$Cu$ _3$O$_x$ for the $x=6.5$, the Ortho II, material where neutron data of the resonance is available for samples from the same source. The mode, as seen in the IR, weakens in a linear fashion as the temperature increases to completely vanish at $\approx 200$ K in parallel with the neutron scattering mode. A phonon model for the bosonic mode would predict a temperature independent strength. Another interesting feature of the mode its frequency which scales with the superconducting transition temperature over a wide range of materials and doping levels in the optimally and over doped regions with an intercept at zero frequency. Model calculations for a $d$-wave superconductor are in accord with this behavior provided both the mode frequency and the gap scale with $T_c$, ruling out the phonon origin for the mode which is expected to have a doping and material independent frequency.