Dynamic spin-response function of the high-temperature Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ superconductor form angle resolved photoemission spectra
We introduce a formalism for calculating dynamic response functions using experimental single particle Green's functions derived from angle resolved photoemission spectroscopy (ARPES). As an illustration of this procedure we estimate the dynamic spin response of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We find good agreement with superconducting state neutron data, in particular the $(\pi,\pi)$ resonance with its unusual `reversed magnon' dispersion. We anticipate our formalism will also be of useful in interpreting results from other spectroscopies, such as optical and Raman responses.