Resonant Inelastic X-Ray Scattering in Cuprate Superconductors

In the search for the mechanism underlying the high-temperature superconductivity, much effort has been made to study the doping dependence of spin-excitation spectra in cuprates and its correlation to the high-Tc. Owing to recent instrumental development, resonant inelastic x-ray scattering (RIXS) has emerged as a powerful tool for studying the ordering and dynamics of various degrees of freedom in solids. Previous RIXS experiments on cuprates have revealed persistent spin excitation over the whole superconducting phase diagram. However, a proper understanding of the experimental spectra is hindered by the complexity of the RIXS intermediate state. Models employing different approximations lead to contradicting interpretation of the observed spin excitation. We present a systematic study of the energy profile of the RIXS spectra over a wide doping range in several cuprates families, and provide strong experimental and numerical evidence demonstrating that the dominant spectral weight of the spin-flip RIXS intensity in doped cuprates arises from magnetic collective modes associated with short-range antiferromagnetic correlations, thereby confirming the viability of the large class of models of unconventional super-conductivity. We further present a non-perturbative expansion scheme that maps the RIXS operator exactly to various spin and density operators, and thus providing a quantitative understanding of RIXS in a general many-body system.