Dynamical spin response in cuprate superconductors from low-energy to high-energy

Within the framework of the kinetic energy driven superconducting mechanism, the dynamical spin response of cuprate superconductors is studied from low-energy to high-energy. The spin self-energy is evaluated explicitly in terms of the collective charge carrier modes in the particle-hole and particle-particle channels, and employed to calculate the dynamical spin structure factor. Our results show the existence of damped but well-defined dispersive spin excitations in the whole doping phase diagram. In particular, the low-energy spin excitations in the superconducting-state have an hour-glass-shaped dispersion, with commensurate resonance that appears in the superconducting-state only, while the low-energy incommensurate spin fluctuations can persist into the normal-state. The high-energy spin excitations in the superconducting-state on the other hand retain roughly constant energy as a function of doping, with spectral weights and dispersion relations comparable to those in the corresponding normal-state. The theory also shows that the unusual magnetic correlations in cuprate superconductors can be ascribed purely to the spin self-energy effects which arise directly from the charge carrier-spin interaction in the kinetic energy of the system.