Theory of the hourglass dispersion of magnetic excitations in high-Tc cuprates

A theory for the dispersion of collective magnetic excitations in superconducting cuprates is presented with the aim to cover both high- and low-doping regimes. Besides of spin fluctuations describable in the random phase approximation (RPA) we allow for local spin rotations within a mode-coupling theory. At low temperatures and moderately large correlation lengths we obtain two branches of excitations which disperse up- and downwards exhibiting the hourglass behavior observed experimentally at intermediate dopings. At large and small dopings our theory essentially reduces to the RPA and spin wave theory, respectively.