  We examine the dynamical magnetic response in a two-component
resonating-valence-bond (RVB) description of the doped Mott insulator. The
half-filled antiferromagnetic phase described by the Schwinger-boson mean-field
theory will evolve into a bosonic-RVB state in the superconducting phase upon
doping, where the doped holes introduce another fermionic itinerant spinon
which forms a BCS-like RVB order. The spin excitations are thus composed of a
resonance-like mode from the former and a weak dispersive mode from the
itinerant component at the mean-field level. These two-component spinons are
shown to give rise to an hourglass-like spin excitation at the RPA level via an
antiferromagnetic coupling between the two modes, which provides an
unconventional explanation of the experimental observations in the cuprate. In
particular, we also discuss an instability towards an incommensurate magnetic
order in this theoretical framework.
