Magnetic response in the underdoped cuprates

We examine the dynamical magnetic response of underdoped cuprates by employing a phenomenological theory of a doped resonant valence bond state where the Fermi surface is truncated into four pockets. This theory predicts a resonant spin response which, with increasing energy (0 to 100 meV), appears as an hourglass. A very-low-energy spin response is found at (pi,pi +/- delta) and (pi +/- delta,pi) and is determined by scattering from the pockets' front side to the tips of opposite pockets where a van Hove singularity resides. At energies beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory thus provides a semiquantitative description of the spin response seen in both inelastic neutron scattering and resonant inelastic x-ray scattering experiments at all relevant energy scales.