Novel neutron resonance mode in $d_{x^2-y^2}$ superconductors

We show that a new resonant magnetic excitation at incommensurate momenta, observed recently by inelastic neutron scattering experiments on YBa$_2$Cu$_3$O$_{6.85}$ and YBa$_2$Cu$_3$O$_{6.6}$, is a {\it spin exciton}. Its location in the magnetic Brillouin zone and its frequency are determined by the momentum dependence of the particle-hole continuum. We identify several features that distinguish this novel mode from the previous resonance mode observed near ${\bf Q}=(\pi,\pi)$, such as its intensity maximum which occurs in a different part of the magnetic Brillouin zone.