  It has long been known that two-dimensional metals with antiferromagnetic
exchange interactions have a weak-coupling instability to the superconductivity
of spin-singlet, d-wave electron pairs. We examine additional possible
instabilities in the spin-singlet particle-hole channel, and study their
interplay with superconductivity. We perform an unrestricted Hartree-Fock-BCS
analysis of bond order parameters in a single band model on the square lattice
with nearest-neighbor exchange and repulsion, while neglecting on-site
interactions. The dominant particle-hole instability is found to be an
incommensurate, bi-directional, bond density wave with wavevectors along the
(1,1) and (1,-1) directions, and an internal d-wave symmetry. The magnitude of
the ordering wavevector is close to the separation between points on the Fermi
surface which intersect the antiferromagnetic Brillouin zone boundary. The
temperature dependence of the superconducting and bond order parameters
demonstrates their mutual competition. We also obtain the spatial dependence of
the two orders in a vortex lattice induced by an applied magnetic field:
"halos" of the bond order appear around the cores of the vortices.
