  Recently, it has been reported that the low-temperature high-magnetic field
phase in CeCoIn5 (Q-phase), has spin-density wave (SDW) order that only exists
within this phase. This indicates that the SDW order is the result of the
development of pair density wave (PDW) order in the superconducting phase that
coexists with d-wave superconductivity. Here we develop a phenomenological
theory for these coexisting orders. This provides selection rules for the PDW
order and further shows that the detailed structure of this order is highly
constrained. We then apply our theory to the the vortex phase. This reveals
vortex phases in which the d-wave vortex cores exhibit charge density wave
(CDW) order and further reveals that the SDW order provides a unique probe of
the vortex phase.
