  We study the interplay between superconductivity and spin density wave order
in graphene doped to 3/8 or 5/8 filling (a Van Hove doping). At this doping
level, the system is known to exhibit weak coupling instabilities to both
chiral d + id superconductivity and to a uniaxial spin density wave. Right at
van Hove doping, the superconducting instability is strongest and emerges at
the highest Tc, but slightly away from van-Hove doping a spin-density-wave
likely emerges first. We investigate whether at some lower temperature
superconductivity and spin-density-waves co-exist. We derive the
Landau-Ginzburg functional describing interplay of the two order parameters.
Our calculations show that superconductivity and spin density wave order do not
co-exist and are separated by first-order transitions, either as a function of
doping or as a function of T.
