  The influence of incommensurate spin density waves (SDW) on superconductivity
in unconventional superconductors is studied by means of the Bogolubov-de
Gennes (BdG) equations. Exploiting translational symmetries of a magnetically
ordered two-dimensional system we propose an approach that allows to solve the
BdG equations on much larger clusters than it is usually possible for
inhomogeneous systems. Applying this approach we demonstrate that the presence
of incommensurate spin density waves induces real-space inhomogeneity of the
superconducting order parameter even in the absence of external magnetic field.
In this case a homogeneous order parameter of the
Bardeen-Cooper-Schrieffer-type superconducting state is slightly modulated, or
equivalently, a small fraction of the charge carriers form Cooper pairs with
non-zero total momentum. However, when a sufficiently strong magnetic field is
applied, the homogeneous component of the order parameter is suppressed and the
system transits to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where the
order parameter oscillates changing sign. We show that for s-wave pairing the
presence of external magnetic field diminishes the destructive influence of the
SDW order on superconductivity. A simple explanation of this effect is also
proposed.
