  Close to half filling and in the limit of strong interactions the Hubbard
model leads a spin Hamiltonian. In its original isotropic form this is the
Heisenberg model with antiferromagnetic coupling $J$. On a square lattice there
is no frustration and the ground state is a classical antiferromagnet denoted
by the commensurate order vector ${\bf Q}=(\pi,\pi)$. In this work we show that
the inclusion of spin orbit coupling (SOC) in the fermionic Hubbard model on a
square lattice leads to an incommensurate spin density wave (ISDW) in the
strong interactions limit at half filling. In this limit the Hubbard model
leads to a non-diagonal and anisotropic spin Hamiltonian which exhibits the
incommensurate spin order as its classical ground state. We note that an ISDW
can be found in systems regardless of spin orbit-coupling due to nesting and
lattice distortion. These effects, however, can usually be recognized by
experimental probes.
