  We study the equilibrium spin configuration of the 2D Hubbard model at low
doping, when a long-range magnetic order is still present. We use the
spin-density-wave formalism and examine the two suggested candidates for a
ground state: the planar spiral $(\pi,Q)$ and $(Q,Q)$ states. In a mean-field
theory, each of these two states is a ground state in a certain range of
parameters. We however show that both states have negative bosonic modes in a
transverse channel which implies that the spiral states are in fact unstable
(the $(Q,Q)$ state, in addition, has a negative longitudinal stiffness). We
searched for a ground state in a parameter range which on a mean-field level
favored the $(\pi,Q)$ phase, and found that the equilibrium spin configuration
is noncoplanar. These findings lead to a novel scenario of spin reorientation
upon doping in Hubbard antiferromagnets.
