  Based on the extended Hubbard model we calculate the energy of stripe and
spiral ground states. We find that uniform spirals get favored by a large
$t'/t$ ratio but are unstable at small doping towards stripes and checkerboard
textures with spin canting. The structure of these inhomogeneities also depends
on t'/t and the associated spin currents may induce a small lattice distortion
associated with local dipole moments. We discuss a new kind of stripe which
appears as a domain wall of the antiferromagnetic (AF) order parameter with a
fractional change of the phase of the AF order. For large |t'/t| spirals can be
stabilized under certain conditions in the overdoped regime which may explain
the elastic incommensurate magnetic response recently observed in iron-codoped
Bi2201 materials.
