Based on the extended Hubbard model we calculate the energy of stripe and spiral ground states. We find that uniform spirals are favored by a large $t^{\prime }/t$ ratio but are unstable at small doping, tending toward stripes and checkerboard textures with spin canting. The structure of these inhomogeneities also depends on $t^{\prime }/t$ and the associated spin currents may induce a small lattice distortion associated with local dipole moments. We discuss a different 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 $|t^{\prime }/t|$, 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.

• Received 19 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.205108