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It is shown that the magnetic structure of high-T-c superconductors is strongly influenced by the next-nearest neighbor hopping parameter t' which distinguishes different families of cuprates. Our investigations indicate that uniform spirals get favored by a large t'/t ratio but are unstable at small doping towards stripes with spin canting. For large vertical bar t'/t vertical bar spirals can be stabilized under certain conditions in the overdoped regime which may explain the elastic incommensurate magnetic response recently observed in iron-co-doped Bi2201 materials.

Magnetic Structure of Electronic Inhomogeneities in Cuprates: Competition between Stripes and Spirals