Ferromagnetism,spiral magnetic structures and phase separation in the two-dimensional Hubbard model

The quasistatic approximation and equation-of-motion decoupling for the electron Green's functions are applied to trace the effect of electronic dispersion and electron correlations on the ferromagnetism of two-dimensional itinerant-electron systems. It is found that next-nearest-neighbor hopping t′$t\prime$ is of crucial importance for ferromagnetism formation yielding the magnetic phase diagram which is strongly asymmetric with respect to half-filling. At small t′$t\prime$ in the vicinity of half-filling the ferromagnetic phase region is restricted by the spin-density wave instability, and far from half-filling by one-particle (spin-polaron) instability. At t′$t\prime$ close to t/2$t/2$ ferromagnetism is stabilized at moderate Hubbard U   due to substantial curvature of the Fermi surface which passes in the vicinity of the van Hove singularity points. The results obtained are of possible importance for high-_Tc$T_{\mathrm{c}}$ compounds and layered ruthenates.