Magnetic phases near the Van Hove singularity ins- andd-band Hubbard models

We investigate the magnetic instabilities of the nondegenerate $(s$-band) and a degenerate $(d$-band) Hubbard model in two dimensions using many-body effects due to particle-particle diagrams and Hund’s rule local correlations. The density of states and the position of the Van Hove singularity change depending on the value of next-nearest-neighbor hopping $t^{\prime }$. The Stoner parameter is strongly reduced in the $s$-band case, and ferromagnetism survives only if the electron density is small and the band has flat regions. Due to next-nearest-neighbor hopping there are flat regions in $\Gamma -X$ and $\Gamma -Y$ directions. In contrast, for the $d$-band case the reduction of the Stoner parameter which follows from particle-particle correlations is much smaller and ferromagnetism survives to a large extent. Inclusion of local spin-spin correlations has a limited destabilizing effect on the magnetic states.