  We consider the ground state magnetic phase diagram of the two-dimensional
Hubbard model with nearest and next-nearest neighbor hopping in terms of
electronic density and interaction. We treat commensurate ferro- and
antiferromagnetic, as well as incommensurate (spiral) magnetic phases. The
first-order magnetic transitions with changing chemical potential, resulting in
a phase separation (PS) in terms of density, are found between ferromagnetic,
antiferromagnetic and spiral magnetic phases. We argue that the account of PS
has a dramatic influence on the phase diagram in the vicinity of half-filling.
The results imply possible interpretation of the unusual behavior of magnetic
properties of one-layer cuprates in terms of PS between collinear and spiral
magnetic phases. The relation of the results obtained to the magnetic
properties of ruthenates is also discussed.
