Effect of electron correlations on the formation of spiral magnetic states in the two-dimensional $t$–$t'$ Hubbard model

The formation of the spiral magnetic order in the ground state of the Hubbard model for a square lattice has been studied within the slave-boson method in a wide range of the parameters of the carrier density and Coulomb interaction. Next-nearest-neighbor electron hopping, as well as the magnetic phase separation, has been taken into account. It has been shown that the electron correlations lead to the suppression of the ferromagnetic and spiral phases in comparison with the Hartree–Fock approximation. The application of the results to the explanation of the experimental data, in particular, to the description of the magnetic state of the high-temperature superconductors of the cuprate-based systems has been discussed.