ИСТИНА

A competition between magnetism and superconductivity in layered quasi-two-dimensional systems is being studied since the discovery of high-T c superconductivity in copper oxide compounds. Both microscopic coexistence and macroscopic phase separation of superconducting and magnetic orderings are experimentally observed in a number of CuO- and FeAs-based materials [1]. Despite the obvious success in the investigating of this intriguing phenomena, there is still no uniform theory which describes both the coexistence and the phase separation of magnetic and superconducting states with different symmetries. We consider a single-band extended t-t' Hubbard model, which includes the on-site repulsion U and the nearest neighbor attraction V0 on the square lattice to describe the competition between magnetic and superconducting orders. Strong electron correlations, which are relevant for iron pnictides and copper oxides, are taken into account by means of slave-boson approach of Kotliar and Ruckenstein [2]. The Hartree-Fock approximation is used as well, and results are compared to trace the role of strong electron correlations. An advantage of our approach is the account of the widest possible range of superconducting and magnetic states. We take into consideration not only the traditional s- and d-wave symmetries of the superconducting order parameter, but the mixed s+id symmetry as well, which is proposed in the literature for the interpretation of some experimental data. The magnetic order is considered in the form of incommensurate spiral structure with an arbitrary wave vector, while the ferro- and antiferromagnetic phases are particular cases of the spiral state. At first, the superconducting order was studied without taking into account magnetism, and the temperature phase diagrams were constructed. It is found that at some parameters the normal state with decrease of temperature goes to the pure s- or d-wave phase and then to the mixed s+id-wave. Further we turn on the magnetism and calculate the ground state phase diagrams in terms of interaction parameters U and V0 and an electron density n. It is found that at certain parameters both the separation and coexistence between superconducting and magnetic phases with different symmetries can be realized. The interplay between superconductivity and magnetism allows to reproduce the dome-shaped doping dependence of the superconducting gap amplitude. The boundaries of phase transitions between different phases are calculated, and the experimental data are interpreted. The reported research was funded by Russian Foundation for Basic Research, grants ʋ 16- 02-00995, 16-42-180516, and the government of the Udmurt State of the Russian Federation, grant ʋ 18-42-183005. [1] Y.S. Lee, et. al., Phys. Rev. B. 60, 3643 (1999). [2] G. Kotliar and A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986).