Phase diagram of t-t' Hubbard model taking into account spin-spiral waves and phase separation at finite temperature

The effect of temperature on the magnetic phase separation and the parameters of spin-spiral waves (SSW) is studied using a two-dimensional (2D) single-band $t-t'$ Hubbard model and the Hubbard-Stratonovich transformation. Both commensurate (antiferromagnetic (AF)) and incommensurate (helical) magnetic phases are considered. It is shown that the temperature significantly affects the collinear and helical magnetic phases. With an increase in the temperature, the phase-separation (PS) regions (AF$+[Q,Q])$, $([Q,Q]+[Q,\pi])$ get substantially reduced but new regions $([Q_{1},\pi]+[Q_{2},\pi])$, (AF$+[Q,\pi])$ arise. The results are used for the interpretation of the magnetic properties of cuprates.