Effect of thermal fluctuations on magnetic phase separation and on the parameters of spin-spiral waves

Effects of temperature on magnetic phase separation and on the parameters of spin-spiral waves are studied. The study is performed using the two-dimensional single-band Hubbard model and the Hubbard-Stratonovich transformation. Both commensurate (antiferromagnetic, ferromagnetic) and incommensurate (spiral) magnetic phases are considered. The problem is solved using the static approximation with allowance for transverse fluctuations of the magnetic moment. It is shown that the temperature significantly affects the collinear and spiral magnetic phases. With an increase in the temperature, the phase-separation region near the half-filling is sufficiently reduced and substituted by the antiferromagnetic phase. The results are used for the interpretation of the magnetic properties of cuprates.