Phase transition of spin-1 frustrated model on square-lattice bilayer

Abstract

In this paper, we investigate the phase transition of the spin-1 frustrated model on a square-lattice bilayer by the double-time Green’s function method. The effects of the interlayer coupling parameter <inline-formula><tex-math id="M9">\begin{document}$ {J_c} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M9.png"/></alternatives></inline-formula> and single-ion anisotropy <i>D</i> on phase transformation between the Nèel state (AF1) and collinear state (AF2) are explored. Our results show that if only the parameters <inline-formula><tex-math id="M11">\begin{document}$ {J_c} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M11.png"/></alternatives></inline-formula> and <i>D</i> are not equal to zero at the same time, the two states can exist and have the same critical temperature at <inline-formula><tex-math id="M13">\begin{document}$ {J_2} = {J_1}/2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M13.png"/></alternatives></inline-formula>, which represents the nearest neighbor exchange. Under such parameters, a first-order phase transformation between these two states below the critical point can occur. For <inline-formula><tex-math id="M14">\begin{document}$ {J_2} \ne {J_1}/2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20211685_M14.png"/></alternatives></inline-formula>, although both states may exist, their Neel temperatures differ from each other. If the Nèel point of the AF1 (AF2) state is larger, then at very low temperature, the AF1 (AF2) state is more stable. Thus, in an intermediate temperature, a first-order phase transition between these two states may also occur.