Phase diagrams near the Lifshitz point. III. Tetragonal crystals with an easy plane of magnetization

Abstract

Phase diagrams near a Lifshitz point are considered for tetragonal crystals with an easy plane of magnetization. The modulated phase is shown to be sinusoidal or helicoidal, depending on whether a certain parameter $\mu$ measuring the strength of tetragonal anisotropy is larger or smaller than 1. The line $T_H\mathrm{}\left(P\right)\mathrm{}$ of first-order phase transitions between the ferromagnetic and modulated phases is shown to be tangent to the order-disorder transition line $T_{\lambda }\mathrm{}\left(P\right)\mathrm{}$ at the Lifshitz point. For $\mu <1\mathrm{}$, the line $T_H\mathrm{}\left(P\right)\mathrm{}$ is shown to be displaced in the direction of the helicoidal phase with the growth of $\mu$. Such displacement of this line with the increase of crystal anisotropy is shown to be a general property of phase diagrams in the vicinity of the Lifshitz point.