Stress-induced change of the Lifshitz point type in A₂BX₄ compounds

The high-temperature transition P6₃/mmc–Pmcn in A₂BX₄ compounds is driven by the unique geometrical factor c/a of the hcp structure and occurs either directly for compounds with c/a≥1.26 or via an intermediate incommensurate phase for compounds with c/a≤1.26. We show that the prominent feature of the Lifshitz point that occurs at c/a = 1.26 is that all three incoming transition lines are of first order. We attribute this property to the interaction of the order parameter with the elastic degrees of freedom and classify the types of Lifshitz point that are possible in this case. We discuss the experimental properties of the Lifshitz point in A₂BX₄ compounds.