Abstract

The coupling between order parameters in systems with several instabilities has been analyzed within Landau theory. The dominant term considered in this paper is linear in one order parameter and quadratic in the second order parameter ~ QP2 , other coupling terms have been treated previously. Typical examples for Q are proper or pseudo-proper ferroelastic instabilities, while P might be octahedral tilting in a perovskite, (anti-) ferromagnetic ordering or (anti) ferroelectric soft modes. Coupling of this type is common in fluorites, Verwey transitions, Jahn Teller systems, pnictide super conductors etc. Analytical solutions and characteristic phase diagrams of the stable configurations are compiled. The coupling can lead to stepwise phase transitions even when the uncoupled systems would show continuous transitions. Mixed phase are common, so that many ‘intermediate phases’ described in literature are in fact the result of this linear-quadratic coupling.