Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many\ncubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of\nthe free energy in the polar order parameter. However, the recent discovery of\na novel monoclinic ferroelectric phase in the PZT system by Noheda et al.\n(Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we\nconfirm that the sixth-order Devonshire theory cannot support a monoclinic\nphase, and consider extensions of the theory to higher orders. We show that an\neighth-order theory allows for three kinds of equilibrium phases in which the\npolarization is confined not to a symmetry axis but to a symmetry plane. One of\nthese phases provides a natural description of the newly observed monoclinic\nphase. Moreover, the theory makes testable predictions about the nature of the\nphase boundaries between monoclinic, tetragonal, and rhombohedral phases. A\nferroelectric phase of the lowest (triclinic) symmetry type, in which the\npolarization is not constrained by symmetry, does not emerge until the\nDevonshire theory is carried to twelfth order. A topological analysis of the\ncritical points of the free-energy surface facilitates the discussion of the\nphase transition sequences.\n