Theory of quantum paraelectrics and the metaelectric transition

We present a microscopic model of the quantum paraelectric-ferroelectric phase transition with a focus on the influence of coupled fluctuating phonon modes. These may drive the continuous phase-transition first order through a metaelectric transition and furthermore stimulate the emergence of a textured phase that preempts the transition. We discuss two further consequences of fluctuations, first for the heat capacity, and second we show that the inverse paraelectric susceptibility displays ${\chi }^{-1}\sim T^2$ quantum critical behavior, and can also adopt a characteristic minimum with temperature. Finally, we discuss the observable consequences of our results.

Figure 1

(Color online) The phase diagram in the $u\text{−}v$ plane at zero temperature in the mean-field approximation. The cross-hatched forbidden region denotes where the polarizability would diverge without higher-order corrections. The solid thick line highlights a first-order phase boundary between the light gray region that denotes diagonal order and the dark gray which labels the Ising phase. In each regime the inset axes illustrate the polarization solution highlighted by the bold (red) vector.

Figure 2

The phase diagram at $\tilde{T}=0$ in the (a) $u\text{−}v$ plane with $r<0$ and (b) $u\text{−}r$ plane with $v>0$, both at zero temperature. The cross-hatched forbidden region denotes where the polarizability would diverge without higher-order corrections, the light gray denotes diagonal ordered polarization, and the dark gray the (a) Ising phase and (b) paraelectric phase. Solid thick lines denote first-order phase boundaries, dashed lines second-order transitions, and the circle the tricritical point.