Quantum saturation of the spontaneous polarisation in ferroelectric materials

The spontaneous polarisation of ferroelectrics becomes temperature independent below a characteristic temperature (T << theta (s)) due to the freezing of fluctuational degrees of freedom. Displacive transitions ale well described by a low temperature expansion of Landau theory with DeltaG = 1/2A theta (s)[coth theta (s)/T - coth theta (s)/T-c]p(2) + 1/4Bp(4) + 1/6p(6) +... A more general solution of the phi (n) model yields mean field self-consistency equations which agree rather well with numerical solutions of 3D-computer simulations. The application of secondary fields x leads to highly non-linear phase boundaries T-x(x) in (T-c,x) space. Perez-Mato and Salje [1] showed that in several cases the function T-c(x) carl be found by direct inversion of the function (2(T) with the mapping gammap(n-2) --> x(H-coupling = gamma xp(2)). An example of multi-phonon coupling is discussed.