Strain-dependent tunnelling in deformable ferroelectric spin models

A pseudo-spin model of a KDP-type ferroelectric is assumed to have strain-dependence in both exchange coupling and tunnelling. A self-consistent molecular field calculation is made of both the polarization and the expectation (X) of the spin-flip operator, for T<T c . In the case of a model with one spin per cell, it is shown that there can never be a second-order phase change when piezoelectric coupling is finite, and that T c to 0K if the coefficient Gamma 1 of strain- dependence of tunnelling is made sufficiently large. A small Gamma 1 is found to augment effects produced by changes in the strain-independent part Gamma 0 of the tunnelling. In the case of zero piezoeffect, an increase in Gamma 1 can reduce the transition from first- to second-order, while small ranges of Gamma 1 values are found within which it is impossible to make T c to 0 as Gamma 0 increases. A two-sublattice model is discussed, in which sublattice polarization can differ for H bonds of differing orientation. Again, for Gamma 1 sufficiently large, the ferroelectric phase disappears.