Sharpness of transition and effect of tunnelling in ferroelectric Bean-Rodbell model of KDP

Abstract

The molecular-field treatment by Bean and Rodbell (1962) of a deformable Ising ferromagnet is modified to include piezoelectricity and spin-lattice coupling, so that it may be applied to deuterated KDP. In this case, the pseudo-spin exchange coupling depends linearly on strain mod sigma 6 mod , and it is seen that this dependence can produce a first-order transition for appropriately chosen values of the coupling parameters. From the condition that the slope of polarisation be infinite at Tc plus a consistency condition on the exchange, it is shown that the mean value (Z) of a pseudo-spin can have a maximum possible value at the Curie point. The value of the spontaneous polarisation ratio Ps(Tc)/Ps(0) which corresponds to maximum (Z) is 0.704. This provides a qualitative understanding of the shape of the polarisation curve to within a fraction of a degree of Tc, where critical fluctuations become important.