Green's function theory of phase transition in PbHPO4and PbDPO4ferroelectrics

Abstract
In this paper, we investigated the newly found order-disorder ferroelectrics PbHPO4 along with its deuterated analogue PbDPO4. Because the major contribution of the spontaneous polarization is the dipoles forming by the proton (or deuteron) ordering, not the displacements of heavy atoms as in the case of KDP-type crystals. Therefore in the Hamiltonian, the influence of the lattice vibration may not be considered, but the 4th order interaction of pseudo-spin is included. By introducing the undetermined-constant into the Green's function method, we carried out the spontaneous polarization of PbHPO4 and PbDPO4 crystals, the results are good agreement with the experimental data.