Origin of the linear term in the pseudo-spin Hamiltonian of compositionally graded ferroelectrics

Abstract

This paper is devoted to the microscopic theory of compositionally graded ferroelectrics (CGF). From a simple microscopic picture of CGF we deduce the so called transverse Ising pseudo-spin model. However the Hamiltonian used in recent papers does not contain a linear term in pseudo-spins. We show that for inhomogeneous material it is necessary to modify the Ising Hamiltonian by addition of the linear term in pseudo-spins. This linear term is equivalent to introduction of an external bias field. The influence of long-range forces is discussed.