Dielectric properties of compositionally graded Ba_1–xSr_xTiO₃ thin films described by the transverse‐field Ising model

Abstract

This investigation reports on the phase transition and dielectric properties of compositionally graded Ba 1-x Sr x TiO 3 (BST) thin films with x decreasing from 0.20 to 0.10 in successive slabs, based on the transverse-field Ising model (TIM) within the framework of mean field theory. The random bond model of related parameters is applied to mimic doping. The effect on polarization and dielectric susceptibility arising from a gradient in composition is taken into account. The peaks of dielectric susceptibility versus temperature become comparatively flat by modulating appropriate thickness in each slab in compositionally graded BST thin films, which means that the thickness may weaken the effect of composition gradient. When increasing the number of slabs of thin films, the dielectric susceptibility shows good temperature stability in a wide temperature range, which is useful for reducing the temperature coefficient of dielectric susceptibility without depressors.

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

“…In contrast to the assumption given in Gao et al [12] and Cao et al [13], the Hamiltonian describing CGF involves the term that is linear in both pseudospins and gradc. Using the mean-field approximation the dependence of polarization on space coordinate, temperature and gradc was derived.…”

“…We used the following values of parameters for pure BaTiO 3 : J 1 = 38.3 × 10 −22 J , β = 0.9 , eb 1 = 2.17e Å, 1 = 4.9 × 10 −21 J, and for pure SrTiO 3 : J 2 = 3.26 × 10 −22 J , eb 2 = 1.51e Å, 2 = 1.1 × 10 −21 J, which were obtained from the fitting of experimental results [12].…”

“…Then gradc (gradc ≡ dc/dz) is constant in the whole sample (gradc ∼ = (c ζ − c 0 )/(ζ a 0 ) ; a 0 = a ζ =0 ). According to the linear Vegard law [12] the dependence of the lattice constant a ζ on the stochiometric ratio c ζ is a ζ = a Sr + c ζ α where in the first approximation α = 0.1Å. So we can write down the dependence of a ζ on the coordinate number ζ…”

“…The basic aim of this paper is to extend the existing microscopic theory of CGF proposed in Gao et al [12] and Cao et al [13], where the pseudospin transverse Ising model was considered. The authors supposed that the inhomogeneous ferroelectrics (gradc = 0) can be described by an assumption that the spin-spin interaction coefficient varies along one direction.…”

“…Since publishing of the pioneering work [1] many papers [2][3][4][5][6][7][8][9][10][11][12][13][14][15] have been devoted to investigation of compositionally graded ferroelectrics (CGF). One of the most interesting results of experimental observation on CGF is discovery of a new type of the pyroelectric effect.…”