A Lattice Model for Ferroelectric Superlattices Khian-Hooi CHEW, Yoshihiro ISHIBASHI 1 and Franklin G. SHIN Department of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 1 Faculty of Business, Aichi Shukutoku University, Nagakute-cho, Aichi 480-1197 (Received March 8, 2006; accepted April 12, 2006; published June 12, 2006) A one-dimensional lattice model based on the Landau–Ginzburg theory to study the intrinsic properties of a periodic superlattice with interfacial coupling is developed. The effects of thickness and interfacial coupling on the properties of a superlattice consisting of alternating ferroelectric and paraelectric constituent layers are investigated. Competition between the thickness effects of each constituent layer is expected and indeed can play an important role in governing the properties of an interface-coupled superlattice, depending on the strength of the interfacial coupling. This work may provide useful information on the possibility of manipulating structures to obtain the desired properties for specific applications. KEYWORDS: ferroelectric, interfacial coupling, interface structure, lattice model, layered structures, superlattice DOI: 10.1143/JPSJ.75.064712 1. Introduction Recently, considerable efforts and interests have been dedicated to the investigation, involving both experimental and theoretical approaches, of superlattice structures of ferroelectrics because of their technological importance. Superlattice structures consisting of at least two different ferroelectric constituent layers offer an approach to manip- ulate the properties of the layered structure for useful applications. The interest is also motivated by the fact that those structures provided the possibility of forming systems with functional properties that are superior to those of their individual layers. 1–4) Since future ferroelectric devices are expected to be in form of heterostructures, understanding and controlling the properties of layered ferroelectrics such as superlattice or multilayer structures are of special importance. While the macroscopic geometrical parameters that control the various properties of such structures are layer thickness, layering order and periods etc, the presence of symmetry-breaking elements such as interfaces underlies the basic mechanism governing their overall behavior, and thus should deserve due attention. At the interface, the polarization of layered ferroelectrics is expected to be different from the bulk. In addition, the polarization may interact strongly with other order parameters such as strain, giving rise to a large extrinsic effect. 5) When the ferroelectric system has superlattice or multi- layer structure, there is an additional interfacial coupling which originates from the interaction across the interface between the ferroelectric constituent layers, which affects the ferroelectric behaviors of the structure, and must be con- sidered. 6,7) The Landau–Ginzburg formulation for the inter- facial coupling was derived using the transverse Ising model to study the BaTiO 3 /PbTiO 3 superlattice structures. 8,9) Within that framework, 8,9) extrapolation lengths 10,11) are in- corporated to differentiate the polarization near the inter- faces and in the bulk. An additional interfacial coupling parameter is introduced in the model 8,9) to describe the interfacial effects because the inhomogeneity of polarization described by the extrapolation lengths 10,11) cannot account for the intrinsic coupling between neighboring layers at the interfaces. More recently, explicit expressions for a ferro- electric superlattice with interlayer coupling are derived based the Landau–Ginzburg theory. 12) In the model, the interaction between layers originates from the depolarization field due to the inhomogeneity of polarization. Based on the Landau–Ginzburg theory, we have devel- oped a continuum model for a heterostructure formed from two different semi-infinite ferroelectric constituents. 13–15) In the model, the intrinsic coupling across the interface between the neighboring constituents is described by an interfacial coupling parameter. The existence of the intrinsic interfacial coupling ‘‘naturally’’ leads to the inhomogeneity of polarization near the interface, which extends into the bulk over a distance governed by the characteristic length scales of the constituents. The inhomogeneity of polarization near the interface assists the polarization reversal by re- ducing the coercive field of the heterostructures. 15) In those works, 13–15) however, the basic element (i.e., interface structure) of a layered ferroelectric is examined in isolation with the layer thickness effect. The latter is crucial for obtaining a general understanding of the interfacial effects in layered structures, which are still poorly understood. In the present work, we develop a one-dimensional lattice model within the framework of the Landau–Ginzburg theory for ferroelectric superlattices. The intrinsic dielectric sus- ceptibility and polarization in a periodic superlattice struc- ture consisting of alternating ferroelectric and paraelectric layers are studied. We address issues related to the effect of the thickness (of the ferroelectric and paraelectric constit- uent layers) and interfacial coupling on the intrinsic proper- ties. The present article is organized as follows: in §2 the methodology used to develop a one-dimensional lattice model for a ferroelectric superlattice is illustrated. We present our results and discussion in §3. A summary is given in §4. 2. Theory We consider an infinite ferroelectric superlattice consist- ing of alternating constituent layers 1 and 2, with a bilinear coupling 13–15) across the interface adjacent layers. Periodic boundary conditions are employed for describing the infinite ferroelectric superlattice. Thus, we only have to consider one Journal of the Physical Society of Japan Vol. 75, No. 6, June, 2006, 064712 #2006 The Physical Society of Japan 064712-1