Physica A 311 (2002) 475–488 www.elsevier.com/locate/physa Magnetic properties in ferroelectric superlattices described by a transverse spin-1= 2 Ising model A. Tabyaoui a , A. Ainane a; b , M. Saber a; b; ∗ a D epartement de Physique, Facult e des Sciences, Universit e Moulay Ismail, B.P. 4010 Mekn es, Maroc b Max-Planck-Institut f ur Physik Complexer Systeme, N othnitzer Strasse 38, 01187 Dresden, Germany Received 18 December 2001 Abstract The temperature dependence of the longitudinal magnetization as well as the longitudinal susceptibility of a ferroelectric superlattice described by a transverse spin- 1 2 Ising model are studied using the eective eld theory with a probability distribution technique that accounts for the self-spin correlations. When the slab thicknesses are larger, the temperature dependence of the magnetization shows a steplike structure. The susceptibility becomes innite at the critical temperature Tc and shows a nite peak corresponding to the rapid decrease in the magnetization near the bulk critical temperature of slab B. The height of the nite peak decreases with the decrease in the slab thicknesses. When they become so thin that the magnetization proles are predominantly controlled by the interface, the nite peak in the susceptibility as well as the steps in magnetization disappear. c 2002 Elsevier Science B.V. All rights reserved. PACS: 75.10.-b; 75.40.Mg; 75.70.Cn Keywords: Ferroelectric superlattice; Magnetic properties; Transverse Ising model 1. Introduction Articially fabricated superlattices have been studied in great detail because their physical properties dier dramatically from simple solids formed from the same materi- als. The development of lm deposition techniques has aroused great interest in the syn- thesis and study of superlattices in other materials. In layered ferromagnetic materials, * Corresponding author. Max-Planck-Inst. fur Physik Complexer System, Nothnitzer Strasse 38, 01187 Dresden, Germany. E-mail address: saber@mpipks-dresden.mpg.de (M. Saber). 0378-4371/02/$-see front matter c 2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(02)00822-1