Journal of Electroceramics

, Volume 20, Issue 1, pp 59–64 | Cite as

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

  • A. Klíč
  • M. Marvan


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.


Compositionally graded ferroelectrics Long-range forces Transverse Ising model 



This work has been sponsored by the Ministry of Education of Czech Republic (Research Program MSM 0021620835).


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute of PhysicsAcademy of Sciences of the Czech RepublicPrahaCzech Republic
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

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