Critical Behaviors in Pb(Zr,Ti)O$_{3}$ Ultrathin films

The first-principles-derived approach of Ref.[1] is used to determine the thickness dependency of Curie temperature and of the spontaneous polarization in Pb(Zr,Ti)O$_{3}$ (PZT) thin films that are under stress-free and open-circuit boundary conditions. It is found that, above a thickness of 7 (B-)monolayers (ML), the Curie temperature follows the finite-size relation of Ref.[2] with a critical exponent $\lambda $ = 1.04. On the other hand, the Curie temperature deviates from this ``usual'' relationship for thickness of 6 monolayers and below, characterizing a crossover from a three- to a two-dimensional behavior. This striking crossover is also reflected in the critical exponent \textit{$\beta $}, that is associated with the power law describing the behavior of the polarization with thickness. As a matter of fact, such exponent decreases drastically from 0.14 to 0.1 between 7 and 4 ML. This work is supported by ONR grants N 00014-01-1-0365, N00014-04-1-0413 and 00014-01-1-0600, by NSF grants DMR-0404335 and DMR-9983678, and by DOE grant DE-FG02-05ER46188. \newline [1] E. Almahmoud, Y. Navtsenya, I. Kornev, H. X. Fu, and L. Bellaiche, \textit{Phys. Rev. B 70, 220102{\textregistered} (2004) } \newline [2] G. A. T. Allan, Phys. Rev. B1, 352 (1970).