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Volumn 81, Issue 6, 2010, Pages

Dependence of Curie temperature on the thickness of an ultrathin ferroelectric film

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EID: 77954828948     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.064105     Document Type: Article
Times cited : (42)

References (42)
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    • Here, we rescaled our theoretical temperature by multiplying it by a constant coefficient, in order to match the experimental Curie temperature of PZT bulk. Such rescaling has been found to accurately reproduce various experimental temperature-dependent data (Ref.), and has no effect on the investigated parameters of Eqs. -as consistent with the fact that these two equations involve a ratio between different temperatures.
    • Here, we rescaled our theoretical temperature by multiplying it by a constant coefficient, in order to match the experimental Curie temperature of PZT bulk. Such rescaling has been found to accurately reproduce various experimental temperature-dependent data (Ref.), and has no effect on the investigated parameters of Eqs. -as consistent with the fact that these two equations involve a ratio between different temperatures.
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    • These fits were practically done by only considering our numerical data for m greater than, or equal to, 7, for two main reasons: (1) to avoid including some possible surface effects that manifest themselves in the thinnest possible films [such effects are the ones that can lead to a deviation of the data with respect to Eq. ]; and (2) because the parameters of both Eqs. are found to be converged (i.e., nearly independent of the points included in the fit) when considering the data above m=5.
    • These fits were practically done by only considering our numerical data for m greater than, or equal to, 7, for two main reasons: (1) to avoid including some possible surface effects that manifest themselves in the thinnest possible films [such effects are the ones that can lead to a deviation of the data with respect to Eq.]; and (2) because the parameters of both Eqs. are found to be converged (i.e., nearly independent of the points included in the fit) when considering the data above m = 5.
  • 42
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    • The insensitivity of the Curie temperature on the P and T parameters of Eq. is due to the fact that the polarization lies in plane for temperature below the critical temperature while these two parameters characterize effects associated with the out-of-plane direction. On the other hand, adding an energetic term characterizing the surface-induced change in in-plane dipoles in Eq. can strongly affect the Curie temperature by, e.g., making it increase as the film thickness decreases.
    • The insensitivity of the Curie temperature on the P and T parameters of Eq. is due to the fact that the polarization lies in plane for temperature below the critical temperature while these two parameters characterize effects associated with the out-of-plane direction. On the other hand, adding an energetic term characterizing the surface-induced change in in-plane dipoles in Eq. can strongly affect the Curie temperature by, e.g., making it increase as the film thickness decreases.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.