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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.
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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.
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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.
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