\begin{thebibliography}{82}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

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\bibitem[{\citenamefont{Ma and Cross}(2006)}]{ma-apl06}
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\bibitem[{ste()}]{stengel-unpub}
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\bibitem[{\citenamefont{Nguyen et~al.}(2013)\citenamefont{Nguyen, Mao, Yeh,
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\bibitem[{zub({\natexlab{a}})}]{zubko-armr13}
\bibinfo{note}{P. Zubko, G. Catalan and A.K. Tagantsev, Annu. Rev. Mater. Res.
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\bibitem[{yud()}]{yudin-unpub}
\bibinfo{note}{P.V. Yudin and A.K. Tagantsev, unpublished.}

\bibitem[{\citenamefont{Le~Quang and He}(2011)}]{quang-prsa11}
\bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Le~Quang}} \bibnamefont{and}
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\bibitem[{exp()}]{explan-cell}
\bibinfo{note}{$V_c$ may be either the conventional or primitive cell volume,
  as long as the sum $\sum_I$ runs over the atoms contained in this volume.}

\bibitem[{\citenamefont{Vanderbilt}(2000)}]{vanderbilt-jpcs00}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Vanderbilt}},
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\bibitem[{zub({\natexlab{b}})}]{zubko-thesis}
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\bibitem[{\citenamefont{Maranganti et~al.}(2006)\citenamefont{Maranganti,
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\bibitem[{\citenamefont{Gharbi et~al.}(2009)\citenamefont{Gharbi, Sun, Sharma,
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\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Gharbi}},
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\bibitem[{\citenamefont{Majdoub et~al.}(2009)\citenamefont{Majdoub, Maranganti,
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\bibitem[{\citenamefont{Sharma et~al.}(2007)\citenamefont{Sharma, Maranganti,
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\bibitem[{\citenamefont{Marvan and Havranek}(1988)}]{marvan-pcps88}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Marvan}} \bibnamefont{and}
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\bibitem[{\citenamefont{Yurkov}(2011)}]{yurkov-jetpl11}
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\bibitem[{\citenamefont{Hong and
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\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Hong}} \bibnamefont{and}
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\bibitem[{\citenamefont{Perdew and Zunger}(1981)}]{perdew-prb81}
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\bibitem[{\citenamefont{Wu and Cohen}(2006)}]{wu-cohen-prb06}
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\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Soler}},
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\bibitem[{\citenamefont{King-Smith and Vanderbilt}(1993)}]{kingsmith-prb93}
\bibinfo{author}{\bibfnamefont{R.~D.} \bibnamefont{King-Smith}}
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\bibitem[{\citenamefont{Wu et~al.}(2005)\citenamefont{Wu, Vanderbilt, and
  Hamann}}]{wu-prb05}
\bibinfo{author}{\bibfnamefont{X.}~\bibnamefont{Wu}},
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\bibitem[{mgo({\natexlab{a}})}]{mgo-e}
\bibinfo{note}{A. J. Bosman and E. E. Havinga, Phys. Rev. {\bf 129}, 1593
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\bibitem[{csc({\natexlab{a}})}]{cscl-e}
\bibinfo{note}{E. E. Havinga and A. J. Bosman, Phys. Rev. {\bf 140}, A292
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\bibitem[{bzo({\natexlab{a}})}]{bzo-e}
\bibinfo{note}{A. Azada and S. Subramaniamb,Materials Research Bulletin, {\bf
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\bibitem[{pto({\natexlab{a}})}]{pto-e}
\bibinfo{note}{A. G. Kalinichev, J. D. Bass, B. N. Sun and D. A. Payne, J.
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\bibitem[{sto({\natexlab{a}})}]{sto-e}
\bibinfo{note}{A. Linz, Phys. Rev. {\bf 91}, 753 (1953).}

\bibitem[{not({\natexlab{a}})}]{notes-Te}
\bibinfo{note}{For \BTO, \PTO\ and \STO, using Eq.~(\ref{eq:muldT}) to
  calculate $\m\pldE$ is not practical because the force-constant matrix $K$ is
  non-physical due to the ferroelectric instability at 0\,K. We use
  Eq.~(\ref{eq:K2d-e}) to convert $T^{\E}$ to $T^D$ and calculate the full
  tensor $\mu\pldD$, which also requires $\mu\pel _{1122}$ and $\mu\pel
  _{1221}$. Then we convert it to the value at fixed $\E$.}

\bibitem[{c()}]{c}
\bibinfo{note}{H. Gercek, Int. J. Rock Mech. \& Min. Sci. {\bf 44}, 1 (2007).}

\bibitem[{si()}]{si}
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\bibitem[{mgo({\natexlab{b}})}]{mgo}
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\bibitem[{nac()}]{nacl}
\bibinfo{note}{F. Birch and J. Geophys. Res. {\bf 83}, 1257 (1978).}

\bibitem[{csc({\natexlab{b}})}]{cscl}
\bibinfo{note}{O. L. Anderson and R. C. Liebermann, Phys. Earth Planet. Inter.
  {\bf 3}, 61 (1970).}

\bibitem[{bzo({\natexlab{b}})}]{bzo}
\bibinfo{note}{K. C. Gorettaa, E. T. Parka, R. E. Koritalaa, M. M. Cubera, E.
  A. Pascuala, N. Chenb, A. R. de Arellano-L\'opezc and J. L. Routborta,
  Physica C, {\bf 309}, 245 (1998).}

\bibitem[{bto()}]{bto}
\bibinfo{note}{W. P. Mason, Phys. Rev. {\bf 72}, 869 (1947).}

\bibitem[{pto({\natexlab{b}})}]{pto}
\bibinfo{note}{N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys.
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\bibitem[{sto({\natexlab{b}})}]{sto}
\bibinfo{note}{G. Rupprecht and W. H. Winter, Phys. Rev. {\bf 155}, 1019
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\bibitem[{not({\natexlab{b}})}]{notes-gpos}
\bibinfo{note}{For example, choosing $\mu\pel_{1122} = 0.088 \, \mu\pel\bltwo$,
  we obtained $g_{1111}=-36.9$\,nC/m, $g_{1221} = -1.3$\,nC/m, and $g_{1122} =
  -3.6$\,nC/m for \STO, which gives a positive $g^{\rm eff}=6.2$\,nC/m and
  agrees well with the experiment results.\cite{zubko-prl07,zubko-prl07-err}}.

\end{thebibliography}
