Figure 10
From: Nonzero spontaneous electric polarization in metals: novel predictive methods and applications
Total, wrapped partial, and corresponding spontaneous polarizations versus \(\lambda\) for (a) LiNbO\(_3\) and (c) LiTaO\(_3\). The partial polarizations are wrapped into [\(-e\text {c}/{\Omega }, e\text {c}/{\Omega }\)], where \(e\text {c}/\Omega =69.80\,\upmu {\text {C}}/\text {cm}^2\) is the quantum of polarization. Unwrapped total, partial, and corresponding spontaneous polarizations versus \(\lambda\) for (b) LiNbO\(_3\) and (d) LiTaO\(_3\). The unit of polarizations is \(\upmu {\text {C}}/\text {cm}^2\). Like Figs. 6 and 9 but unlike Fig. 4, here, only for simplicity, the auxiliary symbols \(\wedge\) and \(\sim\) are not used. All the Berry phases and as a result polarizations are calculated by the standard Berry phase scheme including SP by PBE-GGA for the normal FE LiNbO\(_3\) and by LDA for the normal FE LiTaO\(_3\) along the distortion path as functions of structure \(\lambda\) from \(``\lambda =0\)” to \(``\lambda =1\)” by step 0.1. For comparison, experimental87,87,89 and theoretical84,86,88 SEPs are included in (b) for LiNbO\(_3\) (in (d) for LiTaO\(_3\)).
