Table 1 Calculated partial Berry phases and corresponding polarizations for the non-polar CS R\(\bar{3}\)c and polar NCS R3c hexagonal supercells of LiOsO\(_3\), using the PBE-GGA with mBp and mWf schemes.
From: Nonzero spontaneous electric polarization in metals: novel predictive methods and applications
mBp | mWf | |||
|---|---|---|---|---|
NCS R3c | CS R\(\bar{3}\)c | NCS R3c | CS R\(\bar{3}\)c | |
\(\varphi _{\textit{ion}}\) | 2.7396 | 6.2832 | – | – |
\(\varphi _{\textit{el}}^{{\text { (II)}}}\) | − 2.2402 | 0.0000 | – | – |
\(\phi _{\textit{el}}^{(\text {I}^*)}\) | 0.3267 | − 1.5403 | – | – |
\(\phi _{\textit{el}}=\varphi _{\textit{el}}^{{\text { (II)}}} +\phi _{\textit{el}}^{(\text {I}^*)}\) | − 1.9135 | − 1.5403 | – | – |
\(\phi =\varphi _{\textit{ion}}+2\phi _{\textit{el}}\) | − 1.0784 | 3.2026 | – | – |
\(\textbf{P}_{\textit{ion}}\) | 0.3130 | 0.0000 | 0.3130 | 0.0000 |
\(\textbf{P}_{\textit{el}}^{\text {(II)}}\) | 0.2060 | 0.0000 | 0.2076 | 0.0000 |
\(\textbf{P}_{\textit{el}}^{(\text {I}^*)}\) | 0.0746 | − 0.3519 | 0.0706 | − 0.3584 |
\(\textbf{P}_{\textit{el}}=\textbf{P}_{\textit{el}}^{\text {(II)}} +\textbf{P}_{\textit{el}}^{(\text {I}^*)}\) | 0.2806 | − 0.3519 | 0.2782 | − 0.3584 |
\(\textbf{P}=\textbf{P}_{\textit{ion}}+\textbf{P}_{\textit{el}}\) | 0.5936 | − 0.3519 | 0.5912 | − 0.3584 |
\(\Delta {\textbf{P}}=\textbf{P}\text {(R3c)}-\textbf{P}(\text {R}\bar{3}\text {c})\) | 0.9455 | 0.9496 | ||
