Ferroelectricity and chirality in the Pb_5Ge_3O_11 crystal
arxiv(2023)
摘要
We study from first-principles calculations the ferroelectric structural
phase transition of Pb_5Ge_3O_11 crystal. The calculations of phonons
and Born effective charges of the paraelectric phase allow us to identify a
polar instability that is unstable in both transverse-optic and
longitudinal-optic versions, giving rise to an entire branch of instability
along a propagation vector parallel to the mode polarization (the hexagonal
axe). This is the hint of hyperferroelectricity and the stable head-to-head and
tail-to-tail domain, as recently reported from both experiments and theory.
Then, our analysis of the ferroelectric phase shows that the polarization of
Pb_5Ge_3O_11 is uniaxial along the hexagonal axes and with small
in-plane components due to a piezoelectric effect. The symmetry-adapted mode
analysis shows that the total ferroelectric ground state distortion comes
mainly from polar distortions of the unstable polar phonon mode but also from
an invariant, cooperative mode that amplifies the polar deformation. We also
build a phenomenological model that highlights how the coupling between these
modes is at play and helps us understand how to reproduce the second-order
phase transition. At last, we also quantify the structural chirality through
the continuous symmetry measure method and trace its origin to the polar
unstable mode itself. By extending our approach to the phonon states we further
show that the chirality is poorly affected by the relaxation but could also be
enhanced by activating high frequency modes with polar symmetry. Finally we
study the phonon angular momentum (AM) distribution in both phases and identify
trends in the AM behaviour across the Brillouin zone.
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