Phase competition and negative piezoelectricity in interlayer-sliding ferroelectric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Zr</mml:mi><mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Ning Ding, Jun Chen, Churen Gui, Haipeng You, Xiaoyan Yao, Shuai Dong
Abstract
The so-called interlayer-sliding ferroelectricity was recently proposed as an unconventional route to pursuit electric polarity in van der Waals multilayers, which was already experimentally confirmed in a $\mathrm{W}{\mathrm{Te}}_{2}$ bilayer even though it is metallic. Very recently, another van der Waals system, i.e., the $\mathrm{Zr}{\mathrm{I}}_{2}$ bilayer, was predicted to exhibit the interlayer-sliding ferroelectricity with both in-plane and out-of-plane polarizations [Zhang et al., Phys. Rev. B 103, 165420 (2021)]. Here the $\mathrm{Zr}{\mathrm{I}}_{2}$ bulk is studied, which owns two competitive phases ($\ensuremath{\alpha}$ vs $\ensuremath{\beta}$), both of which are derived from the common parent $s$ phase. The $\ensuremath{\beta}\ensuremath{-}\mathrm{Zr}{\mathrm{I}}_{2}$ owns a considerable out-of-plane polarization ($0.39\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{C}/{\mathrm{cm}}^{2}$), while its in-plane component is fully compensated. Their proximate energies provide the opportunity to tune the ground state phase by moderate hydrostatic pressure and uniaxial strain. Furthermore, the negative longitudinal piezoelectricity in $\ensuremath{\beta}\ensuremath{-}\mathrm{Zr}{\mathrm{I}}_{2}$ is dominantly contributed by the enhanced dipole of $\mathrm{Zr}{\mathrm{I}}_{2}$ layers as a unique characteristic of interlayer-sliding ferroelectricity, which is different from many other layered ferroelectrics with negative longitudinal piezoelectricity like $\mathrm{Cu}\mathrm{In}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$.