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First-principles investigation of ferroelectricity in epitaxially strained<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Pb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi mathvariant="normal">Ti</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>
The structure and polarization of the as-yet hypothetical Ruddlesden--Popper compound ${\mathrm{Pb}}_{2}\mathrm{Ti}{\mathrm{O}}_{4}$ are investigated within density-functional theory. Zone center phonons of the high-symmetry ${\mathrm{K}}_{2}\mathrm{Ni}{\mathrm{F}}_{4}$-type reference structure, space group I4/mmm, were calculated. At the theoretical ground-state lattice constants, there is one unstable infrared-active phonon. This phonon freezes in to give the I2mm …