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The c(2$\times$2) reconstruction of (001) PbTiO$_3$ surfaces is studied bymeans of first principles calculations for paraelectric (non-polar) andferroelectric ([001] polarized) films. Analysis of the atomic displacements inthe near-surface region shows how the surface modifies the antiferrodistortive(AFD) instability and its interaction with ferroelectric (FE) distortions. Theeffect of the surface is found to be termination dependent. The AFD instabilityis suppressed at the TiO$_2$ termination while it is strongly enhanced,relative to the bulk, at the PbO termination resulting in a c(2x2) surfacereconstruction which is in excellent agreement with experiments. We find that,in contrast to bulk PbTiO$_3$, in-plane ferroelectricity at the PbO terminationdoes not suppress the AFD instability. The AFD and the in-plane FE distortionsare instead concurrently enhanced at the PbO termination. This leads to a novelsurface phase with coexisting FE and AFD distortions which is not found inPbTiO$_3$ bulk

physical review. b, condensed matter and materials physics

Coexistence of antiferrodistortive and ferroelectric distortions at the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">PbTiO</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:mspace width="0.2em" /><mml:mo>(</mml:mo><mml:mn>001</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>surface

Coexistence of antiferrodistortive and ferroelectric distortions at thePbTiO3(001)surface