First-principles study of PbTiO$_3$ under uniaxial strains and stresses

TL;DR

This study uses first-principles calculations to analyze how PbTiO$_3$ behaves under uniaxial strains and stresses, revealing stable ferroelectric phases and potential for enhanced piezoelectric response in nanodevices.

Contribution

It provides the first detailed first-principles analysis of PbTiO$_3$ under uniaxial mechanical constraints, highlighting phase stability and structural transitions.

Findings

PbTiO$_3$ remains ferroelectric under uniaxial constraints.

Transition from $FE_x$ to $FE_z$ phase occurs at critical strain $ exteta_{zz}^c \\approx +1\%.

Abrupt structural changes occur at specific stress values, indicating potential for piezoelectric enhancement.

Abstract

The behavior of PbTiO$_3$ under uniaxial strains and stresses is investigated from first-principles calculations within density functional theory. We show that irrespectively of the uniaxial mechanical constraint applied, the system keeps a purely ferroelectric ground-state, with the polarization aligned either along the constraint direction ($FE_z$ phase) or along one of the pseudo-cubic axis perpendicular to it ($FE_x$ phase). This contrasts with the cases of isotropic or biaxial mechanical constraints for which novel phases combining ferroelectic and antiferrodistortive motions have been previously reported. Under uniaxial strain, PbTiO$_3$ switched from a $FE_x$ ground state under compressive strain to $FE_z$ ground-state under tensile strain, beyond a critical strain $\eta_{zz}^c \approx +1$\%. Under uniaxial stress, PbTiO$_3$ exhibits either a $FE_x$ ground state under compression ($\sigma_{zz} < 0$) or a $FE_z$ ground state under tension ($\sigma_{zz} > 0$). Here, however, an abrupt jump of the structural parameters is also predicted under both compressive and tensile stresses at critical values $\sigma_{zz} \approx$ $+2$ GPa and $- 8$ GPa. This behavior appears similar to that predicted under negative isotropic pressure and might reveal practically useful to enhance the piezoelectric response in nanodevices.