Theoretical studies of PbTiO3 and SrTiO3 under uniaxial mechanical constraints combining first-principles calculations and phenomenological Landau theory

Abstract

In the present thesis we present theoretical studies of perovskite compounds under uniaxial mechanical constraints combining first-principles DFT calculations approach and phenomenological Landau theory. ABO3 perovskites form a very important class of functional materials that can exhibit a broad range of properties (e.g., superconductivity, magnetism, ferroelectricity, multiferroism, metal-insulator transitions. . . ) within small distortions of the same simple prototype cubic structure. Though these compounds have been extensively studied both experimentally and computationally, there are still unresolved issues regarding the effect of pressure. In recent years, strain engineering has reported to be an original approach to tune the ferroelectric properties of perovskite ABO3 compounds. While the effect of epitaxial biaxial strain and hydrostatic strain is rather well understood in this class of materials, very little is yet known regarding the effect of uniaxial mechanical constraints. Our study is motivated by the little existing understanding of the effect of uniaxial strain and stress, that has been up to now almost totally neglected. Two prototype compounds are studied in detail: PbTiO3 and SrTiO3. After a general introduction on ABO3 compounds and calculations techniques (ab initio and phenomenological Landau model), we studied the effect of mechanical constraints in these compounds in our thesis. PbTiO3 is a prototypical ferroelectric compound and also one of the parent components of the Pb(Zr,Ti)O3 solid solution (PZT), which is the most widely used piezoelectrics. For PbTiO3, we have shown 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 (FEz phase) or along one of the pseudocubic axis perpendicular to it (FEx phase). This contrasts with the case of isotropic or biaxial mechanical constraints for which novel phases combining ferroelectric and antiferrodistortive motions have been previously reported. Under uniaxial strain, PbTiO3 switches from a FEx ground state under compressive strain to FEz ground-state under tensile strain, beyond a criticalstrain _czz _ +1%. Under uniaxial stress, PbTiO3 exhibits either a FEx ground state under compression (_zz < 0) or a FEz ground state under tension (_zz > 0). Here, however, an abrupt jump of the structural parameters is also predicted under both compressive and tensile stresses at critical values _zz _ +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 nano devices. The second compound of interest is SrTiO3. It has been widely studied in the past decadesdue to its unusual properties at low temperature. In this work, we have extended our previous investigations on PbTiO3 by exploring theoretically the pressure effects on perovskite SrTiO3 combining the first-principles calculations and a phenomenological Landau model. We have discussed the evolution of phonon frequencies of SrTiO3 with the three isotropic, uniaxial and biaxial strains using first-principles calculations. We also reproduce the previous work done in SrTiO3 with epitaxial strain and hydrostatic strain. Finally, we have calculated the phase diagram of SrTiO3 under uniaxial strain, as obtained from Landau theory and discussed how it compares with the first-principles calculations.