Abstract :
[en] 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. ABO$_3$ 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\ldots) 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 ABO$_3$ 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: PbTiO$_3$ and SrTiO$_3$. After a general introduction on ABO$_3$ compounds and calculations techniques (ab initio and phenomenological Landau model), we studied the effect of mechanical constraints in these compounds in our thesis.
PbTiO$_3$ is a prototypical ferroelectric compound and also one of the parent components of the Pb(Zr,Ti)O$_3$ solid solution (PZT), which is the most widely used piezoelectrics. For PbTiO$_3$, 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 ($FE_z$ phase) or along one of the pseudo-cubic axis perpendicular to it ($FE_x$ 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, PbTiO$_3$ switches 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.
The second compound of interest is SrTiO$_3$. It has been widely studied in the past decades due to its unusual properties at low temperature. In this work, we have extended our previous investigations on PbTiO$_3$ by exploring theoretically the pressure effects on perovskite SrTiO$_3$ combining the first-principles calculations and a phenomenological Landau model. We have discussed the evolution of phonon frequencies of SrTiO$_3$ with the three isotropic, uniaxial and biaxial strains using first-principles calculations. We also reproduce the previous work done in SrTiO$_3$ with epitaxial strain and hydrostatic strain. Finally, we have calculated the phase diagram of SrTiO$_3$ under uniaxial strain, as obtained from Landau theory and discussed how it compares with the first-principles calculations.
