Session R12: Recent Computational Advances in the Understanding of Complex Oxides

Hybrid functionals for simulating complex oxides

Hybrid functionals are a class of exchange-correlation (XC) functionals in density functional theory (DFT) that are constructed by a suitable mixing of local/semi-local XC functionals (LDA/GGA) with a certain portion of the exact Hartree-Fock exchange. After being used for years in the chemistry community for studying molecular properties, hybrid functionals are being increasingly widely used for solid state problems, for which standard LDA/GGA approximations provide a defective description. In particular, hybrid functionals appear to account well for the complicated coupling between lattice, charge and spin degrees of freedom in transition metal oxides, a class of materials that has recently attracted a lot of interest due to its technological relevance (all-oxides electronics), the large spectrum of functionalities, and the many challenging issues related to strong electronic correlation [1,2]. The purpose of this talk is to present the essential ideas and physical picture of hybrid functionals and to present a map of recent applications to complex oxides aiming to cover an ample spectra of cases ($sp$, 3$d$, 4$d$ and 5$d$ compounds) and to discuss an extended array of physical phenomena including: metal-to-insulator transitions, electron localization, bandgap prediction, polarons, multiferroism, and spin-orbit coupling. [1] C. Franchini, J. Phys. Condens. Matter 26, 253202 (2014). [2] J. G. He and C. Franchini, Phys. Rev. B 86, 235117 (2012).   

Electron-electron interactions and lattice distortions in the perovskite titanates

A two-dimensional electron gas (2DEG) with the unprecedented high density of 3x10$^{14}$ (corresponding to 1/2 electron per interface unit cell area) can be formed at the interface between SrTiO$_3$ and a rare-earth titanate ($R$TiO$_3$). The 2DEG resides in the SrTiO$_3$, and arises from a polar discontinuity at the interface. The formation of this 2DEG has led us to study these perovskite titanates in detail. Some of these compounds are Mott insulators, where a Mott-Hubbard gap opens up between partially filled Ti 3$d$ bands. This talk focuses on the importance of the interplay between electron-electron interactions and lattice distortions in these complex oxides, which we study with density functional theory using a hybrid functional, capable of correctly describing electron localization and Mott-insulating behavior. These effects are crucial to understanding the metal-to-insulator transition as a function of electron density. Indeed, very thin SrTiO$_3$ layers inserted in GdTiO$_3$ show insulating behavior, in contrast to the metallic character of thicker layers in which the electrons form a 2DEG. The same physics is observed in bulk SrTiO$_3$ when doped with 1/2 electron per Ti atom \footnote{L. Bjaalie, A. Janotti, B. Himmetoglu, and C. G. Van de Walle, Phys. Rev. B. 90, 195117 (2014).}. Charge localization and lattice distortions also govern the formation of small hole polarons in the rare-earth titanates. We demonstrate that these polarons impact the optical absorption measurements commonly used to determine the value of the Mott-Hubbard gap \footnote{L. Bjaalie, D. G. Ouellette, P. Moetakef, T. A. Cain, A. Janotti, B. Himmetoglu, S. J. Allen, S. Stemmer and C. G. Van de Walle, Appl. Phys. Lett. 106, 232103 (2015).}. \\ \\ Work performed in collaboration with Anderson Janotti, Burak Himmetoglu, and Chris G. Van de Walle, and supported by NSF and ARO.   

Transport Properties of Complex Oxides: New Ideas and Insights from Theory and Simulation

Complex oxides are one of the largest and most technologically important materials families. The ABO$_3$ perovskite oxides in particular display an unparalleled variety of physical properties. The microscopic origin of these properties (how they arise from the structure of the material) is often complicated, but in many systems previous research has identified simple guidelines or `rules of thumb’ that link structure and chemistry to the physics of interest. For example, the tolerance factor is a simple empirical measure that relates the composition of a perovskite to its tendency to adopt a distorted structure. First-principles calculations have shown that the tendency towards ferroelectricity increases systematically as the tolerance factor of the perovskite decreases. Can we uncover a similar set of simple guidelines to yield new insights into the ionic and thermal transport properties of perovskites? I will discuss recent research from my group on the link between crystal structure and chemistry, soft phonons and ionic transport in a family of layered perovskite oxides, the Ln$_2$NiO$_{4+\delta}$ Ruddlesden-Popper phases. In particular, we show how the lattice dynamical properties of these materials (their tendency to undergo certain structural distortions) can be correlated with oxide ion transport properties. Ultimately, we seek new ways to understand the microscopic origins of complex transport processes and to develop first-principles-based design rules for new materials based on our understanding.