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Nuclear site analysis methods are used to enumerate the normal modes of $ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes of the fourteen subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the $BX_{6}$ octahedra with different sense and amplitude about high symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing distortions of the $BX_{6}$ octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and would serve as reference point in elucidating the atomic origin of a wide range of physical properties in synthetic perovskite thin films and superlattices., Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed through link specified within manuscript

Ferroic transition metal oxides, which exhibit spontaneous elastic, electrical, magnetic or toroidal order, exhibit functional properties that find use in ultrastable solid-state memories to sensors and medical imaging technologies. To realize multifunctional behavior, where one order parameter can be coupled to the conjugate field of another order parameter, however, requires a common microscopic origin for the long-range order. Here, we formulate a complete theory for a novel form of ferroelectricity, whereby a spontaneous and switchable polarization emerges from the destruction of an antiferroelectric state due to octahedral rotations and ordered cation sublattices. We then construct a materials design framework based on crystal-chemistry descriptors rooted in group theory, which enables the facile design of artificial oxides with large electric polarizations, P, simultaneous with small energetic switching barriers between +P and -P. We validate the theory with first principles density functional calculations on more than 16 perovskite-structured oxides, illustrating it could be operative in any materials classes exhibiting two- or three-dimensional corner-connected octahedral frameworks. We show the principles governing materials selection of the "layered" systems originate in the lattice dynamics of the A cation displacements stabilized by the pervasive BO$_6$ rotations of single phase ABO$_3$ materials, whereby the latter distortions govern the optical band gaps, magnetic order and critical transition temperatures. Our approach provides the elusive route to the ultimate multifunctionality property control by an external electric field., Comment: 13 pages, 11 figures

Increasing demands for electric field-tunable electric, magnetic, and orbital (EMO) materials has renewed interests in ferroelectricity and its coupling to EMO properties in complex perovskite oxides. The historic design strategy to achieve a spontaneous polarization involves the incorporation of second-order Jahn-Teller (SOJT) active cations. The challenge, however, is that this mechanism is limited to specific chemistries and the polar distortions that arise are largely decoupled from EMO properties, limiting their use as field-tunable multifunctional technology materials. Here we report the crystal-chemistry criteria which circumvents those restrictions and enables the rational design of new materials displaying octahedral rotation-induced ferroelectricity - an innovative route to realize electric polarization without the need for SOJT cations - from non-polar building blocks. The strategy exploits the centric octahedral rotation patterns, which strongly couple to EMO properties, and cation ordering commonly observed in non-polar $AB$O$_3$ perovskites. By uniting switchable electric polarizations to the connectivity of the transition-metal oxygen octahedra, electric-field control over materials properties is possible., Comment: Supplementary information available upon request

We use density functional theory (DFT) calculations to study the lattice vibrations and electronic properties of the correlated metal LaNiO$_3$. To characterize the rhombohedral to cubic structural phase transition of perovskite LaNiO$_3$, we examine the evolution of the Raman-active phonon modes with temperature. We find that the $A_{1g}$ Raman mode, whose frequency is sensitive to the electronic band structure, is a useful signature to characterize the octahedral rotations in rhombohedral LaNiO$_3$. We also study the importance of electron--electron correlation effects on the atomic structure with two approaches which go beyond the conventional band theory (local spin density approximation): the local spin density+Hubbard $U$ method (LSDA$+U$) and hybrid exchange-correlation density functionals which include portions of exact Fock-exchange. We find the conventional LSDA accurately reproduces the delocalized nature of the valence states in LaNiO$_3$ and gives the best structural and vibrational agreement to the available experimental data. Based on our calculations, we show that the electronic screening effect from the delocalized Ni 3$d$ and O-2$p$ states mitigate the electronic correlations of the $d^7$ Ni cations, making LaNiO$_3$ a weakly correlated metal., Comment: 14 pages, 9 figures

The confluence of state-of-the-art electronic-structure computations and modern synthetic materials growth techniques is proving indispensable in the search for and discovery of new functionalities in oxide thin films and heterostructures. Here, we review the recent contributions of electronic-structure calculations to predicting, understanding, and discovering new materials physics in thin-film perovskite oxides. We show that such calculations can accurately predict both structure and properties in advance of film synthesis, thereby guiding the search for materials combinations with specific targeted functionalities. In addition, because they can isolate and decouple the effects of various parameters which unavoidably occur simultaneously in an experiment -- such as epitaxial strain, interfacial chemistry and defect profiles -- they are able to provide new fundamental knowledge about the underlying physics. We conclude by outlining the limitations of current computational techniques, as well as some important open questions that we hope will motivate further methodological developments in the field.

Using first-principles density functional theory calculations, we discover an anomalously large bi-axial strain-induced octahedral rotation axis reorientation in orthorhombic perovskites with tendency towards rhombohedral symmetry. The transition between crystallographically equivalent (isosymmetric) structures with different octahedral rotation magnitudes originates from strong strain--octahedral rotation coupling available to perovskites and the energetic hierarchy among competing octahedral tilt patterns. By elucidating these criteria, we suggest many functional perovskites would exhibit the transition in thin film form, thus offering a new landscape in which to tailor highly anisotropic electronic responses., Comment: 5 pages, 3 figures

Using {\it ab initio} density functional theory we explore the behavior of thin layers of metallic $d^4$ SrFeO$_3$ confined between the $d^0$ dielectric SrTiO$_3$ in a superlattice geometry. We find the presence of insulating SrTiO$_3$ spacer layers strongly affects the electronic properties of SrFeO$_3$: For single SrFeO$_3$ layers constrained to their bulk cubic structure, the Fermi surface is two-dimensional, nested and resembles the hole-doped superconducting cuprates. A Jahn-Teller instability couples to an octahedral tilt mode, however, to remove this degeneracy resulting in insulating superlattices., Comment: 4 pages, 4 figures

Using first-principles density functional theory we predict a ferroelectric ground state -- driven by off-centering of the magnetic Mn$^{4+}$ ion -- in perovskite-structure BaMnO$_3$. Our finding is surprising, since the competition between energy-lowering covalent bond formation, and energy-raising Coulombic repulsions usually only favors off-centering on the perovskite $B$-site for non-magnetic $d^0$ ions. We explain this tendency for ferroelectric off-centering by analyzing the changes in electronic structure between the centrosymmetric and polar states, and by calculating the Born effective charges; we find anomalously large values for Mn and O consistent with our calculated polarization of 12.8 $\mu$C/cm$^2$. Finally, we suggest possible routes by which the perovskite phase may be stabilized over the usual hexagonal phase, to enable a practical realization of a single-phase multiferroic., Comment: 6 pages, 3 figures

Using density functional theory within the LSDA + U method, we investigate the effect of strain on the spin state and magnetic ordering in perovskite lanthanum cobaltite, LaCoO3. We show that, while strain-induced changes in lattice parameters are insufficient to stabilize a non-zero spin state, additional heteroepitaxial symmetry constraints -- in particular the suppression of octahedral rotations -- stabilize a ferromagnetic intermediate-spin state. By comparing with experimental data for the bulk material, we calculate an upper bound on the Hubbard U value, and describe the role that the on-site Coulomb interaction plays in determining the spin-state configuration., Comment: RevTeX: 8 pages, 5 figures, expanded discussion and added Figure 5

We calculate the properties of the 4$d$ ferromagnet SrRuO$_3$ in bulk and thin film form with the aim of understanding the experimentally observed metal to insulator transition at reduced thickness. Although the spatial extent of the 4$d$ orbitals is quite large, many experimental results have suggested that electron-electron correlations play an important role in determining this material's electronic structure. In order to investigate the importance of correlation, we use two approaches which go beyond the conventional local density approximation to density functional theory (DFT): the local spin density approximation + Hubbard $U$ (LSDA+$U$) and the pseudopotential self-interaction correction (pseudo-SIC) methods. We find that the details of the electronic structure predicted with the LSDA do not agree with the experimental spectroscopic data for bulk and thin film SrRuO$_3$. Improvement is found by including electron-electron correlations, and we suggest that bulk orthorhombic SrRuO$_3$ is a {\it weakly strongly-correlated} ferromagnet whose electronic structure is best described by a 0.6 eV on-site Hubbard term, or equivalently with corrections for the self-interaction error. We also perform {\it ab initio} transport calculations that confirm that SrRuO$_3$ has a negative spin polarization at the Fermi level, due to the position of the minority Ru 4$d$ band center. Even with correlations included in our calculations we are unable to reproduce the experimentally observed metal-insulator transition, suggesting that the electronic behavior of SrRuO$_3$ ultra-thin films might be dominated by extrinsic factors such as surface disorder and defects., Comment: 15 pages, 12 figures, 3 tables