Octahedral Tilt Pattern Research Articles

Spin canting and lattice symmetry in La2CuO4

While the dominant magnetic interaction in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ is superexchange between nearest-neighbor Cu moments, the pinning of the spin direction depends on weak anisotropic effects associated with spin-orbit coupling. The symmetry of the octahedral tilt pattern allows an out-of-plane canting of the Cu spins, which is compensated by an opposite canting in nearest-neighbor layers. A strong magnetic field applied perpendicular to the planes can alter the spin canting pattern to induce a weak ferromagnetic phase. In light of recent evidence that the lattice symmetry is lower than originally assumed, we take another look at the nature of the field-induced spin-rotation transition. Comparing low-temperature neutron diffraction intensities for several magnetic Bragg peaks measured in fields of 0 and 14 T, we find that a better fit is provided by a model in which spins rotate within both neighboring planes but by different amounts, resulting in a noncollinear configuration. This model allows a more consistent relationship between lattice symmetry and spin orientation at all Cu sites.

Emergence of Rashba-/Dresselhaus effects in Ruddlesden–Popper halide perovskites with octahedral rotations

Ruddlesden–Popper halide perovskites are highly versatile quasi-two-dimensional energy materials with a wide range of tunable optoelectronic properties. Here we use the all-inorganic CsPb n X Ruddlesden–Popper perovskites with X = I, Br, and Cl to systematically model the effect of octahedral tilting distortions on the energy landscape, band gaps, macroscopic polarization, and the emergence of Rashba-/Dresselhaus splitting in these materials. We construct all unique n = 1 and n = 2 structures following from octahedral tilts and use first-principles density functional theory to calculate total energies, polarizations and band structures, backed up by band gap calculations using the GW approach. Our results provide design rules for tailoring structural distortions and band-structure properties in all-inorganic Ruddlesden–Popper perovskites through the interplay of the amplitude, direction, and chemical character of the antiferrodistortive distortion modes contributing to each octahedral tilt pattern. Our work emphasizes that, in contrast to three-dimensional perovskites, polar structures may arise from a combination of octahedral tilts, and Rashba-/Dresselhaus splitting in this class of materials is determined by the direction and Pb-I orbital contribution of the polar distortion mode.

Atomically engineered cobaltite layers for robust ferromagnetism.

Emergent phenomena at heterointerfaces are directly associated with the bonding geometry of adjacent layers. Effective control of accessible parameters, such as the bond length and bonding angles, offers an elegant method to tailor competing energies of the electronic and magnetic ground states. In this study, we construct unit-thick syntactic layers of cobaltites within a strongly tilted octahedral matrix via atomically precise synthesis. The octahedral tilt patterns of adjacent layers propagate into cobaltites, leading to a continuation of octahedral tilting while maintaining substantial misfit tensile strain. These effects induce severe rumpling within an atomic plane of neighboring layers, further triggering the electronic reconstruction between the splitting orbitals. First-principles calculations reveal that the cobalt ions transit to a higher spin state level upon octahedral tilting, resulting in robust ferromagnetism in ultrathin cobaltites. This work demonstrates a design methodology for fine-tuning the lattice and spin degrees of freedom in correlated quantum heterostructures by exploiting epitaxial geometric engineering.

Field-induced heterophase state in PbZrO3 thin films

Applications of epitaxial antiferroelectrics face scientific challenges, such as limited understanding of degraded (in comparison to bulk) switching behavior and its relation to nanoscale structural organization. We report on an unusual structural response of ${\mathrm{PbZrO}}_{3}/{\mathrm{SrRuO}}_{3}/{\mathrm{SrTiO}}_{3}$ (001) heterostructures to precritical (lower than required for switching) electric fields. In situ x-ray diffraction shows a ferrielectric-like structure, which forms gradually upon increasing the applied field and makes up a heterophase state with the host antiferroelectric phase. The field-induced structure is similar to the antiferroelectric parent phase in the octahedral-tilt pattern, but differs from it in the lead-ion displacement pattern. The latter can be encoded as $\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}$ provided that the antiferroelectric structure is encoded as $\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$. We propose that the unusual commensurateness (as opposed to the more ubiquitous incommensuration in similar materials) between the modulation periods of host and guest phases can be explained by accounting for the energy of heterophase boundaries, which is important in dense nanostructures due to the high surface-to-bulk ratio of nanodomains. An analysis using the ab-initio-correlated, but empirical (parametrized) energy model suggests that the observed field-induced structure is likely to be selected in ${\mathrm{PbZrO}}_{3}$ instead of the others in the case when the above commensuration effect is at play. The results point to the mechanism leading to the smearing of polarization-field loops in such heterostructures and suggest a perspective for the controlled creation of delicate dipolar orderings for ferroic-based memory.

Orbital-order phase transition in Pr1−xCaxMnO3 probed by photovoltaics

The phase diagram of $Pr_{1-x}Ca_xMnO_3$ is modified x $\le$ 0.3, which suggests a reevaluation of the phase diagram of other manganites in that doping region. Rather than an orbital ordered phase reaching up to high temperatures of approximately 800-1100 K, we propose a loss of spontaneous orbital order already near room temperature. Above this temperature, the phase is characterized by a finite orbital polarization and octahedral tilt pattern. The tilt pattern couples to the Jahn-Teller distortion and thus induces a remaining orbital order, which persists up to high temperatures, where the tilt order is lost as well. This explains the experimental observation of orbital order up to high temperatures. The reevaluation of the orbital order transition is based on observed anomalies of various physical properties at a temperatures of 220-260 K in epitaxial thin films of $Pr_{1-x}Ca_xMnO_3$ x=0.1, i.e.in the photovoltaic effect, electric transport, magnetization, optical and ultrafast transient pump probe studies. Finite-temperature simulations based on a tight-binding model with carefully adjusted parameters from first-principles calculations exhibit an orbital order phase transition at $T_{OO} \approx$ 300 K for x=0.1. This is consistent with the experimental observation of a temperature dependent change in lattice parameter for bulk samples of the same doping at 300 K for x=0.1 and 350 K for x=0, typical for a second order phase transition. Since our reassignment of the orbital order phase transition towards lower temperatures challenges a well-established and long-accepted picture, we provide results of multiple complementary measurements as well as a detailed discussion.

Structural and magnetic phase diagram of epitaxial La0.7Sr0.3MnO3 from first principles

ABO3 perovskites host a huge range of symmetry lowering structural distortions, each of which can tune, or even switch on or off, different functional properties due to the strong coupling between the lattice, spin and charge degrees of freedom in these materials. The sheer number of different meta-stable structures present in perovskites creates a challenge for materials design via theory and simulation. Here, we tackle this issue using a first principles structure searching method on a prototypical half-metallic perovskite, La0.7Sr0.3MnO3, to predict how epitaxial strain can engineer structural and magnetic properties. We reveal a rich structural phase diagram through strain engineering in which the octahedral tilt pattern, and hence the crystal symmetry, is altered from the bulk. We show how the low-symmetry of the various phases in turn induces new structural modes, an increase in the magnetic anisotropy energy, and weak antiferromagnetic spin-canting.

Liftout of High-Quality Thin Sections of a Perovskite Oxide Thin Film Using a Xenon Plasma Focused Ion Beam Microscope.

It is shown that a xenon plasma focused ion beam (FIB) microscope is an excellent tool for high-quality preparation of functional oxide thin films for atomic resolution electron microscopy. Samples may be prepared rapidly, at least as fast as those prepared using conventional gallium FIB. Moreover, the surface quality after 2 kV final polishing with the Xe beam is exceptional with only about 3 nm of amorphized surface present. The sample quality was of a suitably high quality to allow atomic resolution high-angle annular dark field imaging and integrated differential phase contrast without any further preparation, and the resulting images were good enough for quantitative evaluation of atomic positions to reveal the oxygen octahedral tilt pattern. This suggests that such xenon plasma FIB instruments may find widespread application in transmission electron microscope and scanning transmission electron microscope specimen preparation.

Correlation between epitaxial strain and magnetic properties in La0.7Sr0.3CoO3/La0.7Sr0.3MnO3 bilayers

Magnetic properties arising at interfaces of perovskite oxides such as La0.7Sr0.3CoO3 (LSCO) and La0.7Sr0.3MnO3 (LSMO) depend sensitively on the fine details of their structural properties. In this work, we use high-resolution transmission electron microscopy and spectroscopy to examine the structural and electronic phenomena at the interfaces in two LSCO/LSMO bilayers with reversed growth order. Two different strain mechanisms are at work in these films: compressive or tensile epitaxial strain, and distortion of the octahedral tilt pattern to maintain a network of corner-sharing octahedra. While the epitaxial strain is constant regardless of the growth order, the modification of the octahedral tilt pattern depends on whether the film is grown directly on the substrate or as the second sublayer. As a consequence, exchange spring behavior is observed only when the LSCO sublayer is grown first. The different mechanisms of strain accommodation within the oxygen octahedra network in each material proved to be of critical importance in determining the interfacial structure and thus magnetic and electronic properties of the bilayers.

Structural analysis of LaVO3 thin films under epitaxial strain

Rare earth vanadate perovskites exhibit a phase diagram in which two different types of structural distortions coexist: the strongest, the rotation of the oxygen octahedra, comes from the small tolerance factor of the perovskite cell (t = 0.88 for LaVO3) and the smaller one comes from inter-site d-orbital interactions manifesting as a cooperative Jahn-Teller effect. Epitaxial strain acts on octahedral rotations and crystal field symmetry to alter this complex lattice-orbit coupling. In this study, LaVO3 thin film structures have been investigated by X-ray diffraction and scanning transmission electron microscopy. The analysis shows two different orientations of octahedral tilt patterns, as well as two distinct temperature behaviors, for compressive and tensile film strain states. Ab initio calculations capture the strain effect on the tilt pattern orientation in agreement with experimental data.

Phase transformations in the relaxor Na1/2Bi1/2TiO3 studied by means of density functional theory calculations

AbstractThe relaxor material Na1/2Bi1/2TiO3 (NBT) is an important basis for the development of lead‐free piezoceramics, but still many features of this material are not well understood. Here, we study the kinetics of phase transformations by octahedral tilts and A‐cation displacements in NBT by means of density functional theory calculations, employing ab initio molecular dynamics and nudged elastic band calculations. Our results show that the energetic differences between the low temperature rhombohedral, intermediate orthorhombic and other metastable phases are close to the room temperature thermal energy. Therefore, it is likely that above room temperature, several octahedral tilt patterns are present simultaneously on the local scale, just because of thermal vibration of the oxygen ions. Octahedral tilt transformations and A‐cation displacements show similarly high energy barriers, however, since the vibrational frequency of oxygen is higher, tilt transformations occur more frequently. Further, tilt transformations in which the oxygen octahedra get deformed the least are more probable to occur. We also find that the chemical A‐cation order affects energy barriers, influences the coupling between rotational and displacive modes and determines the stability of certain octahedral tilt orders. We conclude that the so‐called polar nanoregions in this material result from local octahedral tilt transformations and subsequent A‐cation displacements, which are driven by thermal vibration and are mediated by the underlying chemical order.

Polar phase transitions in heteroepitaxial stabilized La0.5Y0.5AlO3 thin films

We report on the fabrication of epitaxial La0.5Y0.5AlO3 ultrathin films on (001) LaAlO3 substrates. Structural characterizations by scanning transmission electron microscopy and x-ray diffraction confirm the high quality of the film with a−b+c− AlO6 octahedral tilt pattern. Unlike either of the nonpolar parent compound, LaAlO3 and YAlO3, second harmonic generation measurements on the thin films suggest a nonpolar–polar phase transition at Tc near 500 K, and a polar–polar phase transition at Ta near 160 K. By fitting the angular dependence of the second harmonic intensities, we further propose that the two polar structures can be assigned to the Pmc21 and Pmn21 space group, while the high temperature nonpolar structure belongs to the Pbnm space group.

Strain And Symmetry-induced Structural Transitions in Ultra-thin BiFeO3 Films

As one of very few room temperature multiferroic materials, bismuth ferrite (BiFeO3: BFO) has been studied extensively in recent years. The bulk form of BFO is known to have a rhombohedrally distorted quasi-cubic perovskite structure with an (a–,a–,a–) octahedral tilt pattern, exhibiting both anti-ferrodistortive displacements and a spontaneous polarization along the <111> axes. Investigating epitaxial thin films under compressive strain, several studies have reported that the polarization direction is tilted towards the [001] out-of-plane direction, while maintaining a significant in-plane component. This effect is accompanied by a significant enhancement of the spontaneous polarization and a series of phase transitions from rhombohedral (R) for small strains to R-like monoclinic (MA) to T-like monoclinic (MC) and to tetragonal (T) for larger strains [1]. Through synchrotron-based 3-dimensional reciprocal space mapping (RSM), facilitated by using X-ray area detectors (Pilatus 100K pixel detector), we have investigated the structure of ultra-thin BFO films grown on SrTiO3 (STO), LaAlO3 (LAO), and TbScO3 (TSO) substrates with thicknesses of only several unit cells. In this thickness regime, the influence of the substrate atomic structure on the properties of the ultra-thin films is very pronounced, and the films exhibit perfect heteroepitaxy up to a critical thickness when the build up of strain energy forces the films into a relaxed structure. Both on STO [2] and LAO, the ultra-thin BFO undergoes a monoclinic to tetragonal phase transition, but with very different c/a axis ratios. On TSO, a very pronounced and well-ordered stripe domainstructure evolves where the domain sizes are strongly thickness- dependent. Argonne National Laboratory's work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357.

Splitting of the transition to the antiferroelectric state in PbZr0.95Ti0.05O3into polar and antiferrodistortive components

The phase transformations of ceramic PbZr${}_{1\ensuremath{-}x}$Ti${}_{x}$O${}_{3}$ are studied at the composition $x=0.05$ close to the morphotropic phase boundary between antiferroelectric orthorhombic $Pbam$ and ferroelectric rhombohedral phases by elastic, dielectric, and x-ray diffraction measurements. Temperature scans at different rates show that the kinetics of the transition from $R3m$ to $Pbam$ is very sluggish, and is actually split into a slower polar component, appearing in the dielectric susceptibility and a nonpolar component, visible as a sharp stiffening of the Young's modulus. The latter is assigned to the establishment of the oxygen octahedral tilt pattern of the $Pbam$ phase, and occurs at once at a temperature that decreases with increasing cooling rate. On heating, the transition occurs at a temperature 65 K higher than on quasistatic cooling, so that both components occur with a faster rate almost together. The Young's modulus presents a variety of apparently different types of anomalies, depending on temperature rate and history, which, however, can be well reproduced in terms of steplike anomalies corresponding to the two components of the $Pbam\ensuremath{\leftrightarrow}R3m$ transition and the tilt $R3c\ensuremath{\leftrightarrow}R3m$ transition in the region of coexistence of the FE and AFE phases.

Normal mode determination of perovskite crystal structures with octahedral rotations: theory and applications

Nuclear site analysis methods are used to enumerate the normal modes of ABX3 perovskite polymorphs with octahedral rotations. We provide the modes of the 14 subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the BX6 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 BX6 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 could serve as a reference point in elucidating the atomic origins of a wide range of physical properties of synthetic perovskite thin films and superlattices.

First-principles prediction of oxygen octahedral rotations in perovskite-structure EuTiO3

We present a systematic first-principles study of the structural and vibrational properties of perovskite-structure EuTiO3. Our calculated phonon spectrum of the high-symmetry cubic structural prototype shows strong M- and R-point instabilities, indicating a tendency to symmetry-lowering structural deformations composed of rotations and tilts of the oxygen octahedra. Subsequent explicit study of 14 different octahedral tilt-patterns showed that the I4/mcm, Imma, and R\bar{3}c structures, all with antiferrodistortive rotations of the octahedra, have significantly lower total energy than the prototype Pm\bar{3}m structure. We discuss the dynamical stability of these structures, and the influence of the antiferrodistortive structural distortions on the vibrational, optical, and magnetic properties of EuTiO3, in the context of recent unexplained experimental observations.

Large Isosymmetric Reorientation of Oxygen Octahedra Rotation Axes in Epitaxially Strained Perovskites

Using first-principles density functional theory calculations, we discover an anomalously large biaxial 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.

Local structure ofLa1.65Eu0.2Sr0.15CuO4determined by63CuNMR spectroscopy and Van Vleck paramagnetism ofEu3+ions

We investigate the local symmetry of the tilting of the CuO$_6$ octahedra in La$_{\rm 1.65}$Eu$_{\rm 0.2}$Sr$_{\rm 0.15}$CuO$_{4}$ by means of $^{63}$Cu NMR spectroscopy and the Van Vleck susceptibility of the $\rm Eu^{3+}$ ions. The Cu NMR central line lineshape is sensitive to local structure through the coupling of the $^{63}\rm Cu$ nuclear quadrupole moment to the local electric field gradient.The $\rm Eu^{3+}$ Van Vleck susceptibility, as a single ion effect, locally probes the symmetry of the crystal field at the Eu site. Both techniques independently provide clear evidence for a change of the local tilt symmetry at the first order structural transition from the orthorhombic to the low temperature tetragonal phase, in excellent agreement with the average structure obtained by diffraction techniques. We conclude that the symmetry of the average crystal structure accurately represents the symmetry of the octahedral tilt pattern on a local scale.