Geometric frustration of Jahn-Teller order in the infinite-layer lattice.

The Jahn-Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations1. Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO3 (refs. 2,3). Although many examples occur in octahedrally4 or tetrahedrally5 coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper6,7, nickel8,9, iron10,11 and manganese oxides12. Here we synthesize single-crystal CaCoO2 thin films by topotactic reduction of the brownmillerite CaCoO2.5 phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn-Teller degeneracy of the dxz and dyz orbitals in the d7 electronic configuration along with substantial ligand-transition metal mixing. A complex pattern of distortions arises in a [Formula: see text] tetragonal supercell, reflecting the competition between an ordered Jahn-Teller effect on the CoO2 sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO2 structure forms an extended two-in-two-out type of Co distortion following 'ice rules'13.

Linear-in-temperature resistivity for optimally superconducting (Nd,Sr)NiO2.

The occurrence of superconductivity in proximity to various strongly correlated phases of matter has drawn extensive focus on their normal state properties, to develop an understanding of the state from which superconductivity emerges1-4. The recent finding of superconductivity in layered nickelates raises similar interests5-8. However, transport measurements of doped infinite-layer nickelate thin films have been hampered by materials limitations of these metastable compounds: in particular, a high density of extended defects9-11. Here, by moving to a substrate (LaAlO3)0.3(Sr2TaAlO6)0.7 that better stabilizes the growth and reduction conditions, we can synthesize the doping series of Nd1-xSrxNiO2 essentially free from extended defects. In their absence, the normal state resistivity shows a low-temperature upturn in the underdoped regime, linear behaviour near optimal doping and quadratic temperature dependence for overdoping. This is phenomenologically similar to the copper oxides2,12 despite key distinctions-namely, the absence of an insulating parent compound5,6,9,10, multiband electronic structure13,14 and a Mott-Hubbard orbital alignment rather than the charge-transfer insulator of the copper oxides15,16. We further observe an enhancement of superconductivity, both in terms of transition temperature and range of doping. These results indicate a convergence in the electronic properties of both superconducting families as the scale of disorder in the nickelates is reduced.

Chemical gradients in human enamel crystallites.

Dental enamel is a principal component of teeth1, and has evolved to bear large chewing forces, resist mechanical fatigue and withstand wear over decades2. Functional impairment and loss of dental enamel, caused by developmental defects or tooth decay (caries), affect health and quality of life, with associated costs to society3. Although the past decade has seen progress in our understanding of enamel formation (amelogenesis) and the functional properties of mature enamel, attempts to repair lesions in this material or to synthesize it in vitro have had limited success4-6. This is partly due to the highly hierarchical structure of enamel and additional complexities arising from chemical gradients7-9. Here we show, using atomic-scale quantitative imaging and correlative spectroscopies, that the nanoscale crystallites of hydroxylapatite (Ca5(PO4)3(OH)), which are the fundamental building blocks of enamel, comprise two nanometric layers enriched in magnesium flanking a core rich in sodium, fluoride and carbonate ions; this sandwich core is surrounded by a shell with lower concentration of substitutional defects. A mechanical model based on density functional theory calculations and X-ray diffraction data predicts that residual stresses arise because of the chemical gradients, in agreement with preferential dissolution of the crystallite core in acidic media. Furthermore, stresses may affect the mechanical resilience of enamel. The two additional layers of hierarchy suggest a possible new model for biological control over crystal growth during amelogenesis, and hint at implications for the preservation of biomarkers during tooth development.

Publisher Correction: Chemical gradients in human enamel crystallites.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Real-space imaging of periodic nanotextures in thin films via phasing of diffraction data.

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO3/SrTiO3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca2RuO4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca2RuO4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

Resolving the polar interface of infinite-layer nickelate thin films.

Nickel-based superconductors provide a long-awaited experimental platform to explore possible cuprate-like superconductivity. Despite similar crystal structure and d electron filling, however, superconductivity in nickelates has thus far only been stabilized in thin-film geometry, raising questions about the polar interface between substrate and thin film. Here we conduct a detailed experimental and theoretical study of the prototypical interface between Nd1-xSrxNiO2 and SrTiO3. Atomic-resolution electron energy loss spectroscopy in the scanning transmission electron microscope reveals the formation of a single intermediate Nd(Ti,Ni)O3 layer. Density functional theory calculations with a Hubbard U term show how the observed structure alleviates the polar discontinuity. We explore the effects of oxygen occupancy, hole doping and cation structure to disentangle the contributions of each for reducing interface charge density. Resolving the non-trivial interface structure will be instructive for future synthesis of nickelate films on other substrates and in vertical heterostructures.

Doping evolution of the Mott-Hubbard landscape in infinite-layer nickelates.

The recent observation of superconductivity in [Formula: see text] has raised fundamental questions about the hierarchy of the underlying electronic structure. Calculations suggest that this system falls in the Mott-Hubbard regime, rather than the charge-transfer configuration of other nickel oxides and the superconducting cuprates. Here, we use state-of-the-art, locally resolved electron energy-loss spectroscopy to directly probe the Mott-Hubbard character of [Formula: see text] Upon doping, we observe emergent hybridization reminiscent of the Zhang-Rice singlet via the oxygen-projected states, modification of the Nd 5d states, and the systematic evolution of Ni 3d hybridization and filling. These experimental data provide direct evidence for the multiband electronic structure of the superconducting infinite-layer nickelates, particularly via the effects of hole doping on not only the oxygen but also nickel and rare-earth bands.

Superconductivity in a quintuple-layer square-planar nickelate.

Since the discovery of high-temperature superconductivity in copper oxide materials1, there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials2. One prime materials platform has been the rare-earth nickelates and, indeed, superconductivity was recently discovered in the doped compound Nd0.8Sr0.2NiO2 (ref. 3). Undoped NdNiO2 belongs to a series of layered square-planar nickelates with chemical formula Ndn+1NinO2n+2 and is known as the 'infinite-layer' (n = ∞) nickelate. Here we report the synthesis of the quintuple-layer (n = 5) member of this series, Nd6Ni5O12, in which optimal cuprate-like electron filling (d8.8) is achieved without chemical doping. We observe a superconducting transition beginning at ~13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd6Ni5O12 interpolates between cuprate-like and infinite-layer nickelate-like behaviour. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors that can be tuned via both doping and dimensionality.

Atomic-Scale Mapping and Quantification of Local Ruddlesden-Popper Phase Variations.

The Ruddlesden-Popper (An+1BnO3n+1) compounds are highly tunable materials whose functional properties can be dramatically impacted by their structural phase n. The negligible differences in formation energies for different n can produce local structural variations arising from small stoichiometric deviations. Here, we present a Python analysis platform to detect, measure, and quantify the presence of different n-phases based on atomic-resolution scanning transmission electron microscopy (STEM) images. We employ image phase analysis to identify horizontal Ruddlesden-Popper faults within the lattice images and quantify the local structure. Our semiautomated technique considers effects of finite projection thickness, limited fields of view, and lateral sampling rates. This method retains real-space distribution of layer variations allowing for spatial mapping of local n-phases to enable quantification of intergrowth occurrence and qualitative description of their distribution suitable for a wide range of layered materials.

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data.

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 µm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

A Superconducting Praseodymium Nickelate with Infinite Layer Structure.

A variety of nickel oxide compounds have long been studied for their manifestation of various correlated electron phenomena. Recently, superconductivity was observed in nanoscale infinite layer nickelate thin films of Nd0.8Sr0.2NiO2, epitaxially stabilized on SrTiO3 substrates via topotactic reduction from the perovskite precursor phase. Here, we present the synthesis and properties of PrNiO2 thin films on SrTiO3. Upon doping in Pr0.8Sr0.2NiO2, we observe superconductivity with a transition temperature of 7-12 K and robust critical current density at 2 K of 334 kA/cm2. These findings indicate that superconductivity in the infinite layer nickelates is relatively insensitive to the details of the rare earth 4f configuration. Furthermore, they motivate the exploration of a broader family of compounds based on two-dimensional NiO2 planes, which will enable systematic investigation of the superconducting and normal state properties and their underlying mechanisms.

Superconducting Dome in Nd_{1-x}Sr_{x}NiO_{2} Infinite Layer Films.

We report the phase diagram of Nd_{1-x}Sr_{x}NiO_{2} infinite layer thin films grown on SrTiO_{3}. A superconducting dome spanning 0.125

Atomic-Resolution Cryo-STEM Across Continuously Variable Temperatures.

Atomic-resolution cryogenic scanning transmission electron microscopy (cryo-STEM) has provided a path to probing the microscopic nature of select low-temperature phases in quantum materials. Expanding cryo-STEM techniques to broadly tunable temperatures will give access to the rich temperature-dependent phase diagrams of these materials. With existing cryo-holders, however, variations in sample temperature significantly disrupt the thermal equilibrium of the system, resulting in large-scale sample drift. The ability to tune the temperature without negative impact on the overall instrument stability is crucial, particularly for high-resolution experiments. Here, we test a new side-entry continuously variable temperature dual-tilt cryo-holder which integrates liquid nitrogen cooling with a 6-pin micro-electromechanical system (MEMS) sample heater to overcome some of these experimental challenges. We measure consistently low drift rates of 0.3-0.4 Å/s and demonstrate atomic-resolution cryo-STEM imaging across a continuously variable temperature range from ~100 K to well above room temperature. We conduct additional drift stability measurements across several commercial sample stages and discuss implications for further developments of ultra-stable, flexible cryo-stages.

Consequences and Control of Multiscale Order/Disorder in Chiral Magnetic Textures.

Transition metal intercalated transition metal dichalcogenides (TMDs) are promising platforms for next-generation spintronic devices based on their wide range of electronic and magnetic phases, which can be tuned by varying the host lattice or intercalant's identity, stoichiometry, or spatial order. Some of these compounds host a chiral magnetic phase in which the helical winding of magnetic moments propagates along a high-symmetry crystalline axis. Previous studies have demonstrated that variation in intercalant concentrations can have a dramatic effect on the formation of chiral domains and ensemble magnetic properties. However, a systematic and comprehensive study of how atomic-scale order and disorder impact these chiral magnetic textures is so far lacking. Here, we leverage a combination of imaging modes in the (scanning) transmission electron microscope (S/TEM) to directly probe (dis)order across multiple length scales and show how subtle changes in the atomic lattice can tune the mesoscale spin textures and bulk magnetic response in Cr1/3NbS2, with direct implications for the fundamental understanding and technological implementation of such compounds.

Synthesis of graded CdS1-xSex nanoplatelet alloys and heterostructures from pairs of chalcogenoureas with tailored conversion reactivity.

A mixture of N,N,N'-trisubstituted thiourea and cyclic N,N,N',N'-tetrasubstituted selenourea precursors were used to synthesize three monolayer thick CdS1-xSex nanoplatelets in a single synthetic step. The microstructure of the nanoplatelets could be tuned from homogeneous alloys, to graded alloys to core/crown heterostructures depending on the relative conversion reactivity of the sulfur and selenium precursors. UV-visible absorption and photoluminescence spectroscopy and scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS) images demonstrate that the elemental distribution is governed by the relative precursor conversion kinetics. Slow conversion kinetics produced nanoplatelets with larger lateral dimensions, behavior that is characteristic of precursor conversion limited growth kinetics. Across a 10-fold range of reactivity, CdS nanoplatelets have 4× smaller lateral dimensions than CdSe nanoplatelets grown under identical conversion kinetics. The difference in size is consistent with a rate of CdSe growth that is 4× greater than the rate of CdS. The influence of the relative sulfide and selenide growth rates, the duration of the nucleation phase, and the solute composition on the nanoplatelet microstructure are discussed.

Encoding multistate charge order and chirality in endotaxial heterostructures.

High-density phase change memory (PCM) storage is proposed for materials with multiple intermediate resistance states, which have been observed in 1T-TaS2 due to charge density wave (CDW) phase transitions. However, the metastability responsible for this behavior makes the presence of multistate switching unpredictable in TaS2 devices. Here, we demonstrate the fabrication of nanothick verti-lateral H-TaS2/1T-TaS2 heterostructures in which the number of endotaxial metallic H-TaS2 monolayers dictates the number of resistance transitions in 1T-TaS2 lamellae near room temperature. Further, we also observe optically active heterochirality in the CDW superlattice structure, which is modulated in concert with the resistivity steps, and we show how strain engineering can be used to nucleate these polytype conversions. This work positions the principle of endotaxial heterostructures as a promising conceptual framework for reliable, non-volatile, and multi-level switching of structure, chirality, and resistance.