Multiple Sublattices Research Articles

Hierarchical Nanostructures Constructed by Soft Epitaxial Self-Assembly of Organic-Inorganic Hybrid Giant Amphiphiles.

2D nanomaterials with ångström-scale thicknesses offer a unique platform for confining molecules at an unprecedentedly small scale, presenting novel opportunities for modulating material properties and probing microscopic phenomena. In this study, mesogen-tethered polyhedral oligomeric silsesquioxane (POSS) amphiphiles with varying numbers of mesogenic tails to systematically influence molecular self-assembly and the architecture of the ensuing supramolecular structures, are synthesized. These organic-inorganic hybrid amphiphiles facilitate precise spatial arrangement and directional alignment of the primary molecular units within highly ordered supramolecular structures. The correlation between molecular design and the formation of superlattices through comprehensive structural analyses, incorporating molecular thermodynamics and kinetics, is explored. The distinct intermolecular interactions of the POSS core and the mesogenic tails drive the preferential formation of a 2D inorganic sublattice while simultaneously guiding the hierarchical assembly of organic lamellae via soft epitaxy. The findings reveal the intricate balance between shape, size, and interaction strengths of the inorganic and organic components, and how these factors collectively influence the structural hierarchy of the superstructures, which consist of multiple sublattices. By controlling this unique molecular behavior, it is possible to modulate or maximize the anisotropy of optical, mechanical, and electrical properties at the sub-nanometer scale for nanotechnology applications.

A new compositional microscopic degree of freedom at grain boundaries in complex compounds: a case study in spinel.

The accurate computational treatment of polycrystalline materials requires the rigorous generation of grain boundary (GB) structures as many quantities of interest depend strongly on the specifics of the macroscopic and microscopic degrees of freedom (DoFs) used in their creation. In complex materials, containing multiple sublattices and where atomic composition can vary spatially through the system, we introduce a new microscopic DoF based on this compositional variation which we find governs observable properties. In spinel - a wide class of complex oxides where this compositional variation manifests as cation inversion - we exploit this DoF to generate and analyze low-energy microstates of two GBs with three spinel chemistries (FeCr2O4, NiCr2O4 and MgAl2O4). This treatment is found to allow for the co-redistribution of cations at the GBs which acts to modify the spatial charge distribution, defect segregation energy and defect transport through these regions. Additionally, we generate low-energy metastable microstates of the GB system with an induced cation disorder, simulating those which may develop as a result of damage events. These are then analyzed to discover their composition and defect transport properties which depend strongly on the amount of induced damage. We conclude that considering this new DoF is important in describing the properties of GBs in complex materials.

Generalization of the mixed-space cluster expansion method for arbitrary lattices

Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.

XAI USING FORMAL CONCEPT LATTICE FOR IMAGE DATA

A Formal concept lattice can be used to generate explanations from a black box model. This novel approach has been applied and proven for tabular data. It has also been compared to popular techniques in XAI. In this work, we apply the approach to image data. Image data, in general, comprises large dimensions and hence poses a challenge to build a formal concept lattice from such large data. We break the image into parts and build multiple sub-lattices. Using the combination of sub-lattice explanations, we generate the complete explanation for the entire image. We present our work beginning with a simple synthetic dataset for providing an intuitive idea of explanations and its credibility. This is followed by explanations of a model built on the popular MNIST dataset proving consistency of explanations on a real dataset. Text explanations from the lattice are converted to images for ease of visual understanding. We compare our work with DeepLIFT by viewing image masks obtained through contrastive explanation for specific digits from the MNIST dataset. This work proves the feasibility of using formal concept lattices for image data.

Unified lattice sums accommodating multiple sublattices for solutions of the Helmholtz equation in two and three dimensions

The authors derive expressions for lattice sums of solutions of the Helmholtz equation in two and three dimensions that can be efficiently evaluated in numerical implementations. The results are applicable to complex materials involving multiple sublattices, describing systems including metasurfaces and moire superlattices.

Sublattice-sensitive Majorana modes

For two- and three-dimensional topological insulators whose unit cells consist of multiple sublattices, the boundary terminating at which type of sublattice can affect the time-reversal invariant momentum at which the Dirac points of helical boundary states are located. By incorporating a generic theory and a representative model, we reveal that this interesting property allows the realization of Majorana modes at sublattice domain walls forming on the boundary when the boundary Dirac points of the topological insulator are gapped by appropriate superconductivity in proximity. Remarkably, we find that the sensitive sublattice dependence of the Majorana modes allows their positions to be precisely manipulated by locally controlling the terminating sublattices or boundary potential. Our work reveals that the sublattice degrees of freedom commonly found in materials open a different route to realize and manipulate Majorana modes.

Exchange scaling of ultrafast angular momentum transfer in 4f antiferromagnets

Ultrafast manipulation of magnetism bears great potential for future information technologies. While demagnetization in ferromagnets is governed by the dissipation of angular momentum1–3, materials with multiple spin sublattices, for example antiferromagnets, can allow direct angular momentum transfer between opposing spins, promising faster functionality. In lanthanides, 4f magnetic exchange is mediated indirectly through the conduction electrons4 (the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction), and the effect of such conditions on direct spin transfer processes is largely unexplored. Here, we investigate ultrafast magnetization dynamics in 4f antiferromagnets and systematically vary the 4f occupation, thereby altering the magnitude of the RKKY coupling energy. By combining time-resolved soft X-ray diffraction with ab initio calculations, we find that the rate of direct transfer between opposing moments is directly determined by this coupling. Given the high sensitivity of RKKY to the conduction electrons, our results offer a useful approach for fine tuning the speed of magnetic devices.

Understanding complex multiple sublattice magnetism in double double perovskites

Understanding magnetism in multiple magnetic sublattice system, driven by the interplay of varied nature of magnetic exchanges, is on one hand challenging and on other hand intriguing. Motivated by the recent synthesis of AA^{prime }BB^{prime }O_6 double double perovskites with multiple magnetic ions both at A- and B-sites, we investigate the mechanism of magnetic behavior in these interesting class of compounds. We find that the magnetism in such multiple sublattice compounds is governed by the interplay and delicate balance between two distinct mechanisms, (a) kinetic energy-driven multiple sublattice double exchange mechanism and (b) the conventional super-exchange mechanism. The derived spin Hamiltonian based on first-principles calculations is solved by classical Monte Carlo technique which reproduces the observed magnetic properties. Finally, the influence of off-stoichiometry, as in experimental samples, is discussed. Some of these double double perovskite compounds are found to possess large total magnetic moment and also are found to be half-metallic with reasonably high transition temperature, which raises the hope of future applications of these large magnetic moment half-metallic oxides in spintronics and memory devices.

Multisublattice cluster expansion study of short-range ordering in iron-substituted strontium titanate

Owing to the challenges in obtaining realistic atomic configurations in large chemical phase spaces, it is not straightforward to describe structure–property relations in materials exhibiting configurational disorder. One example is iron-substituted strontium titanate (SrTi1−xFexO3−d, STF), a promising perovskite-derivative cathode material in solid oxide fuel cells that exhibits full solid solubility 0≤x≤1 and a tendency to exhibit short-range order. Here we demonstrate a multisublattice cluster expansion (CE) framework and apply it to STF across the full composition range. The CE approach is distinct from more traditional CE formulations in that clusters are defined explicitly by the chemical species distributed among multiple sublattices, rather than via cluster functions of occupation variables with decoration. The modified CE approach makes it easy to distinguish meaningful chemical interactions that are harder to extract from conventional CE, since for the latter chemical identity in a cluster is expressed as a product of site occupations. The least absolute shrinkage and selection operator (LASSO) is implemented as a regression analysis tool to select key clusters and avoid overfitting. We demonstrate this formulation on STF, and show that it can accurately predict configurational energies in comparison to conventional CE. From the key clusters, we identify that short-range ordering between substitutional Fe and oxygen vacancies (VO) results in the formation of Fe–VO strings. In addition, we consider the stability of STF through CE-based Monte Carlo (MC) simulations and confirm the presence of superstructures that were previously observed in transmission electron microscopy. Analysis of atomic configurations from MC samples reveals variations in the oxidation state of Fe atoms, which can be explained by the ordering tendency of Fe and VO. The cluster description and selection formalism described here may be applied to other disordered multisublattice systems for accurate and efficient material modeling.

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multi-point ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multi-point ordering are often only applicable for very specific cases and/or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this work, a cluster order parameter (ClstOP) is introduced to systematically quantify arbitrary multi-point ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multi-point chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined within and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on alloy nanocage stability are discussed. It is demonstrated that approximating 4-point probabilities from superpositions of lower order pair probabilities is not sufficient in cases where 3 and 4-body terms are included in the energy expression. Conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

A universal configurational entropy metric for high-entropy materials

In recent years, high-entropy materials have become increasingly complex, outgrowing simple solid-solution based calculations of configurational entropy, and with that, the previously established metrics for high-, medium-, and low-entropy. Those previous metrics are derived from metals-specific approximations of the entropy of fusion and the internal energy of a monatomic gas, and thus, do not apply to other materials. A new entropy metric is proposed that is universally applicable for crystalline materials, from simple solid-solution high-entropy alloys to high-entropy materials with complex crystal structures and multiple sublattices. Additionally, the methods for calculating configurational entropy in complex crystal structures are discussed.

Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb–Schultz–Mattis and Oshikawa–Yamanaka–Affleck theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the S = 1/2 kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a two-fold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at 1/3. Our results are in broad agreement with numerical and experimental studies.

Proper dissipative torques in antiferromagnetic dynamics

There is little doubt that the magnetization dynamics of ferromagnetic systems is governed by the Landau-Lifshitz-Gilbert equation or its generalization with various spin torques. In contrast, there are several sets of dynamic equations for two-sublattice antiferromagnets (AFMs) in the literature that have different forms of dissipative torques and no proper dynamic equations for multi-sublattice AFMs and ferrimagnets in general. Here we introduce the general Rayleigh dissipation functional into the Lagrange equation and derive the proper form of the dissipative torques in the phenomenological equations for the AFMs with multiple sublattices. A new type of dissipative torque arising from the inter-sublattice drag effect is discovered which has important effects on the magnon lifetime and domain wall motion.

A Thermodynamic Modelling of the Stability of Sigma Phase in the Cr-Fe-Ni-V High-Entropy Alloy System

The addition of vanadium (V) to the representative Co-Cr-Fe-Mn-Ni high-entropy alloy (HEA) system is attracting attention expecting a large solid solution hardening effect. For the design of V-added HEAs, prediction of the sigma (σ) phase formation has been mainly issued because it affects a significant influence on the mechanical properties. Although the CALculation of PHAse Diagram (CALPHAD) approach can be a good tool for prediction of phase structures, robust thermodynamic database is still required for an accurate prediction of V-added HEA systems. The present work aims at providing a thermodynamic description for the Cr-Fe-Ni-V HEA system, focusing on the thermodynamic stability of the σ phase. A parameterization technique which minimizes the number of fitting parameter and simplifies the extension into higher-order systems is proposed and applied to the σ phase with multiple sublattice during modelling the Cr-Ni-V and Fe-Ni-V systems. The reliability of the developed thermodynamic description for the Cr-Fe-Ni-V quaternary system is experimentally confirmed by designing, fabricating and analysing the phase structures of a series of Cr-Fe-Ni-V HEAs.

MODELS OF HAMILTONIAN AND LOW-FREQUENCY SPECTRA OF COLLECTIVE EXCITATIONS IN SPIN S = 1 MAGNETICS

The paper studies the dynamic description of non-equilibrium processes in single-sublattice and multisublattice magnets with the spin s=1. In case of magnets with the spin s=1 and SU(3) symmetry of the exchange interaction, there are eight magnetic integrals of motion: the spin and the quadrupole matrix. If there are multiple sublattices, the number of additional magnetic quantities characterizing the state increases to sixteen. The presence of the Casimir invariants makes it possible to reduce the number of independent degrees of freedom. Exchange energy models are presented in terms of Casimir invariants corresponding to SO(3) or SU(3) symmetry groups for all four types of magnetic degrees of freedom. For the homogeneous part of the exchange energy, we have found conditions for the existence of local minima, which correspond to equilibrium values of the magnet. Along with the known waves (quadrupole and Goldstone – for the spin nematic), spectra of collective excitations that take into account ferro-quadrupole excitation, quadro-nematic, quadro- antiferromagnetic, and antiferro-nematic waves excitation, are also obtained. In the case of many-sublattice magnetic systems, we have shown that the selected form of the homogeneous energy model allows us to find possible magnetic orderings and to investigate them for stability.

Big data in reciprocal space: Sliding fast Fourier transforms for determining periodicity

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 (LCMO) films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis and Independent Component Analysis of the Sliding FFT dataset reveal the distinct changes in crystallography, step edges, and boundaries between the multiple sub-lattices. The implications for the LCMO system are discussed. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.

Role of the lattice structure in determining the magnon-mediated interactions between charge carriers doped into a magnetically ordered background

We use two recently proposed methods to calculate exactly the spectrum of two spin-$\frac{1}{2}$ charge carriers moving in a ferromagnetic background, at zero temperature, for three types of models. By comparing the low-energy states in both the one-carrier and the two-carrier sectors, we analyze whether complex models with multiple sublattices can be accurately described by simpler Hamiltonians, such as one-band models. We find that while this is possible in the one-particle sector, the magnon-mediated interactions which are key to properly describe the two-carrier states of the complex model are not reproduced by the simpler models. We argue that this is true not just for ferromagnetic, but also for antiferromagnetic backgrounds. Our results question the ability of simple one-band models to accurately describe the low-energy physics of cuprate layers.

Disorder in materials with complex crystal structures: the Non-Local Coherent Potential Approximation for compounds with multiple sublattices

Over the last few years the Non-Local Coherent Potential Approximation (NL-CPA) has been shown to provide an effective way to describe the electronic structure and related properties of disordered systems, where short-range order (SRO) and other local environment effects are important. Here we present its generalization to materials with multi-atom per unit cell lattices. The method is described using a Green function formalism and illustrated by an implementation for a simplified one-dimensional tight-binding model with substitutional disorder. This development paves the way for a natural reimplementation of the Korringa-Kohn-Rostoker (KKR) multiple scattering solution of Kohn-Sham equations for ab-initio calculations of real materials.

Ab initioaugmented space recursion to study complex multicomponent materials: Application to the pseudobinary alloyNi1−xPtxAl

Using first-principles density-functional calculations, we studied the electronic structure and phase stability of the pseudobinary alloys. The calculations have been carried out using the augmented space recursion based on the all electron, tight-binding linear muffin-tin orbital basis. This work, in particular, provides a further generalization of our earlier developed technique to the case of systems of multiple sublattices with varying degree of disorder on them. We showcase the feasibility of our formalism by applying to a face-centered tetragonal-based pseudobinary ${({\text{Ni}}_{1\ensuremath{-}x}{\text{Pt}}_{x})}_{3}\text{Al}$ alloy system. Based on the calculation of effective pair interactions and their lattice Fourier transform, our phase stability search yields two stable superordered structures, namely, $\text{L}{1}_{0}$-type ${\text{Ni}}_{2}\text{PtAl}$ and $\text{L}{1}_{0}$-type ${\text{NiPt}}_{2}\text{Al}$ of which the latter has been observed experimentally. An estimate of the minima in the effective pair potential surface $V(\mathbf{k})$ predicted the order-disorder transition temperatures of the two stable structures to be $\ensuremath{\sim}1027$ and $\ensuremath{\sim}1379\text{ }\text{K}$, respectively. The results are in agreement with the previous findings, proving the effectiveness of augmented space recursive technique in dealing with systems of multiple sublattices with varying degree of disorder on them. Our calculated additional physical quantities such as short-range order maps can be compared with future experimental studies.

Solution-based thermodynamic modeling of the Ni–Ta and Ni–Mo–Ta systems using first-principle calculations

Solution-based thermodynamic descriptions of the Ni–Ta and Ni–Mo–Ta systems are developed with supporting first-principles calculations and reported experimental data for parameter evaluation. For the Ni–Ta system, the liquid, bcc and fcc phases are described with a random solution model, D0 22–Ni 3Ta is treated as a stoichiometric compound, and the remaining compounds are modeled as solid solutions on multiple sublattices. The resulting model for the Ni–Ta system is integrated with reported treatments of the Ni–Mo and Mo–Ta systems, and a thermodynamic model for the ternary Ni–Mo–Ta system is developed. The zero-Kelvin enthalpies of formation for the intermetallic compounds in the Ni–Mo–Ta system and the enthalpies of mixing for the bcc and fcc special quasirandom structures (SQS) in the binary Ni–Ta system are computed using the Vienna Ab-initio Simulation Package (VASP). Phase equilibria modeling results for the ternary Ni–Mo–Ta system are summarily presented in the form of isothermal sections and liquidus projections, with appropriate comparisons with available experimental data.