Fluorite ferroelectrics are exciting candidates for next-generation non-volatile memory devices because their unique ferroelectric mechanism, which arises from unconventional oxygen displacements, permits ferroelectricity with minimal thickness constraints. However, the polarisation switching mechanism remains the subject of intense debate due to a limited understanding of the atomic-scale dynamics which are extremely challenging to detect and measure. Here, we observe directly the polarisation switching pathways by visualising oxygen site dynamics in ZrO2 and Hf0.5Zr0.5O2 freestanding membranes using an advanced atomic-column imaging technique-optimum bright-field scanning transmission electron microscopy. We observe that the 180- and 90-degree polarisation pathways involve different nonpolar intermediate states with distinct spatial scales. Coupled with density functional theory, we also reveal how different cation species in fluorite oxides impact the accessible polarisation switching pathways. Our atomic-level insights into the polarisation switching dynamics open new avenues for the advanced engineering of fluorite ferroelectric materials and resulting memory devices.

Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.

A computer algorithm to search symmetries of crystal structures as implemented in the \texttt{spglib} code is described. An iterative algorithm is employed to robustly identify space group types tolerating a certain amount of distortion in the crystal structures. The source code is distributed under the 3-Clause BSD License, a permissive open-source software license. This paper focuses on the algorithm for identifying the space group symmetry of the crystal structures.

Many rotational invariants for crystal structure representations have been used to describe the structure-property relationship by machine learning. The machine learning interatomic potential (MLIP) is one of the applications of rotational invariants, which provides the relationship between the energy and the crystal structure. Since the MLIP requires the highest accuracy among machine learning estimations of the structure-property relationship, the enumeration of rotational invariants is useful for constructing MLIPs with the desired accuracy. In this study, we introduce high-order linearly independent rotational invariants up to the sixth order based on spherical harmonics and apply them to linearized MLIPs for elemental aluminum. A set of rotational invariants is derived by the general process of reducing the Kronecker products of irreducible representations (Irreps) for the SO(3) group using a group-theoretical projector method. A high predictive power for a wide range of structures is accomplished by using high-order invariants with low-order invariants equivalent to pair and angular structural features.

Lattice thermal conductivities (LTCs) of \alpha-, \beta-, and \gamma-Si$_3$N$_4$ single crystals are investigated from ab initio anharmonic lattice dynamics, within the single-mode relaxation-time approximation of the linearized phonon Boltzmann transport equation. At a temperature of 300 K, a \kappa$_{xx}$ of 70 and a \kappa$_{zz}$ of 98 (in units of Wm$^{-1}$K$^{-1}$) are obtained for \alpha-Si$_3$N$_4$. For \beta-Si$_3$N$_4$, \kappa$_{xx}$ and \kappa$_{zz}$ are found to be 71 and 194, respectively, which are consistent with the reported experimental values of 69 and 180 for individual \beta-Si$_3$N$_4$ grains in a ceramic. The theoretical \kappa$_{xx}$ values of \alpha- and \beta-Si$_3$N$_4$ are comparable, while the \kappa$_{zz}$ value of \beta-Si$_3$N$_4$ is almost twice that of \alpha-Si$_3$N$_4$, which demonstrates the very large anisotropy in the LTC of the \beta phase. It is found that the large anisotropy in the LTC of \beta-Si$_3$N$_4$ was caused by the elongated Brillouin zone along the c* axis, where the acoustic phonons mostly contribute to LTC and have large group velocities even near the Brillouin zone boundary. The LTC of \gamma-Si$_3$N$_4$ is 81, which is as small as that of \alpha-Si$_3$N$_4$, although \gamma-Si$_3$N$_4$ has much larger elastic constants. This means that elastic constants are not always a good indicator of LTC. We show that knowing the detailed distributions of both the group velocities and phonon lifetimes in the Brillouin zones is important for characterizing the LTC of the three phases.

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for the atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

Ion-conducting solid electrolytes are widely used for a variety of purposes. Therefore, designing highly ion-conductive materials is in strongly demand. Because of advancement in computers and enhancement of computational codes, theoretical simulations have become effective tools for investigating the performance of ion-conductive materials. However, an exhaustive search conducted by theoretical computations can be prohibitively expensive. Further, for practical applications, both dynamic conductivity as well as static stability must be satisfied at the same time. Therefore, we propose a computational framework that simultaneously optimizes dynamic conductivity and static stability; this is achieved by combining theoretical calculations and the Bayesian multi-objective optimization that is based on the Pareto hyper-volume criterion. Our framework iteratively selects the candidate material, which maximizes the expected increase in the Pareto hyper-volume criterion; this is a standard optimality criterion of multi-objective optimization. Through two case studies on oxygen and lithium diffusions, we show that ion-conductive materials with high dynamic conductivity and static stability can be efficiently identified by our framework.

A combination of systematic density functional theory (DFT) calculations and machine learning techniques has a wide range of potential applications. This study presents an application of the combination of systematic DFT calculations and regression techniques to the prediction of the melting temperature for single and binary compounds. Here we adopt the ordinary least-squares regression (OLSR), partial least-squares regression (PLSR), support vector regression (SVR) and Gaussian process regression (GPR). Among the four kinds of regression techniques, the SVR provides the best prediction. In addition, the inclusion of physical properties computed by the DFT calculation to a set of predictor variables makes the prediction better. Finally, a simulation to find the highest melting temperature toward the efficient materials design using kriging is demonstrated. The kriging design finds the compound with the highest melting temperature much faster than random designs. This result may stimulate the application of kriging to efficient materials design for a broad range of applications.

Lattice thermal conductivities of zincblende- and wurtzite-type compounds with 33 combinations of elements are calculated with the single-mode relaxation-time approximation and linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations. In 9 zincblende-type compounds, distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary non-smoothly with respect to wave vector, which is explained from the imaginary parts of the self energies. It is presented that detailed combination of phonon-phonon interaction strength and three phonon selection rule is critically important to determine phonon lifetime for these compounds. This indicates difficulty to predict phonon lifetime quantitatively without anharmonic force constants. However it is shown that joint density of states weighted by phonon numbers, which is calculated only from harmonic force constants, can be potentially used for a screening of the lattice thermal conductivity of materials.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them have even an electronic band gap < 1 eV, what makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which chemistry of materials are required to be optimized.

The representations of a compound, called "descriptors" or "features", play an essential role in constructing a machine-learning model of its physical properties. In this study, we adopt a procedure for generating a systematic set of descriptors from simple elemental and structural representations. First it is applied to a large dataset composed of the cohesive energy for about 18000 compounds computed by density functional theory (DFT) calculation. As a result, we obtain a kernel ridge prediction model with a prediction error of 0.041 eV/atom, which is close to the "chemical accuracy" of 1 kcal/mol (0.043 eV/atom). The procedure is also applied to two smaller datasets, i.e., a dataset of the lattice thermal conductivity (LTC) for 110 compounds computed by DFT calculation and a dataset of the experimental melting temperature for 248 compounds. We examine the performance of the descriptor sets on the efficiency of Bayesian optimization in addition to the accuracy of the kernel ridge regression models. They exhibit good predictive performances.

The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but also can a set of structures satisfying given constraints be extracted from the ZDD efficiently. Here, we present a ZDD-based efficient algorithm for exhaustively searching for special quasirandom structures (SQSs) that mimic the perfectly random substitutional structure. We demonstrate that the current approach can extract only a tiny number of SQSs from a ZDD composed of many substitutional structures (>$10^{12}$). As a result, we find SQSs that are optimized better than those proposed in the literature. A series of SQSs should be helpful for estimating the properties of substitutional solid solutions. Furthermore, the present ZDD-based algorithm should be useful for applying the ZDD to the other structure enumeration problems.

Zirconia ceramics have been known as a structural material with high fracture toughness and strength since Garvie et al. discovered phase transformation toughening in 1975 [1]. Although these mechanical properties are the most excellent among the advanced ceramics, the toughness has not yet reached the level of metallic materials. Here, we demonstrate for the first time that 2.9 mass% Y2O3-stabilized ZrO2s doped with Al2O3 greatly exceed the toughness of conventional zirconia ceramics which is comparable to those of metallic materials, even with slightly higher strength. The excellent mechanical properties in the proposed ceramic materials will be useful for further expanding the application of advanced ceramics to many engineering fields.

Using first-principles calculations we examine the crystal structures and phase transitions of nitride perovskite LaWN$_3$. Lattice dynamics calculations indicate that the ground-state structure belongs to space group $R3c$. Two competitive phase transition pathways are identified which are characterized by symmetry-adapted distortion modes. The results suggest that $R3c$ LaWN$_3$ should be an excellent ferroelectric semiconductor: its large spontaneous polarization of around 61 $\mu$C/cm$^2$ is comparable to that of PbTiO$_3$, and its band gap is about 1.72 eV. Ferroelectricity is found to result from the \emph{B}-site instability driven by hybridization between W-5$d$ and N-2$p$ orbitals. These properties make LaWN$_3$ an attractive candidate material for use in ferroelectric memory devices and photovoltaic cells.

The addition of artificial pinning centers has led to an impressive increase in critical current density ($J_{\rm c}$) in a superconductor, enabling record-breaking all-superconducting magnets and other applications. $J_{\rm c}$ has reached $\sim 0.2$-$0.3$ $J_{\rm d}$, where $J_{\rm d}$ is the depairing current density, and the numerical factor depends on the pinning optimization. By modifying $\lambda$ and/or $\xi$, the penetration depth and coherence length, respectively, we can increase $J_{\rm d}$. For (Y$_{0.77}$Gd$_{0.23}$)Ba$_2$Cu$_3$O$_y$ ((Y,Gd)123) we achieve this by controlling the carrier density, which is related to $\lambda$ and $\xi$. We also tune $\lambda$ and $\xi$ by controlling the chemical pressure in the Fe-based superconductors, BaFe$_2$(As$_{1-x}$P$_x$)$_2$ films. The variation of $\lambda$ and $\xi$ leads to an intrinsic improvement of $J_{\rm c}$, via $J_{\rm d}$, obtaining extremely high values of $J_{\rm c}$ of $130$ MA/cm$^2$ and $8.0$ MA/cm$^2$ at $4.2$ K, consistent with an enhancement of $J_{\rm d}$ of a factor of $2$ for both incoherent nanoparticle-doped (Y,Gd)123 coated conductors (CCs) and BaFe$_2$(As$_{1-x}$P$_x$)$_2$ films, showing that this new material design is useful to achieving high critical current densities for a wide array of superconductors. The remarkably high vortex-pinning force in combination with this thermodynamic and pinning optimization route for the (Y,Gd)123 CCs reached $\sim 3.17$ TN/m$^3$ at $4.2$ K and 18 T (${\bf H}\parallel c$), the highest values ever reported in any superconductor.

Scientific simulation codes are public property sustained by the community. Modern technology allows anyone to join scientific software projects, from anywhere, remotely via the internet. The phonopy and phono3py codes are widely used open source phonon calculation codes. This review describes a collection of computational methods and techniques as implemented in these codes and shows their implementation strategies as a whole, aiming to be useful for the community. Some of the techniques presented here are not limited to phonon calculations and may therefore be useful in other area of condensed matter physics.

Using first-principles calculations we examine the crystal structures and phase transitions of nitride perovskite LaWN$_3$. Lattice dynamics calculations indicate that the ground-state structure belongs to space group $R3c$. Two competitive phase transition pathways are identified which are characterized by symmetry-adapted distortion modes. The results suggest that $R3c$ LaWN$_3$ should be an excellent ferroelectric semiconductor: its large spontaneous polarization of around 61 $\mu$C/cm$^2$ is comparable to that of PbTiO$_3$, and its band gap is about 1.72 eV. Ferroelectricity is found to result from the \emph{B}-site instability driven by hybridization between W-5$d$ and N-2$p$ orbitals. These properties make LaWN$_3$ an attractive candidate material for use in ferroelectric memory devices and photovoltaic cells.

The use of a special quasirandom structure (SQS) is a rational and efficient way to approximate random alloys. A wide variety of physical properties of metallic and semiconductor random alloys have been successfully estimated by a combination of an SQS and density functional theory (DFT) calculation. Here, we investigate the application of an SQS to the ionic multicomponent systems with configurations of heterovalent ions, including point-charge lattices, MgAl$_2$O$_4$ and ZnSnP$_2$. It is found that the physical properties do not converge with the supercell size of the SQS. This is ascribed to the fact that the correlation functions of long-range clusters larger than the period of the supercell are not optimized in the SQS. However, we demonstrate that the physical properties of the perfectly disordered structure can be estimated by linear extrapolation using the inverse of the supercell size.

Functionalities in crystalline materials are determined by 3-dimensional collective interactions of atoms. The confinement of dimensionality in condensed matter provides an exotic research direction to understand the interaction of atoms, thus can be used to tailor or create new functionalities in material systems. In this study, a 2-dimensional transition metal oxide monolayer is constructed inside complex oxide heterostructures based on the theoretical predictions. The electrostatic boundary conditions of oxide monolayer in the heterostructure is carefully designed to tune the chemical, electronic, and magnetic states of oxide monolayer. The challenge of characterizing such an oxide monolayer is overcome by a combination of transmission electron microscopy, x-ray absorption spectroscopy, cross-sectional scanning tunneling microscopy, and electrical transport measurements. An intriguing metal-insulator transition associated with a magnetic transition is discovered in the MnO2 monolayer. This study paves a new route to understand the confinement of dimensionality and explore new intriguing phenomena in condensed matters.

The electromagnetic properties of type-II superconductors depend on vortices-magnetic flux lines whose motion introduces dissipation that can be mitigated by pinning from material defects. The material disorder landscape is tuned by the choice of materials growth technique and incorporation of impurities that serve as vortex pinning centers. For example, metal organic deposition (MOD) and pulsed laser deposition (PLD) produce high-quality superconducting films with uncorrelated versus correlated disorder, respectively. Here, we study vortex dynamics in PLD-grown EuBa2Cu3Oy films containing varying concentrations of BaHfO3 inclusions and compare our results with those of MOD-grown (Y,Gd)Ba2Cu3Oy films. Despite both systems exhibiting behavior consistent with strong pinning theory, which predicts the critical current density J_c based on vortex trapping by randomly distributed spherical inclusions, we find striking differences in the vortex dynamics owing to the correlated versus uncorrelated disorder. Specifically, we find that the EuBa2Cu3Oy films grown without inclusions exhibit surprisingly slow vortex creep, comparable to the slowest creep rates achieved in (Y,Gd)Ba2Cu3Oy films containing high concentrations of BaHfO3. Whereas adding inclusions to (Y,Gd)Ba2Cu3Oy is effective in slowing creep, BaHfO3 increases creep in EuBa2Cu3Oy even while concomitantly improving J_c. Lastly, we find evidence of variable range hopping and that J_c is maximized at the BaHfO3 concentration that hosts a vortex or Bose glass state.