arXiv subjects

Atsushi Togo

Publications and source records attributed to Atsushi Togo.

At least 19 recordsLinked to original sources

arXiv2026

Axial thermal expansion from free-energy minimization with temperature-dependent force constants in phonopy: a technical report, with $α$- and $ω$-Ti as the worked example

In a hexagonal crystal the $a$ and $c$ axes change their lengths at different rates with increasing temperature, and the thermal expansion is described by two coefficients, one for each axis. The equilibrium lattice parameters at each temperature are found by minimizing the Helmholtz free energy over the lattice parameters, and the coefficients are their logarithmic derivatives with respect to temperature. This report describes a procedure for this minimization as implemented in phonopy. The free energy is computed with harmonic force constants at a finite set of values of $a$ and $c$, and a free-energy surface over $a$ and $c$ is fitted to these values. In a variant, the harmonic force constants are replaced by temperature-dependent force constants from a self-consistent harmonic approximation, with the forces computed by a machine-learning potential fitted at each of these values. The $α$ and $ω$ phases of titanium are the worked example. Both calculations give negative thermal expansion of the $c$ axis of $α$-Ti at low temperature and none in $ω$-Ti, and they differ most for the $c$ axis of $α$-Ti. The axial coefficients are harder to compute than the volumetric one, because the two axes are coupled in the free energy. In both phases of titanium the thermal effect that lengthens $a$ also shortens $c$. The coefficient of the $c$ axis is then the sum of two terms of opposite sign that partly cancel, and a small error in either term gives a large relative error in the coefficient. The report measures how much each setting of the procedure changes the thermal expansion coefficients, with the $c$ axis of $α$-Ti as the most sensitive case.

cond-mat.mtrl-sci↗

arXiv2026

Scalable construction of force-constant basis sets for large-scale anharmonic lattice-dynamical calculations

A projector-based formulation of force constants in crystalline materials provides a systematic framework for constructing force-constant bases and determining force constants from force--displacement datasets while rigorously satisfying crystal symmetry, permutation symmetry, and translational invariance. In this work, we develop an efficient eigenvalue solver for projection matrices and integrate it into the projector-based framework. The proposed method substantially reduces the computational cost and enables practical calculations for large-scale systems, low-symmetry crystals, and higher-order force constants that are difficult to treat using conventional approaches. Applications to self-consistent phonon calculations for assessing the grain-boundary excess free energy, lattice thermal conductivity calculations in complex compounds, and fourth-order force-constant estimations demonstrate the efficiency and robustness of the proposed framework for large and complex materials systems.

cond-mat.mtrl-sci↗

arXiv2025

Ab initio calculations of the thermoelectric figure of merit, within the relaxation time approximation

In this paper, we propose a computational framework, based on the VASP and phono3py computer codes, to obtain the thermoelectric figure of merit from the electron-phonon and phonon-phonon interactions using finite displacements in supercells. Several numerical techniques are developed for efficiency. The method is applied to several thermoelectric materials. We found different behaviors for the lifetimes of the electrons in PbTe, PbSe, and in compounds of the half-Heusler and magnesium silicide family. This is traced back to the different frequencies of the phonons involved in the scattering around the Fermi level. They have a lower frequency in PbTe and PbSe. The magnitude of the thermoelectric figures of merit we computed compare well with experiments, but the agreement is far from perfect. The role of the defects, not explicitly considered in our calculations, but abundant in thermoelectric materials, is discussed as a possible explanation. It is also shown that the choice of the exchange-correlation functional can strongly impact the results.

cond-mat.mtrl-sci↗

arXiv2024

Projector-based efficient estimation of force constants

Estimating force constants for crystal structures is crucial for calculating various phonon-related properties. However, this task becomes particularly challenging when dealing with a large number of atoms or when third- and higher-order force constants are required. In this study, we propose an efficient approach that involves constructing a complete orthonormal basis set for the force constants. We formulate this approach using projection matrices and their eigenvectors to meet the requirements for the force constants. This basis set enables precise inference of the force constants from displacement-force datasets. Our efficient algorithms for basis-set construction and force constant estimation are implemented in the symfc code. Furthermore, several applications demonstrated in this study indicate that the current approach facilitates the efficient and accurate determination of force constants.

cond-mat.mtrl-sci↗

arXiv2024

On-the-fly training of polynomial machine learning potentials in computing lattice thermal conductivity

The application of first-principles calculations for predicting lattice thermal conductivity (LTC) in crystalline materials, in conjunction with the linearized phonon Boltzmann equation, has gained increasing popularity. In this calculation, the determination of force constants through first-principles calculations is critical for accurate LTC predictions. For material exploration, performing first-principles LTC calculations in a high-throughput manner is now expected, although it requires significant computational resources. To reduce computational demands, we integrated polynomial machine learning potentials on-the-fly during the first-principles LTC calculations. This paper presents a systematic approach to first-principles LTC calculations. We designed and optimized an efficient workflow that integrates multiple modular software packages. We applied this approach to calculate LTCs for 103 compounds of the wurtzite, zincblende, and rocksalt types to evaluate the performance of the polynomial machine learning potentials in LTC calculations. We demonstrate a significant reduction in the computational resources required for the LTC predictions.

cond-mat.mtrl-sci↗

arXiv2024

Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism

Recent studies identified spin-order-driven phenomena such as spin-charge interconversion without relying on the relativistic spin-orbit interaction. Those physical properties can be prominent in systems containing light magnetic atoms due to sizable exchange splitting and may pave the way for realization of giant responses correlated with the spin degree of freedom. In this paper, we present a systematic symmetry analysis based on the spin crystallographic groups and identify the physical property of a vast number of magnetic materials up to 1500 in total. By decoupling the spin and orbital degrees of freedom, our analysis enables us to take a closer look into the relation between the dimensionality of spin structures and the resultant physical properties and to identify the spin and orbital contributions separately. In stark contrast to the established analysis with magnetic space groups, the spin crystallographic group manifests richer symmetry including spin-translation symmetry and leads to emergent responses. For representative examples, we discuss the geometrical nature of the anomalous Hall effect and magnetoelectric effect and classify the spin Hall effect arising from the nonrelativistic spin-charge coupling. Using the power of computational analysis, we apply our symmetry analysis to a wide range of magnets, encompassing complex magnets such as those with noncoplanar spin structures as well as collinear and coplanar magnets. We identify emergent multipoles relevant to physical responses and argue that our method provides a systematic tool for exploring sizable electromagnetic responses driven by spin order.

cond-mat.mtrl-sci↗

arXiv2024

$\texttt{Spglib}$: a software library for crystal symmetry search

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.

cond-mat.mtrl-sci↗

arXiv2024

Layer group classification of two-dimensional materials

The symmetry of a crystal structure with a three-dimensional (3D) lattice can be classified by one of the 230 space group types. For some types of crystals, e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate to assume a 2D lattice. With this assumption, the structure can be classified by one of the 80 layer group types. We have implemented an algorithm to determine the layer group type of a 3D structure with a 2D lattice, and applied it to more than 15,000 monolayer structures in the Computational 2D Materials (C2DB) database. We compare the classification of monolayers by layer groups and space groups, respectively. The latter is defined as the space group of the 3D bulk structure obtained by repeating the monolayer periodically in the direction perpendicular to the 2D lattice (AA-stacking). By this correspondence, nine pairs of layer group types are mapped to the same space group type due to the inability of the space group to distinguish the in-plane and out-of-plane axes. In total 18% of the monolayers in the C2DB belong to one of these layer group pairs and are thus not properly classified by the space group type.

cond-mat.mtrl-sci↗

arXiv2023

Algorithm for spin symmetry operation search

A spin space group provides a suitable way to fully exploit the symmetry of a spin arrangement with a negligible spin-orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the field of magnetism. However, there is no established algorithm to search for spin symmetry operations of the spin space group. This paper presents an exhaustive algorithm for determining spin symmetry operations of commensurate spin arrangements. The present algorithm searches for spin symmetry operations from the symmetry operations of a corresponding nonmagnetic crystal structure and determines their spin-rotation parts by solving a Procrustes problem. An implementation is distributed under a permissive free software license in spinspg v0.1.1: https://github.com/spglib/spinspg.

cond-mat.mtrl-sci↗

arXiv2023

Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structure

A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs) remains limited. In this paper, algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types of given MSGs, searching for transformations to a BNS setting, and symmetrizing the magnetic crystal structures using the MSGs are presented. The determination of magnetic symmetry operations is numerically stable and is implemented with minimal modifications from the existing crystal symmetry search. Magnetic space-group types and transformations to the BNS setting are identified by a two-step approach combining space-group type identification and the use of affine normalizers. Point coordinates and magnetic moments of the magnetic crystal structures are symmetrized by projection operators for the MSGs. An implementation is distributed with a permissive free software license in spglib v2.0.2: https://github.com/spglib/spglib.

cond-mat.mtrl-sci↗

arXiv2023

Implementation strategies in phonopy and phono3py

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.

cond-mat.mtrl-sci↗

arXiv2022

Zero-point Renormalization of the Band Gap of Semiconductors and Insulators Using the PAW Method

We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fröhlich model, as discussed in Phys. Rev. Lett. 115, 176401 (2015) and Phys. Rev. B 92, 054307 (2015). The data are compared to recent calculations, npj Computational Materials 6, 167 (2020), and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find however that the pseudo version converges more rapidly with respect to the number of included unoccupied states.

cond-mat.mtrl-sci↗

arXiv2022

LO-mode phonon of KCl and NaCl at 300 K by inelastic X ray scattering measurements and first principles calculations

Longitudinal-optical (LO) mode phonon branches of KCl and NaCl were measured using inelastic X-ray scattering (IXS) at 300 K and calculated by the first-principles phonon calculation with the stochastic self-consistent harmonic approximation. Spectral shapes of the IXS measurements and calculated spectral functions agreed well. We analyzed the calculated spectral functions that provide higher resolutions of the spectra than the IXS measurements. Due to strong anharmonicity, the spectral functions of these phonon branches have several peaks and the LO modes along $Γ$--L paths are disconnected.

cond-mat.mtrl-sci↗

arXiv2020

Phonon structure of titanium under shear deformation along $\{10\bar{1}2\}$ twinning mode

We investigated phonon behavior of hexagonal close packed titanium under homogeneous shear deformation corresponding to the $\{10\bar{1}2\}$ twinning mode using first-principles calculation and phonon calculation. By this deformation, we found that a phonon mode located at a point on Brillouin zone boundary is drastically soften increasing the shear and finally it triggers a spontaneous structural transition by breaking the crystal symmetry toward twin from parent.

cond-mat.mtrl-sci↗

arXiv2019

Group-theoretical high-order rotational invariants for structural representations: Application to linearized machine learning interatomic potential

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.

physics.comp-ph↗

arXiv2018

Lattice thermal conductivities of two SiO$_2$ polymorphs by first-principles calculation and phonon Boltzmann transport equation

Lattice thermal conductivities of two SiO$_2$ polymorphs, i.e., $α$-quartz (low) and $α$-cristobalite (low), were studied using first-principles anharmonic phonon calculation and linearized phonon Boltzmann transport equation. Although $α$-quartz and $α$-cristobalite have similar phonon densities of states, phonon frequency dependencies of phonon group velocities and lifetimes are dissimilar, which results in largely different anisotropies of the lattice thermal conductivities. For $α$-quartz and $α$-cristobalite, distributions of the phonon lifetimes effective to determine the lattice thermal conductivities are well described by energy and momentum conservations of three phonon scatterings weighted by phonon occupation numbers and one parameter that represents the phonon-phonon interaction strengths.

cond-mat.mtrl-sci↗

arXiv2017

Descriptors for Machine Learning of Materials Data

Descriptors, which are representations of compounds, play an essential role in machine learning of materials data. Although many representations of elements and structures of compounds are known, these representations are difficult to use as descriptors in their unchanged forms. This chapter shows how compounds in a dataset can be represented as descriptors and applied to machine-learning models for materials datasets.

cond-mat.mtrl-sci↗

arXiv2017

DynaPhoPy: A code for extracting phonon quasiparticles from molecular dynamics simulations

We have developed a computational code, DynaPhoPy, that allow us to extract the microscopic anharmonic phonon properties from molecular dynamics (MD) simulations using the normal-mode-decomposition technique as presented by Sun et al. [T. Sun, D. Zhang, R. Wentzcovitch, 2014]. Using this code we calculated the quasiparticle phonon frequencies and linewidths of crystalline silicon at different temperatures using both of first-principles and the Tersoff empirical potential approaches. In this work we show the dependence of these properties on the temperature using both approaches and compare them with reported experimental data obtained by Raman spectroscopy [M. Balkanski, R. Wallis, E. Haro, 1983 and R. Tsu, J. G. Hernandez, 1982].

cond-mat.mtrl-sci↗