arXiv subjects

Nobuhisa Fujita

Publications and source records attributed to Nobuhisa Fujita.

17 recordsLinked to original sources

arXiv2026

Complete Structural Determination of Mesostructural Dodecagonal Quasicrystalline Particles

Quasicrystals have revolutionized our understanding of order in solids by demonstrating exotic structural and physicochemical properties with diverse potential applications. Despite the development of various theoretical models and experimental techniques to describe quasicrystal structures, the precise determination of local three dimensional (3D) arrangements of constituent atoms, or of secondary building units such as clusters or micelles, remains elusive. This challenge is particularly acute in self assembled soft matter quasicrystalline systems, where the complex assembly of molecular groups introduces additional defects and structural modulations. Herein, we report the first complete structural determination of self-assembled mesostructural dodecagonal quasicrystalline particles. Employing advanced electron tomography, combined with dedicated structural tracing and processing workflows, the 3D coordinates of all nodal sites were extracted. This approach reveals that the actual structure deviates from the conventionally assumed tetrahedral close packing geometry, exhibiting diverse coordination environments and displacive fluctuations. We identified and quantified rotational intergrowths arising from node exchange, as well as various defects and disorder, with these features discernible only through 3D analysis. Additionally, we propose a simplified two-layer stacking of isomorphic hexagonal model to form dodecagonal quasicrystal. This work advances our understanding of soft-matter dodecagonal quasicrystals and paves the way for detailed structural elucidation of self-assembled systems.

cond-mat.mes-hall↗

arXiv2025

Monte Carlo study on critical exponents of the classical Heisenberg model in ferromagnetic icosahedral quasicrystal

Quasicrystals (QCs) lack three-dimensional periodicity of atomic arrangement but possess long-range structural order, which are distinct from periodic crystals and random systems. Here, we show how the ferromagnetic (FM) order arises in the icosahedral QC (i-QC) on the basis of the Monte Carlo simulation of the Heisenberg model on the Yb lattice of Cd$_{5.7}$Yb composed of regular icosahedrons. By finite-size scaling of the Monte Carlo data, we identified the critical exponents of the magnetization, magnetic susceptibility, and spin correlation length, $β=0.508(30)$, $γ=1.361(59)$, and $ν=0.792(17)$, respectively. We confirmed that our data satisfy the hyperscaling relation and estimated the other critical exponents $α=-0.376(51)$, $δ=3.68(23)$, and $η=0.282(65)$. These results show a new universality class inherent in the i-QC, which is different from those in periodic magnets and spin glasses. In the i-QC, each Yb site at vertices of the regular icosahedrons is classified into 8 classes with respect to the coordination numbers of the nearest-neighbor and next-nearest-neighbor bonds. We revealed the FM-transition mechanism by showing that the difference in the local environment of each site is governed by cooperative evolution of spin correlations upon cooling, giving rise to the critical phenomena.

cond-mat.str-el↗

arXiv2025

A novel variant of rhombic Penrose tiling

We present a novel variant of a planar quasiperiodic tiling with tenfold symmetry, employing the same thick and thin rhombuses as the celebrated rhombic Penrose tiling. Despite its distinct visual appearance, this new tiling shares several key features with its predecessor, including similar vertex environments, polygonal acceptance domains based on regular pentagons, and an inflation/deflation symmetry associated with the golden mean as its fundamental scaling ratio. Additional complexities arise from an increased number of prototiles and a dual grid pattern that incorporates folded lines alongside ordinary straight lines. This tiling exhibits a high density of a compact decagonal motif forming a two-tiered, five-petaled flower pattern, which spans a substantial portion of the tiling. We identify a slightly enhanced degree of hyperuniform order compared to the standard rhombic Penrose tiling.

math-ph↗

arXiv2024

Anomalous magnetic transition in a disordered quasicrystal approximant with heavy-fermion nature

Quasicrystal approximant (CexY1-x)Cd6 (0 < x < 1) forms a network of corner-sharing octahedra. We report that (Ce0.8Y0.2)Cd6 exhibits an anomalous magnetic transition which can be classified neither into the conventional static magnetic ordering nor into spin glasses. The anomalous transition is characterized by the coexistence of a static order and a frequency-dependent sharp positive anomaly in the 3rd-harmonic susceptibility. Based on the investigation of the reference systems CeCd6 and (Ce0.05Y0.95)Cd6, we speculate that the anomalous transition could be induced by disorder in the possible frustrated Ce-network in the presence of the Kondo effect.

cond-mat.str-el↗

arXiv2020

Structural-transition-driven antiferromagnetic to spin-glass transition in Cd-Mg-Tb 1/1 approximants

The magnetic susceptibility of the 1/1 approximants to icosahedral quasicrystals in a series of Cd85-xMgxTb15 (x = 5, 10, 15, 20) alloys was investigated in detail. The occurrence of antiferromagnetic to spin-glass-like transition was noticed by increasing Mg. Transmission electron microscopy analysis evidenced a correlation between the magnetic transition and suppression of the monoclinic superlattice ordering with respect to the orientation of the Cd4 tetrahedron at T > 100 K. The possible origins of this phenomenon were discussed in detail. The occurrence of the antiferromagnetic to spin-glass -like magnetic transition is associated with the combination of chemical disorder due to a randomized substitution of Cd with Mg and the orientational disorder of the Cd4 tetrahedra.

cond-mat.mtrl-sci↗

arXiv2020

Magnetic properties of icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems

A systematic investigation has been performed to elucidate effects of Rare-Earth (RE) type and local atomic configuration on magnetic properties of icosahedral quasicrystal (iQC) and their cubic approximants (2/1 and 1/1 ACs) in the ternary Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems. At low temperatures, iQC and 2/1 ACs exhibit spin-glass-like freezing for RE = Gd, Tb, Dy, and Ho, while Er and Tm systems do not show freezing behaviour down to the base temperature ~ 2 K. The 1/1 ACs exhibit either spin-glass-like freezing or antiferromagnetic (AFM) ordering depending on their constituent Mg content. The Tf values show increasing trend from iQC to 2/1 and 1/1 ACs. In contrast, the absolute values of Weiss temperature for iQCs are larger than those in 2/1 and 1/1 ACs, indicating that the total AFM interactions between the neighboring spins are larger in aperiodic, rather than periodic systems. Competing spin interactions originating from the long-range Ruderman-Kittel-Kasuya-Yoshida mechanism along with chemical disorder of Cd/Mg ions presumably account for the observed spin-glass-like behavior in Cd-Mg-RE iQCs and ACs.

cond-mat.mtrl-sci↗

arXiv2013

Cluster packing geometry for Al-based F-type icosahedral alloys

This paper presents a new highly stable periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al-Pd-TM (TM=transition metals). The structure of this intermetallic Al-Pd-Cr-Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be Pa-3 and the lattice constant 40.5 angstrom. The structure is well described as a dense packing of clusters of two kinds, which are known in the literature as the pseudo-Mackay type and the Bergman type clusters. The clusters are centered at the vertices of a canonical cell tiling, in which the parity of each vertex determines the kind of the associated cluster. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the crystal can be designated as a 2x2x2 superstructure of the ordinary cubic 3/2 rational approximant. The superlattice ordering is shown to be of a different kind from the P-type superlattice ordering previously reported in i-Al-Pd-Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.

cond-mat.mtrl-sci↗

arXiv2009

A family of ternary decagonal tilings

A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings are composed of three prototiles: an acute rhombus, a regular pentagon and a barrel shaped hexagon. In the perpendicular space, these tilings have windows with fractal boundaries, and the windows are analytically derived as the fixed sets of the conjugate maps associated with the relevant substitution rules. It is shown that the family contains an infinite number of local isomorphism classes which can be grouped into several symmetry classes (e.g., $C_{10}$, $D_5$, etc.). The member tilings are transformed into one another through collective simpleton flips, which are associated with the reorganization in the window boundaries.

math-ph↗

arXiv2009

Point processes for decagonal quasiperiodic tilings

A general construction principle of inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of an expansion and a division of the tiles, where the expanded tiles can be divided arbitrarily as far as the set of prototiles is maintained. A certain kind of point decoration processes turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quarternary and the other ternary. Properties of the ternary tilings with rhombic, pentagonal, and hexagonal prototiles are investigated in detail.

math-ph↗

arXiv2005

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.

cond-mat.mtrl-sci↗

arXiv2004

Superquasicrystals: selfsimilar ordered structures with non-crystallographic point symmetries

We present a systematic method of constructing limit-quasiperiodic structures with non-crystallographic point symmetries. Such structures are different aperiodic ordered structures from quasicrystals, and we call them "superquasicrystals". They are sections of higher-dimensional limit-periodic structures constructed on "super-Bravais-lattices". We enumerate important super-Bravais-lattices. Superquasicrystals with strong selfsimilarities form an important subclass. A simplest example is a two-dimensional octagonal superquasicrystal.

cond-mat.mtrl-sci↗

arXiv2004

A self-similar ordered structure with a non-crystallographic point symmetry

A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice structures. Such structures turn out to be limit-quasiperiodic, distinguishing themselves from quasicrystals which are quasiperiodic. There exist a few real materials that seem to be promising candidates for superquasicrystals.

cond-mat.mtrl-sci↗

arXiv2004

Quantum Particles Constrained on Cylindrical Surfaces with Non-constant Diameter

We present a theoretical formulation of the one-electron problem constrained on the surface of a cylindrical tubule with varying diameter. Because of the cylindrical symmetry, we may reduce the problem to a one-dimensional equation for each angular momentum quantum number $m$ along the cylindrical axis. The geometrical properties of the surface determine the electronic structures through the geometry dependent term in the equation. Magnetic fields parallel to the axis can readily be incorporated. Our formulation is applied to simple examples such as the catenoid and the sinusoidal tubules. The existence of bound states as well as the band structures, which are induced geometrically, for these surfaces are shown. To show that the electronic structures can be altered significantly by applying a magnetic field, Aharonov-Bohm effects in these examples are demonstrated.

cond-mat.mes-hall↗

arXiv2003

Universalities in One-electron Properties of Limit Quasi-periodic Lattices

We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the structure of its attractor. It allows us to obtain the three new features of the present system: 1) The multi-fractal characters of the energy spectra are {\it universal}. 2) The supports of the $f(α)$-spectra extend over the whole unit interval, $[0, 1]$. 3) There exist marginal critical states.

cond-mat.mtrl-sci↗

arXiv2002

Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.

cond-mat.mtrl-sci↗

arXiv2001

Electronic properties of ternary quasicrystals in one dimension

The one-electron properties of a certain class of one-dimensional ternary quasicrystals are investigated. In particular, we show in detail the presence of a special kind of critical states called marginal critical states in these QCs. By the use of a real-space renormalization-group method, it is shown that the scaling properties of marginal critical states are characterized by stretched exponentials. These states are virtually localized, so that their presence may make a QC less conductive.

cond-mat.mtrl-sci↗

arXiv2001

New Classes of Quasicrystals and Marginal Critical States

One-dimensional quasilattices, namely, the geometrical objects to represent quasicrystals, are classified into mutual local-derivability (MLD) classes. Besides the familiar class, there exist an infinite number of new MLD classes, and different MLD classes are distinguished by the inflation rules of their representatives. It has been found that electronic properties of a new MLD class are characterized by the presence of marginal critical states, which are considered to be nearly localized states.

cond-mat.mtrl-sci↗