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Shintaro Suzuki

Publications and source records attributed to Shintaro Suzuki.

At least 19 recordsLinked to original sources

Re-examination of electronic structure of dilute Kondo transition-metal ions substituted into a Heavy Fermion compound

Correlations between the localized and conductive spins/charges have been the central issue of various fascinating quantum phenomena found on itinerant electron systems. Here, the obvious multiplet structures are presented on the Mn 2$p$ to 3$d$ x-ray absorption for a heavy fermion $\alpha$-(Yb,Lu)(Al$_{1-x}$Mn$_x$)B$_4$, indicating that the unoccupied electronic structure of the Mn site is described as the correlated high-spin 2+, even though magnetic measurements show the Mn sites to be nonmagnetic. This apparently paradoxical result demonstrates that a ligand field can effectively appear between localized Mn 3$d$ and surrounding B 2$p$ orbitals, which has been anticipated as a manifestation of a Kondo effect but not been clearly confirmed for most itinerant metals in spectroscopy. By contrast, the Mn 2$p$ photoemission indicates that the occupied Mn$^{2+}$ 3$d$ electrons still exhibit itinerant and nonlocally screened nature also owing to the Kondo-like correlation with the conductive B 2$p$, and heavier Yb 4$f$ and 5$d$ bands below the Fermi energy. The asymmetry on the particle-hole stimulates a reconsideration of the correlation and screening effects in the core-level spectroscopies.

cond-mat.str-el

A generalization of the Takagi function for beta-expansions

We consider a generalized Takagi function for beta-expansions with the base $1<\beta\leq2$, motivated by multifractal analysis for digit frequency sets of beta-expansions [20]. We show that it is pointwise $\alpha$-H\"older continuous for any $\alpha\in(0,1)$ but not pointwise Lipschitz continuous on the unit interval except a Lebesgue null set. Our proof relies on a formula for the generalized Takagi function reflecting its oscillations of the sum of digits and some basic limit theorems for the corresponding beta-map.

math.DS

Dimension spectrum of digit frequency sets for beta-expansions

For any beta-shift $(X_\beta,\sigma)$ on two symbols, i.e., the symbolic coding of the beta-map for $1<\beta\leq2$, we give an exact formula for the Hausdorff dimension $\dim_{H} \Lambda_{\alpha(t)}$ as a function of $t\in\mathbb{R}$, where $\Lambda_\alpha$ denotes the frequency set of the digit $1$ defined by \[\Lambda_\alpha=\Biggl\{(x_i)_{i=1}^\infty\in X_\beta;\ \lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^{n}x_i=\alpha \Biggr\}\] for $\alpha\in[0,1]$ and $\alpha(t)$ is an explicit function related to the quasi-greedy expansion of $1$. The formula is derived from explicit formulae for eigenfunctions and eigenfunctionals corresponding to the leading eigenvalue $\lambda_t$ of the transfer operator $\mathcal{L}_t$ with the potential $t\chi_{C_1}$ for $t\in\mathbb{R}$, where $\chi_{C_{1}}$ denotes the indicator function of the cylinder set $C_1=\{(x_i)_{i=1}^\infty\in X_\beta; x_1=1\}$. These formulae can be applied not only to the leading eigenvalue but also to the other isolated eigenvalues of $\mathcal{L}_t$, which yields a precise spectral decomposition of $\mathcal{L}_t$. As a further application, we investigate the distribution function of the push-forward of the eigenmeasure corresponding to $\lambda_t$ by the inverse map of the coding map. We show that the distribution function after a change of variables for $t$ is equal to the Lebesgue singular function if $\beta=2$ and satisfies an analogy of the Hata-Yamaguchi formula, which yields a generalization of the Takagi function for beta-expansions with the base $1<\beta<2$.

math.DS

Annealed and quenched representations of the Gauss-Rényi measure by "periodic points"

We consider independently identically distributed random compositions of the Gauss and Rényi maps that generate random continued fractions. Using methods of ergodic theory, thermodynamic formalism and large deviations, we show that weighted cycles of this random dynamical system equidistribute with respect to the Gauss-Rényi measure. We present both annealed (sample-averaged) and quenched (samplewise) results.

math.DS

Soft and hard x-ray orbital-resolved photoemission study of a strongly correlated Cd-Ce quasicrystal approximant

We have investigated the orbital-dependent electronic states of Cd6Ce, a prototype of strongly correlated rare-earth-based Tsai-type quasicrystals and approximants (ACs) by soft and hard x-ray photoemission spectroscopy. Our results reveal that the 4f orbitals are predominantly hybridized with the valence-band electrons far from the Fermi level (EF), in sharp contrast to the hybridization with conduction electrons at EF seen for the intermetallic Ce-based compounds. This anomalous hybridization should be taken into account in discussing the unresolved magnetic ground state in Cd6Ce. These findings suggest that Cd-based ACs, some of which show the multi-step magnetic transitions, could provide a new platform for investigating novel magnetic properties that cannot be understood within the conventional framework of hybridization at EF.

cond-mat.str-el

Anomalous magnetic response in the Au-Al-Gd 1/1 quasicrystal approximant

The magnetic response of the Tsai-type 1/1 Au-Al-Gd approximant crystals (ACs) was quantitatively investigated in terms of the magnetic entropy change ($ΔS_{M}$) for different magnetic ground states. A comprehensive $ΔS_{M}$ map over a wide electron concentration range has been established, demonstrating the detailed variation of $ΔS_{M}$ across the entire magnetic phase diagram in the Tsai-type 1/1 ACs. Near the boundaries of the ferromagnetic (FM) phase, a clear deviation from the mean-field theory (MFT) was observed in both the Curie temperature ($T_{C}$) and magnetic field ($H$) dependences of the maximum magnetic entropy change ($ΔS_{M}^{max}$). Contrary to general expectations, a high $ΔS_{M}^{max}$ (7.2 J/K mol-Gd under a 5 T field variation), even comparable to those of candidate materials for low-temperature magnetic refrigeration, was obtained within the antiferromagnetic (AFM) region near the FM / AFM phase boundary. The unexpected enhancement of $ΔS_{M}^{max}$ toward the AFM region under high magnetic fields indicates an anomalous magnetic response in the present Tsai-type 1/1 AC, which is presumably associated with the breakdown of the MFT. The present finding suggests that tuning the magnetic ground state across the phase boundary is an effective strategy to enhance $ΔS_{M}$, even in general rare-earth intermetallic compounds.

cond-mat.mtrl-sci

Non-leading eigenvalues of the Perron-Frobenius operators for beta-maps

We consider the Perron-Frobenius operator defined on the space of functions of bounded variation for the beta-map $τ_β(x)=βx$ (mod $1$), for $β\in(1,\infty)$, and investigate its isolated eigenvalues except $1$, called non-leading eigenvalues in this paper. We show that the set of $β$'s such that the corresponding Perron-Frobenius operator has at least one non-leading eigenvalue is open and dense in $(1,\infty)$. Furthermore, we establish the Hölder continuity of each non-leading eigenvalue as a function of $β$ and show in particular that it is continuous but non-differentiable, whose analogue was conjectured by Flatto et.al. in \cite{Fl-La-Po}. In addition, for an eigenfunctional of the Perron-Frobenius operator corresponding to an isolated eigenvalue, we give an explicit formula for the value of the functional applied to the indicator function of every interval. As its application, we provide three results related to non-leading eigenvalues, one of which states that an eigenfunctional corresponding to a non-leading eigenvalue can not be expressed by any complex measure on the interval, which is contrast to the case of the leading eigenvalue $1$.

math.DS

Absolutely continuous invariant measures for random dynamical systems of beta-transformations

We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval $T_β(x)=βx$ (mod $1$), $x\in[0,1]$, $β>0$, which are the so-called beta-transformations. For such a random dynamical system, including the case that it is generated by uncountably many maps, we give an explicit formula for the density function of a unique stationary measure under the assumption that the random dynamics is expanding in mean. As an application, in the case that the random dynamics is generated by finitely many maps and the maps are chosen according to a Bernoulli measure, we show that the density function is analytic as a function of parameter in the Bernoulli measure and give its derivative explicitly. Furthermore, for a non-i.i.d. random dynamical system of beta-transformations, we also give an explicit formula for the random densities of a unique absolutely continuous invariant measure under a certain strong expanding condition or under the assumption that the maps randomly chosen are close to the beta-transformation for a non-simple number in the sense of parameter $β$.

math.DS

Galois conjugates for some family of generalized beta-maps

A real number $β>1$ is called an Yrrap (or Ito-Sadahiro) number if the corresponding negative $β$-transformation defined by $x\mapsto 1-\{βx\}$ for $x\in[0,1]$, where $\{y\}$ denotes the fraction part of $y\in\mathbb{R}$, has a finite orbit at $1$. Yrrap numbers are an analogy of Parry numbers for positive $β$-transformations given by $x\mapsto \{βx\}$ for $x\in[0,1]$, $β>1$. In this paper, we determine the closure of the set of Galois conjugates of Yrrap numbers. In addition, we show an analogy of the result to the family of piecewise linear continuous maps each of which is obtained by changing the odd-numbered branches (left-most one is regarded as $0$-th) of the $β$-transformation to negative ones for $β>1$. As an application, we see that both the set of Yrrap numbers which are non-Parry numbers and that of Parry numbers which are non-Yrrap numbers are countable.

math.DS

Revisit of magnetic orders in 1/1 approximant crystals of Tsai-type quasicrystal from theoretical points of view

The various magnetic orders observed in approximant crystals of Tsai-type quasicrystal are important for deepening our understanding of mysterious magnetism in quasicrystals. Using an icosahedral cluster model with inter-cluster interactions, we give an intuitive explanation of the mechanism of magnetic orders previously reported by classical Monte-Carlo simulations for an approximant-crystal model describing a Gd-based Tsai-type 1/1 approximant crystal.

cond-mat.mtrl-sci

Unveiling exotic magnetic phase diagram of a non-Heisenberg quasicrystal approximant

A magnetic phase diagram of the non-Heisenberg Tsai-type 1/1 Au-Ga-Tb approximant crystal (AC) has been established across a wide electron-per-atom (e/a) range via magnetization and powder neutron diffraction measurements. The diagram revealed exotic ferromagnetic (FM) and antiferromagnetic (AFM) orders that originate from the unique local spin icosahedron common to icosahedral quasicrystals (iQCs) and ACs; The noncoplanar whirling AFM order is stabilized as the ground state at the e/a of 1.72 or less whereas a noncoplanar whirling FM order was found at the larger e/a of 1.80, with magnetic moments tangential to the Tb icosahedron in both cases. Moreover, the FM/AFM phase selection rule was unveiled in terms of the nearest neighbour (J1) and next nearest neighbour (J2) interactions by numerical calculations on a non-Heisenberg single icosahedron. The present findings will pave the way for understanding the intriguing magnetic orders of not only non-Heisenberg FM/AFM ACs but also non-Heisenberg FM/AFM iQCs, the latter of which are yet to be discovered.

cond-mat.str-el

Atomic structure and magnetism of the Au-Ga-Ce 1/1 approximant crystal

We report a new Au-Ga-Ce 1/1 approximant crystal (AC) which possesses a significantly wide single-phase region of 53 - 70 at% Au and 13.6 - 15.1 at% Ce. Single crystal X-ray structural analyses reveal the existence of two types of structural degrees of freedom, i.e., the Au/Ga mixing sites and the fractional Ce occupancy site: the former enables a large variation in the electron concentration and the latter allows a variation in the occupancy of a magnetic impurity atom at the center of the Tsai-type cluster. Following these findings, the influences of two types of structural modifications on the magnetism are thoroughly investigated by means of magnetic susceptibility and specific heat measurements on the Au-Ga-Ce 1/1 AC. The spin-glass (SG) state is found to be the ground state over the entire single-phase region, showing a robust nature of the SG state against both structural modifications. In addition, a gigantic specific heat (C/T) is commonly observed at low temperatures for all the compositions, which is consistently explained as a consequence of the spin-freezing phenomenon, not of a heavy Fermion behavior as reported elsewhere. Moreover, the origin of the SG state in the 1/1 Au-Ga-Ce AC is attributed to the existence of non-magnetic atom disorder in the Au/Ga mixing sites. Furthermore, a Kondo behavior is observed in the electrical resistivity at low temperatures, which is enhanced by increasing the Ce concentration, verifying that a Ce atom introduced at the cluster center behaves as a Kondo impurity for the first time.

cond-mat.str-el

Superconductivity in a van der Waals layered quasicrystal

van der Waals (vdW) layered transition-metal chalcogenides are attracting significant attention owing to their fascinating physical properties. This group of materials consists of abundant members with various elements, having a variety of different structures. However, all vdW layered materials studied to date have been limited to crystalline materials, and the physical properties of vdW layered quasicrystals have not yet been reported. Here, we report on the discovery of superconductivity in a vdW layered quasicrystal of Ta1.6Te. The electrical resistivity, magnetic susceptibility, and specific heat of the Ta1.6Te quasicrystal fabricated by reaction sintering, unambiguously validated the occurrence of bulk superconductivity at a transition temperature of ~1 K. This discovery can pioneer new research on assessing the physical properties of vdW layered quasicrystals as well as two-dimensional quasicrystals; moreover, it paves the way toward new frontiers of superconductivity in thermodynamically stable quasicrystals, which has been the predominant challenge facing condensed matter physics since the discovery of quasicrystals almost four decades ago.

cond-mat.mtrl-sci

Emergence of long-range magnetic order from spin-glass state by tuning electron density in a stoichiometric Ga-based quasicrystal approximant

This study reports the first observation of ferromagnetic (FM) order in the non-Au-based approximant crystals (ACs) using a novel approach whereby a total electron-per-atom (e/a) ratio of the spin-glass Ga50Pd36Gd14 1/1 AC is lowered by simultaneously substituting certain ratios of a tri-valent Ga and a zero-valent Pd by a mono-valent Au. The emergence of FM order by this method was confirmed via magnetic susceptibility, magnetization, and specific heat measurements. The findings of this study open up vast opportunities in developing long-range magnetic orders from stoichiometric ACs, quasicrystals, and even other RKKY compounds with spin-glass ground state.

cond-mat.str-el

Distribution of cycles for one-dimensional random dynamical systems

We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the uniqueness of equilibrium state for the associated skew product map, we establish a samplewise (quenched) almost-sure level-2 weighted equidistribution of "random cycles", with respect to a natural stationary measure as the periods of the cycles tend to infinity. This result implies an analogue of Bowen's theorem on periodic orbits of topologically mixing Axiom A diffeomorphisms. We also prove another almost-sure convergence theorem, as well as an averaged (annealed) theorem that is related to semigroup actions. We apply our results to the random $β$-expansion of real numbers, and obtain almost-sure convergences of average digital quantities in random $β$-expansions of random cycles that do not follow from the application of the ergodic theorems of Birkhoff or Kakutani. Our main results are applicable to random dynamical systems generated by finitely many maps with common neutral fixed points.

math.DS

Observation of a Critical Charge Mode in a Strange Metal

Quantum electronic matter has long been understood in terms of two limiting behaviors of electrons: one of delocalized metallic states, and the other of localized magnetic states. Understanding the strange metallic behavior which develops at the brink of localization demands new probes of the underlying electronic charge dynamics. Using a state-of-the-art technique, synchrotron-radiation-based Mossbauer spectroscopy, we have studied the longitudinal charge fluctuations of the strange metal phase of beta-YbAlB4 as a function of temperature and pressure. We find that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. This spectrum is naturally interpreted as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time-scales are further enhanced, due to the formation of charged polarons. Our results represent a direct observation of critical charge fluctuations as a new signature of strange metals.

cond-mat.str-el

High temperature antiferromagnetism in Yb based heavy fermion systems proximate to a Kondo insulator

Given the parallelism between the physical properties of Ce and Yb based magnets and heavy fermions due to the electron-hole symmetry, it has been rather odd that the transition temperature of the Yb based compounds is normally very small, as low as $\sim$ 1 K or even lower, whereas Ce counterparts may often have the transition temperature well exceeding 10 K. Here, we report our experimental discovery of the transition temperature reaching 20 K for the first time in a Yb based compound at ambient pressure. The Mn substitution at the Al site in an intermediate valence state of $α$-YbAlB$_{4}$ not only induces antiferromagnetic transition at a record high temperature of 20 K but also transforms the heavy fermion liquid state in $α$-YbAlB$_{4}$ into a highly resistive metallic state proximate to a Kondo insulator.

cond-mat.str-el

Thermodynamic formalism for random non-uniformly expanding maps

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered $C^1$-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.

math.DS