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Kotaro Shimizu

Publications and source records attributed to Kotaro Shimizu.

At least 19 recordsLinked to original sources

Gröbner Bases for Alexander Fitting Ideals of Links

Multivariable Alexander theory produces Fitting ideals without preferred generators. After fixing a coefficient field and a monomial order, we represent these ideals by reduced Gröbner bases of their polynomial contractions, obtaining Alexander--Gröbner invariants of links. Over \(\mathbb Q\), for the maximal free-abelian coefficient system of a connected compact oriented \(3\)-manifold whose nonempty boundary is a disjoint union of tori, we deduce determinant-divisor reciprocity from Blanchfield duality. We compute these invariants for torus links and low-crossing links, and we determine \(\AG_2\) for a two-component pretzel family.

math.GT

Weaving Hopfions from Emergent Monopoles in a Chiral Magnet

Recent advances in three-dimensional magnetization imaging techniques have opened new avenues for exploring topological spin textures beyond domain walls and skyrmions. Among them, magnetic hopfions are particularly promising, as their knotted topology is expected to give rise to unconventional dynamics and responses; however, their controlled creation remains challenging. Here we propose a simple mechanism for generating hopfions from magnetic torons, three-dimensional textures hosting an emergent monopole-antimonopole pair. Using Landau-Lifshitz-Gilbert simulations, we show that an electric current drives the annihilation of this pair, converting a toron into a hopfion. The initial toron length determines the number of generated hopfions, while the current direction selects the sign of the Hopf invariant. We further find that the threshold current depends sensitively on material parameters, indicating a close connection to skyrmion dynamics. Our results establish an experimentally accessible route to hopfion creation and reveal a pathway from monopole defects to knotted topological textures.

cond-mat.mes-hall

Design Principles for Quasi-Isotropic Exchange in Rare-Earth Quantum Magnets

Rare-earth quantum materials provide a promising platform for emergent phenomena ranging from quantum spin liquids with long-range entanglement to topological magnetic textures. However, the strong spin-orbit coupling that stabilizes their low-energy pseudospin degrees of freedom also tends to generate strongly anisotropic exchange interactions, complicating the realization of quasi-isotropic Heisenberg magnetism. Here we investigate the microscopic origin of superexchange in $\mathrm{Ce}^{3+}$- and $\mathrm{Yb}^{3+}$-based insulators with edge-sharing octahedral geometry. Using degenerate perturbation theory for a multiorbital Hubbard model, we show that isotropic exchange originates predominantly from virtual hopping within the ground-state Kramers doublet, whereas anisotropic interactions arise primarily from processes involving excited multiplets. This leads to a simple orbital design principle: quasi-isotropic exchange is promoted when the ground-state doublet has a strong maximal-angular-momentum character with respect to the quantization axis perpendicular to the superexchange plane spanned by rare-earth and ligand ions. We demonstrate this mechanism for both ideal and distorted geometries and show that it is broadly consistent with experimentally studied Yb-based insulators. Our results establish a practical framework for engineering quasi-isotropic interactions in rare-earth quantum materials.

cond-mat.str-el

Creating and Driving a Twist Soliton on a Magnetic Skyrmion Tube

A magnetic skyrmion tube is a three-dimensional topological soliton formed by stacking two-dimensional skyrmions along the out-of-plane direction. Recent real-space observations of skyrmion tubes have stimulated growing interest in their dynamics and emergent properties. Here, we go beyond simple skyrmion stacking and investigate how a ``twist" introduced along the tube direction affects the dynamics and emergent responses of skyrmion tubes. We find that such a twist can be created as a localized texture, termed a twist soliton, through thermal quench dynamics. By complementarily combining large-scale numerical simulations with analytical calculations based on collective coordinates, we clarify its current-driven nonlinear motions that depend on its twist chirality. Remarkably, its velocity can be substantially enhanced by a magnetic-field component perpendicular to the tube. Furthermore, the associated emergent electric field enables identification of the twist soliton, including the sign of its chirality, through Hall measurements. Our results reveal the twist degree of freedom as an essential ingredient of skyrmion-tube physics and pave the way for the development of spintronic devices exploiting the three-dimensional nature of spin textures.

cond-mat.str-el

Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via Deep Learning Segmentation

Labyrinthine stripe patterns are common in many physical systems, yet their lack of long-range order makes quantitative characterization challenging. We investigate the evolution of such patterns in bismuth-doped yttrium iron garnet (Bi:YIG) films subjected to a magnetic field annealing protocol. A U-Net deep learning model, trained with synthetic degradations including additive white Gaussian and Simplex noise, enables robust segmentation of experimental magneto-optical images despite noise and occlusions. Building on this segmentation, we develop a geometric analysis pipeline based on skeletonization, graph mapping, and spline fitting, which quantifies local stripe propagation through length and curvature measurements. Applying this framework to 444 images from 12 annealing protocol trials, we analyze the transition from the "quenched" state to a more parallel and coherent "annealed" state, and identify two distinct evolution modes (Type A and Type B) linked to field polarity. Our results provide a quantitative analysis of geometric and topological properties in magnetic stripe patterns and offer new insights into their local structural evolution, and establish a general tool for analyzing complex labyrinthine systems.

cond-mat.mtrl-sci

Coarsening dynamics of fingerprint labyrinthine patterns: Machine learning assisted characterization

Fingerprint labyrinthine patterns exhibit a level of structural complexity beyond simple stripe phases, combining local stripe order with a dense network of point-like defects. Unlike symmetry-breaking phases, where coarsening proceeds via diffusive defect annihilation, or conventional stripe phases, where curvature-driven motion of extended grain boundaries dominates, the coarsening of fingerprint labyrinths is governed primarily by localized junction and terminal defects. Using the Turing-Swift-Hohenberg equation, we study the nonequilibrium relaxation of fingerprint labyrinthine patterns following a quench. To go beyond conventional Fourier-based diagnostics, we employ a template-matching convolutional neural network (TM-CNN) to identify and track junctions and terminals directly in real space, enabling a quantitative characterization of defect statistics and spatial correlations. We show that, although these point-like defects drive coarsening, their motion is strongly constrained by the surrounding stripe geometry, leading to slow, nondiffusive dynamics that are qualitatively distinct from both conventional phase ordering and stripe coarsening. Together, these results establish defect-mediated dynamics as the central organizing principle of fingerprint labyrinthine coarsening and demonstrate the effectiveness of machine-learning-assisted approaches for complex pattern-forming systems.

cond-mat.soft

Laser Mössbauer spectroscopy of ^{229}Th

Mössbauer spectroscopy is widely used in biochemistry, geology, and solid-state physics to obtain structural information on materials. Here, we extend this technique into the optical range using a vacuum ultraviolet laser to probe the low-energy nuclear transitions of thorium-229, doped in calcium fluoride crystals. We discover four distinct doping sites for the thorium ions, determine the characteristic electric field gradients emerging in the interaction with the host crystal, and identify the microscopic structure of the two dominant configurations. Site-selective laser excitation allows to study the isomeric state lifetime and laser-induced quenching for all sites. This laser-based Mössbauer spectroscopy provides a powerful probe of the nuclear environment, yielding foundational data for designing future solid-state nuclear clocks.

nucl-ex

X-ray-induced quenching of the $^{229}$Th clock isomer in CaF$_2$

Thorium-229 has the lowest nuclear-excited state (an isomer state) at approximately 8.356 eV, making it excitable with tabletop vacuum-ultraviolet lasers. Despite the recent success of laser excitation, the isomer quenching inside the solid-state environment remains unresolved. In this letter, we present experiments investigating X-ray-induced isomer quenching in the CaF$_2$ host, focusing on the effects of X-ray flux and temperature on the lifetime and yield of the isomer state. Our studies reveal a correlation between isomer production, isomer lifetime during irradiation, and post-irradiation afterglow of the target crystal across different temperatures, highlighting a strong relationship between isomer quenching and color-center dynamics. We developed a model to interpret the isomer quenching and the crystal's luminescence.

cond-mat.mtrl-sci

Machine Learning Force-Field Approach for Itinerant Electron Magnets

We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant representations of spin configurations. The crucial properties that such magnetic descriptors must satisfy are differentiability with respect to spin rotations and invariance to both lattice point-group symmetry and internal spin rotation symmetry. We propose an efficient implementation based on the concept of reference irreducible representations, modified from the group-theoretical power-spectrum and bispectrum methods. The ML framework is demonstrated using the s-d models, which are widely applied in spintronics research. We show that LLG simulations based on local fields predicted by the trained ML models successfully reproduce representative non-collinear spin structures, including 120$^\circ$, tetrahedral, and skyrmion crystal orders of the triangular-lattice s-d models. Large-scale thermal quench simulations enabled by ML models further reveal intriguing freezing dynamics and glassy stripe states consisting of skyrmions and bi-merons. Our work highlights the utility of ML force-field approach to dynamical modeling of complex spin orders in itinerant electron magnets.

cond-mat.str-el

Three-dimensional Topological Superstructure of Magnetic Hopfions Threaded by Meron Strings in Easy-plane Magnets

Topological spin textures exhibit a hierarchical nature. For instance, magnetic skyrmions, which possess a particle-like nature, can aggregate to form superstructures such as skyrmion strings and skyrmion lattices. Magnetic hopfions are also regarded as superstructures constructed from closed loops of twisted skyrmion strings, which behave as another independent particles. However, it remains elusive whether such magnetic hopfions can also aggregate to form higher-level superstructures. Here, we report a stable superstructure with three-dimensional periodic arrangement of magnetic hopfions in a frustrated spin model with easy-plane anisotropy. By comprehensively examining effective interactions between two hopfions, we construct the hopfion superstructure by a staggered arrangement of one-dimensional hopfion chains with Hopf number $H=+1$ and $H=-1$ running perpendicular to the easy plane. Each hopfion chain is threaded by a magnetic meron string, resulting in a nontrivial topological texture with skyrmion number $N_{\rm sk}=2$ per magnetic unit cell on any two-dimensional cut parallel to the easy plane. We show that the hopfion superstructure remains robust as a metastable state across a range of the hopfion density. Furthermore, we demonstrate that superstructures with higher Hopf number can also be stabilized. Our findings extend the existing hierarchy of topological magnets and pave the way for exploring new quantum phenomena and spin dynamics.

cond-mat.str-el

Machine Learning Assisted Characterization of Labyrinthine Pattern Transitions

We present a comprehensive approach to characterizing labyrinthine structures that often emerge as a final steady state in pattern forming systems. We employ advanced machine learning based pattern recognition techniques to identify the types and locations of topological defects of the local stripe ordering. Applying this method to single-crystal Bi-substituted Yttrium Iron Garnet films, we uncover a distinct morphological transition between two zero-field labyrinthine structures. Crucially, the pair distribution functions of the topological defects reveal subtle differences between labyrinthine structures which are beyond conventional characterization methods. By systematically analyzing the spatial correlations and geometric properties of these defects, we provide new insights into the athermal dynamics governing the observed morphological transitions. Our work demonstrates that machine learning based recognition techniques enable novel studies of rich and complex labyrinthine type structures universal to many pattern formation systems.

cond-mat.soft

Soliton penetration from edges in a monoaxial chiral magnet

The magnetic solitons such as chiral solitons, magnetic skyrmions, and magnetic hopfions, exhibiting particlelike nature widely emerge in magnets depending on spatial dimension. As their number directly gives rise to an impact on magnetic properties and electronic properties, it is of great importance to control the number of solitons. However, a systematic study on dynamical processes to control the number of solitons, particularly by adding the desired number of solitons to the ground state exhibiting periodic arrangements of solitons, has been limited thus far. Here, we theoretically perform the systematic analysis for the dynamical control of the number of chiral solitons in monoaxial chiral magnets by effectively utilizing the edge modes whose excitation is localized near the edges. By studying the dynamical process associated with this edge mode in an applied rotating magnetic field by using the Landau-Lifshitz-Gilbert equation, we show that multiple soliton penetrations can take place until the system reaches the nonequilibrium steady state, and the number of infiltrated solitons successively increases with the amplitude of the rotating magnetic field after surpassing the threshold. We also clarify that the threshold amplitude of the rotating magnetic field can be reduced through the static magnetic field. Our results reveal that the desired number of solitons can be added within a certain range by taking advantage of the edge modes that appear without any special processing at the edges of the system. These results contribute to the development of an experimental way to control the number of solitons and are expected to be further applied to a wide range of magnetic solitons, not limited to chiral solitons.

cond-mat.str-el

Characterization of Magnetic Labyrinthine Structures Through Junctions and Terminals Detection Using Template Matching and CNN

Defects influence diverse properties of materials, shaping their structural, mechanical, and electronic characteristics. Among a variety of materials exhibiting unique defects, magnets exhibit diverse nano- to micro-scale defects and have been intensively studied in materials science. Specifically, defects in magnetic labyrinthine patterns, called junctions and terminals are ubiquitous and serve as points of interest. While detecting and characterizing such defects is crucial for understanding magnets, systematically investigating large-scale images containing over a thousand closely packed junctions and terminals remains a formidable challenge. This study introduces a new technique called TM-CNN (Template Matching - Convolutional Neural Network) designed to detect a multitude of small objects in images, such as the defects in magnetic labyrinthine patterns. TM-CNN was used to identify 641,649 such structures in 444 experimental images, and the results were explored to deepen understanding of magnetic materials. It employs a two-stage detection approach combining template matching, used in initial detection, with a convolutional neural network, used to eliminate incorrect identifications. To train a CNN classifier, it is necessary to annotate a large number of training images. This difficulty prevents the use of CNN in many practical applications. TM-CNN significantly reduces the manual workload for creating training images by automatically making most of the annotations and leaving only a small number of corrections to human reviewers. In testing, TM-CNN achieved an impressive F1 score of 0.991, far outperforming traditional template matching and CNN-based object detection algorithms.

cs.CV

Current-induced motion of nanoscale magnetic torons over the wide range of the Hall angle

Current-driven dynamics of spin textures plays a pivotal role in potential applications for electronic devices. While two-dimensional magnetic skyrmions with topologically nontrivial spin textures have garnered significant interest, their practical use is hindered by the skyrmion Hall effect $\unicode{x2014}$ a transverse motion to the current direction that occurs as a counteraction to the topological Hall effect of electrons by an emergent magnetic field arising from the Berry phase effect. Here, we explore current-driven dynamics of three-dimensional topological spin textures known as magnetic torons, composed of layered skyrmions with two singularities called Bloch points at their ends. Through extensive numerical simulations, we show that the torons also exhibit a Hall motion, but surprisingly over a wide range spanning from the zero Hall effect, a purely longitudinal motion, to the perfect Hall effect, a purely transverse motion accompanied by no longitudinal motion. Such flexible and controllable behaviors stem from anisotropic potential barriers on the discrete lattice, which can be particularly relevant for nanoscale torons recently discovered. Our results not only provide an experimental method to probe topology of three-dimensional magnetic textures but also pave the way for future developments in topological spintronics beyond the realm of skyrmions.

cond-mat.str-el

Combined Pre-Supernova Alert System with Kamland and Super-Kamiokande

Preceding a core-collapse supernova, various processes produce an increasing amount of neutrinos of all flavors characterized by mounting energies from the interior of massive stars. Among them, the electron antineutrinos are potentially detectable by terrestrial neutrino experiments such as KamLAND and Super-Kamiokande via inverse beta decay interactions. Once these pre-supernova neutrinos are observed, an early warning of the upcoming core-collapse supernova can be provided. In light of this, KamLAND and Super-Kamiokande, both located in the Kamioka mine in Japan, have been monitoring pre-supernova neutrinos since 2015 and 2021, respectively. Recently, we performed a joint study between KamLAND and Super-Kamiokande on pre-supernova neutrino detection. A pre-supernova alert system combining the KamLAND detector and the Super-Kamiokande detector was developed and put into operation, which can provide a supernova alert to the astrophysics community. Fully leveraging the complementary properties of these two detectors, the combined alert is expected to resolve a pre-supernova neutrino signal from a 15 M$_{\odot}$ star within 510 pc of the Earth, at a significance level corresponding to a false alarm rate of no more than 1 per century. For a Betelgeuse-like model with optimistic parameters, it can provide early warnings up to 12 hours in advance.

hep-ex

Emergent electric field from magnetic resonances in a one-dimensional chiral magnet

The emergent electric field (EEF) is a fictitious electric field acting on conduction electrons through the Berry phase mechanism. The EEF is generated by the dynamics of noncollinear spin configurations and becomes nonzero even in one dimension. Although the EEF has been studied for several one-dimensional chiral magnets, most of the theoretical studies were limited with respect to the strength and direction of the magnetic fields. Furthermore, the effect of edges of the system has not been clarified, whereas it can be crucial in nano- and micro-scale samples. Here, we perform a theoretical study on the momentum-frequency profile of the EEF in a one-dimensional chiral magnet while changing the strength and direction of the magnetic field for both bulk and finite-size chains with edges. As the bulk contributions, we find that the EEF is resonantly enhanced at the magnetic resonance frequencies; interestingly, the higher resonance modes are more clearly visible in the EEF response than in the magnetic one. Furthermore, we show that the EEF is amplified along with the solitonic feature of the spin texture introduced by the static magnetic field perpendicular to the chiral axis. We also show that the static magnetic field parallel to the chiral axis drives the EEF in the field direction, in addition to much slower drift motion in the opposite direction associated with the Archimedean screw dynamics, suggesting a DC electric current generation. As the edge contributions, we find additional resonance modes localized at the edges of the system that are also more clearly visible in the EEF response than the magnetic one. Our results reveal that the emergent electric phenomena in one-dimensional chiral magnets can be tuned by the magnetic field and the sample size, and provide not only a good probe of the magnetic resonances but also a platform for the applications to electronic devices.

cond-mat.mes-hall

Crystallization dynamics of magnetic skyrmions in a frustrated itinerant magnet

We investigate the phase ordering kinetics of skyrmion lattice (SkL) in a metallic magnet. The SkL can be viewed as a superposition of magnetic stripes whose periods are determined by the quasi-nesting wave vectors of the underlying Fermi surface. An effective magnetic Hamiltonian that describes the electron-mediated spin-spin interaction is obtained for a two-dimensional s-d model with the Rashba spin-orbit coupling. Large-scale Landau-Lifshitz-Gilbert dynamics simulations based on the effective spin Hamiltonian reveal a two-stage phase ordering of the SkL phase after a thermal quench. The initial fast crystallization of skyrmions is followed by a slow relaxation dominated by the annihilation dynamics of dislocations, which are topological defects of the constituent magnetic stripe orders. The late-stage phase ordering also exhibits a dynamical scaling symmetry. We further show that the annihilation of dislocations follows a power-law time dependence with a logarithmic correction that depends on magnetic fields. Implications of our results for SkL phases in magnetic materials are also discussed.

cond-mat.str-el

Phase degree of freedom and topology in multiple-$Q$ spin textures

A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple-$Q$ spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully elucidated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple-$Q$ spin textures with the phase degree of freedom. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple-$Q$ spin textures. Applying the framework to the two-dimensional 3$Q$ spin textures, we clarify the complete topological phase diagram while changing the phase and magnetization, which depends on the types of the superposed waves. We also study the three-dimensional 4$Q$ spin textures and clarify even richer topological phase diagrams. In particular, we find novel topological phase transitions associated with the previously unidentified Dirac strings on which the hedgehogs and antihedgehogs cause pair creation and fusion. Moreover, we demonstrate that phase shifts are caused by an external magnetic field in both 3$Q$ and 4$Q$ cases by analyzing the numerical data in the previous studies. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple-$Q$ textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.

cond-mat.str-el