Beyond conventional electric and magnetic monopoles, electric and magnetic toroidal monopoles, which are rank-0 multipoles distinguished by opposite parities under spatial inversion and time reversal, can exist in nature. The recent observation of electric-field-induced directional dichroism in antiferromagnetic olivine ${\mathrm{Co}}_2{\mathrm{SiO}}_4$ has provided the first concrete example of a magnetic toroidal monopole; however, its microscopic origin remains elusive. Here, we propose a minimal spin model that incorporates magnetoelectric coupling via the $d\text{−}p$ hybridization mechanism and analyze it within the mean-field approximation. The model qualitatively reproduces the experimentally observed temperature dependence of the dielectric constant and its pronounced sensitivity to the direction of the applied electric field. Furthermore, it elucidates the temperature evolution of the magnetic toroidal monopole and the strong electric-field-direction dependence of the magnetic toroidal moment. Our calculations also predict a second-order nonlinear magnetoelectric response, consistent with the symmetry classification of ${\mathrm{Co}}_2{\mathrm{SiO}}_4$ as an altermagnet. Additionally, we demonstrate that the same framework is applicable to other antiferromagnetic olivines with analogous magnetic order, indicating the robustness and generality of the toroidal-type magnetoelectric response in this material family.

The Kitaev model belongs to an unconventional class of two-dimensional spin systems characterized by anisotropic, bond-dependent interactions that give rise to quantum spin liquid (QSL) states. These exotic phases, marked by the absence of magnetic ordering even at zero temperature, support fractionalized excitations and emergent gauge fields. A particularly compelling feature of the Kitaev model is its exact solvability, which reveals low-energy excitations in the form of itinerant Majorana fermions—quasiparticles that obey non-Abelian statistics—and are of central interest in topological quantum computation because of their inherent robustness against local perturbations and decoherence. Despite extensive theoretical advancements, the experimental identification of QSLs remains challenging, as conventional magnetic probes fail to detect their defining properties. In this work, we present a theoretical investigation of spin-current injection from a superconducting metal into a Kitaev quantum spin liquid. By employing a spintronic framework, we derive the dynamics of the injected spin current and demonstrate how its signatures can be traced back to the underlying Majorana excitations in the spin liquid phase. Superconductivity plays a pivotal role in this context, not only as a source of coherent quasiparticles but also as a platform with potential for interfacing with topological quantum devices. The interplay between superconductivity and the Kitaev QSL enables a novel mechanism for probing the spin transport mediated by Majorana fermions. Our analysis contrasts the Kitaev-superconductor interface with conventional ferromagnetic junctions, where spin transport is carried by magnons, and highlights distinctive features in the spin-current response. These findings suggest approaches for the detection of QSLs and contribute to the broader effort of integrating topological quantum materials into scalable quantum technologies.

Using first-principles density functional theory and determinant quantum Monte Carlo methods, we show that Janus graphene nanoribbons with topological defect arrays ($m=2$) exhibit robust intrinsic ferromagnetism across widths $W=2\text{–}6$, with bandgaps exceeding $200\mathrm{meV}$ and stable ferromagnetic ground states. Notably, uniaxial tensile strain significantly enhances their ferromagnetic properties: at 25% strain, the Curie temperature increases to $222\mathrm{K}$—a fivefold improvement over unstrained systems and the highest reported for graphene-based nanoribbons. Strain also induces a reversible transition to a bipolar magnetic semiconductor, with spin-flipped valence and conduction band edges beyond 10% strain. This dual functionality—strain-enhanced ferromagnetism and strain-induced spin flip—stems from strain-modulated $p_z$ orbital hybridization and strong direct exchange interaction. Among these, $W=5$ Janus graphene nanoribbons emerge as potential candidates for room-temperature spintronic devices and strain-programmable quantum transport systems.

We theoretically demonstrate high harmonic generation (HHG) of the ac charge current, in which the emitted current contains integer multiples of the fundamental frequency. By solving the Landau-Lifshitz-Gilbert equation under a GHz ac magnetic field and evaluating the pumped charge current using Brouwer's formula, we find that standing spin waves generate ac charge currents containing exclusively even-order harmonics. Remarkably, the harmonic order exceeds 800 where electron scattering due to the spin waves is resonant, reaching to the THz regime. Our numerical results are explained by a microscopic theory based on spin gauge fields, revealing a mechanism driven solely by interaction between conduction electrons spin and spin waves.

Disorder in frustrated quantum systems can critically influence their magnetic ground states and drive exotic correlated behavior. In the $S=\frac{1}{2}$ system ktenasite, ${\mathrm{Cu}}_{\text{2.7}}{\mathrm{Zn}}_{\text{2.3}}{\left({\mathrm{SO}}_{\text{4}}\right)}_{\text{2}}{\left(\mathrm{OH}\right)}_{\text{6}}·6{\mathrm{H}}_{\text{2}}\mathrm{O}$, we show that structural disorder drives an unexpected dimensional crossover and stabilizes a rare coexistence of distinct magnetic states. Neutron diffraction reveals significant Cu/Zn mixing at the Cu2 site, which tunes the ${\mathrm{Cu}}^{2+}$ sublattice from a two-dimensional scalene-distorted triangular lattice into a one-dimensional spin-chain network. Magnetic susceptibility, neutron diffraction, ac susceptibility, and specific heat measurements collectively indicate magnetic duality: a coexistence of incommensurate long-range magnetic order below $T_{\text{N}}=4$ K and a cluster spin-glass state with $T_{\text{f}}=3.28$ K at $\nu =10$ Hz. Our findings highlight ktenasite as a rare platform where structural disorder tunes the effective dimensionality and stabilizes coexisting ordered and glassy magnetic phases, offering a unique opportunity to explore the interplay of frustration, disorder, and dimensional crossover in quantum magnets.

This study numerically investigates magnetization reversal processes driven by an external magnetic field in three-dimensional antiferromagnetic spin models with weak random-field disorder. Considering an extremely weak disorder and low temperature, we observe a stepwise hysteresis loop and the appearance of short magnetization bursts of a characteristic triangular shape; the number of bursts increases with disorder, indicative of Barkhausen-type noise. These phenomena are attributed to the simultaneous reversal at a given external field of segments composed of spins with identical neighborhoods. A local random field orients one or more spin neighbors, resulting in small, ferromagneticlike clusters distributed throughout the system. As disorder increases, these clusters may merge to form a labyrinthine structure within the antiferromagnetic background, facilitating brief avalanche propagation. The results demonstrate that, compared with familiar random-field ferromagnets, the observed antiferromagnetic Barkhausen noise and the related avalanche sequence have a profoundly different structure, organized into peaks associated with the transition between magnetization plateaus. They exhibit prominent cyclical trends and disorder-dependent multifractal fluctuations, with the singularity spectrum quantifying the degree of disorder. The activity avalanches exhibit scale invariance resembling that recently found in experiments with disordered $\text{ferr}i\text{magnets}$ and martensites, as well as in quantum Barkhausen noise, which are associated with active geometric regions rather than individual-spin dynamics. The observed scaling behavior is interpreted in terms of self-organized critical dynamics.

We present a single-shot near-field technique, where the near-field scan is performed on a single sample without repeating measurements or averaging over multiple samples, to reconstruct the isofrequency surfaces of metamaterials in the microwave regime. In our approach, we excite resonant modes using a fixed source in a resonator composed of the material under test and map the in-plane field distribution with a movable probe. Applying a fast Fourier transform to the measured field reveals the sample's in-plane dispersion. By extending this analysis over multiple frequencies and comparing the results with Fabry-Pérot resonances, we retrieve the full three-dimensional dispersion relation. When we apply the method to a double nonconnected wire metamaterial, it accurately captures the low-frequency hyperbolic isofrequency surface, providing both a precise experimental tool and conceptual insight into spatially dispersive metamaterials.

We develop a Fokker-Planck approach to describe the dynamics of staggered magnetization and thermal fluctuations in a two-dimensional antiferromagnetic system with uniaxial anisotropy. Beginning with a classical model for the antiferromagnetic system, we incorporate a Landau-Lifshitz-Gilbert equation augmented by Langevin fields to account for thermal fluctuations, and we derive the Fokker-Planck equation governing the probability distribution function of the spin configuration. Employing the mean-field approximation, we derive the equations of motion for the spin polarization and the two-time spin-spin correlation functions. The methodology is applied to the study of spin-wave dynamics and to the formulation of a phenomenological model for resistance fluctuations in two-dimensional antiferromagnetic semiconductors.

In the framework of tight-binding models and the Green's function method, the mechanical modulation of the chirality-induced spin selectivity (CISS) in chiral molecular junctions is investigated. The results demonstrate that the CISS is weakened monotonically by stretching the molecule, while the change is nonmonotonic in the case of compression. A moderate compression enhances the CISS effect, while a strong compression induces destructive quantum interference (DQI) in the transmission, which generates large spin polarization around the DQI features associated with discrete and irregular spin polarization peaks. We explain the DQI mechanism in terms of interference of multiple paths in a simplified model for the chiral molecule. The variations of long-range electron hopping and spin-orbit coupling under molecular deformation are found to be crucial. For very strong compression, the DQI and the CISS are suppressed. This work proposes a feasible way to modulate the CISS in chiral molecular junctions by deepening our understanding of CISS in the presence of deformation.

${\mathrm{LaNiGa}}_2$, as a time-reversal symmetry breaking superconductor, has garnered significant attention due to distinctive Dirac points and nonunitary triplet pairing. Here, we investigate the superconducting properties of ${\mathrm{LaNiGa}}_2$ under high pressure and uncover a dome-like behavior in its superconducting phase, with a maximum critical temperature $T_{\mathrm{C}}$ of 3.2 K at approximately 16 GPa. Remarkably, superconductivity abruptly vanishes above 26 GPa, coinciding with an orthorhombic-to-monoclinic structural transition. This pressure-driven evolution may be closely linked to distinct energy shifts of Dirac points and electron-phonon coupling enhancement. Our findings reveal a profound interplay between topological electronic band structure and time-reversal symmetry breaking superconductivity in ${\mathrm{LaNiGa}}_2$, offering new insights into the engineering of quantum materials through symmetry and band structure control.

Inspired by recent developments in electron chirality, we reconsider some microscopic physical quantities that have been overlooked or have received little attention in condensed-matter physics, based on the nonrelativistic limit of the Dirac bilinears in relativistic quantum theory. We identify the expression of physical quantities defined by the four-component Dirac field in terms of the two-component Schrödinger field, which is usually used in condensed-matter physics, and clarify its conjugate electromagnetic field. This consideration bridges the fields of condensed-matter physics, quantum chemistry, and particle physics, and paves the way to electromagnetic control of matter. Our findings provide a means of ab initio quantification of material characters such as chirality and axiality that are unique to low-symmetry materials, and stimulate the systematic search for useful, new functionalities.

We determine the finite-temperature phase diagram and critical behavior of the classical square-lattice Heisenberg-compass model using large-scale Monte Carlo simulations and finite-size scaling. Six symmetry-distinct ordered phases are identified. The four phases that simultaneously break the spin-lattice $C_4$ and in-plane spin-inversion symmetries undergo continuous transitions in the Ashkin-Teller universality class, with the associated critical lines terminating at four-state Potts points, beyond which the transitions become first order. In contrast, the two $z$-polarized phases display conventional two-dimensional Ising criticality. Our results reveal how the interplay between Heisenberg exchange and compass anisotropy organizes these distinct critical regimes, thereby completing the characterization of the model's thermal phase transitions.

We study charge and spin transport in systems composed of itinerant electrons and localized magnetic moments of a Kitaev quantum spin liquid (QSL) phase. For example, $\alpha \text{−}{\mathrm{RuCl}}_3$ either is intrinsically doped or in proximity to graphene. Our analysis reveals distinct temperature-dependent transport behaviors due to the QSL gap and the Majorana excitation spectrum, which are greatly enhanced when the velocities of itinerant electrons and QSL excitations become comparable. These transport characteristics could potentially be employed to reveal the fractionalized excitations of the spin liquid. Furthermore, the observed proportionality between spin and charge relaxation rates identifies a novel realization of Elliott-Yafet relaxation mediated by the fractionalized excitations of a quantum spin liquid.

We present two quantum-classical hybrid methods for simulating the time-dependence of electron-phonon systems that treat electronic correlations numerically exactly and optical-phonon degrees of freedom classically. These are a time-dependent Lanczos and a matrix-product state method, each combined with the multitrajectory Ehrenfest approach. Due to the approximations, reliable results are expected for the adiabatic regime of small phonon frequencies. We discuss the convergence properties of both methods for a system of interacting spinless fermions in one dimension and provide a benchmark for the Holstein chain. As a first application, we study the decay of charge-density wave order in a system of interacting spinless fermions coupled to Einstein oscillators and in the presence of quenched disorder. We investigate the dependence of the relaxation dynamics on the electron-phonon coupling strength and provide numerical evidence that the coupling of strongly disordered systems to classical oscillators leads to delocalization, thus destabilizing the (finite-size) many-body localization in this system.

Atomically thin metallenes have emerged as a new member of the two-dimensional (2D) materials family. Recent experimental realization of metallenes in the Ångström limit has further intensified interest in this class of 2D materials. However, achieving subatomic insight into them demands the most detailed and systematic characterization of their electronic structure. Such understanding is essential for the rational design and exploitation of their properties in plasmonics, catalysis, and quantum optics. Existing electronic-structure studies are either scattered or focus on a few selected systems, and a comprehensive view of their band structures and Fermi surfaces remains missing. Here, we address this gap by studying 45 elemental metallenes in six monolayer lattices (honeycomb, square, hexagonal, and their buckled forms) using density-functional theory. We found that lattice type primarily fixes the shape and radial placement of the Fermi lines, while out-of-plane buckling introduces controlled modifications: it shortens long straight Fermi-line segments, and occasionally creates, removes, or merges small Fermi-line pockets. The electronic configuration determines which orbital type dominates the Fermi level. We summarized Fermiology using a single score for each element, termed pocketness, derived from four descriptors that combine element properties (symmetry, coordination) with electronic characteristics (dispersion, Fermi-surface topology). This score enables targeted angle-resolved photoemission spectroscopy (ARPES) tests, controlled Lifshitz transitions, and provides a predictive basis for transport and device applications.

A quantum spin liquid hosts massive quantum entanglement whose identification is one of the most significant problems in physics. Yet, its detection is known to be notoriously difficult because of featureless properties without a symmetry order parameter. Here, we demonstrate dynamic signatures of a quantum spin liquid state by investigating Kitaev's spin model on the hyperhoneycomb lattice, where a quantum spin liquid state is stabilized as a stable thermodynamic phase. The real-time dynamics of spin correlation function is obtained with the large-scale quantum Monte Carlo simulation. We find the onset of a characteristic oscillation in dynamic local spin correlation as entering the quantum spin liquid phase. Our results show that an isotrophic three-dimensional Kitaev spin liquid can be characterized by a sharp growth of coherent spin dynamics of the system, which we refer to as a dynamic order. We further propose that a dynamic order may help detect a class of featureless symmetric thermal transitions.

The nuclear quantum effects (NQEs) induce pronounced displacements of light nuclei (e.g., hydrogen and positive muons) from their equilibrium positions, profoundly altering material properties. Conventional treatments of zero-point motion often fail to accurately predict experimental observables, particularly for ultralight particles like the positive muon. In this work, we employ a combination of ab initio methods to explicitly simulate the nuclear spatial distributions in muoniated benzene (${\mathrm{C}}_6{\mathrm{H}}_6\mathrm{Mu}$). Our simulations reveal pronounced anharmonic effect and strong temperature dependence in nuclear distributions. Moreover, the hyperfine couplings for muons and protons obtained from path integral molecular dynamics (PIMD) simulations show quantitative agreement with muon spin resonance ($\mu \mathrm{SR}$) experiments. These results demonstrate that PIMD offers a reliable framework for capturing NQEs and provides unique insights into the behavior of light nuclei in $\mu \mathrm{SR}$ spectroscopy.

The development of predictive theories for spin and valley properties in $\mathrm{W}{\mathrm{S}}_2/{\mathrm{CrBr}}_3$ heterostructures requires fundamental understanding of nonmagnetic vacancy effects. Using density functional theory calculations, we find that nonmagnetic vacancies significantly enhance the spin-orbit splitting at the $K$ and $K$′ valleys in the conduction band minimum of monolayer $\mathrm{W}{\mathrm{S}}_2$ (78.2 meV for W vacancies). However, valley splitting remains prohibited due to preserved time-reversal symmetry. By constructing a van der Waals heterostructure with a monolayer ${\mathrm{CrBr}}_3$ magnetic substrate induces weak exchange interactions, generating a minor valley splitting (−0.8 meV). Remarkably, vacancy engineering amplifies this effect: sulfur vacancies (${\mathrm{V}}_1-{\mathrm{V}}_4$) induce valley splitting ranging from 3.2 to 9.0 meV, while specific tungsten vacancies (${\mathrm{V}}_6$) achieve a maximum valley splitting of 13.2 meV. Our findings reveal that vacancy-induced orbital hybridization and asymmetric potential gradients enhance Rashba spin-orbit coupling. Furthermore, the combining between nonmagnetic vacancy symmetry in $\mathrm{W}{\mathrm{S}}_2$ and weak magnetic exchange from ${\mathrm{CrBr}}_3$ establishes an unconventional symmetry protection mechanism for valley splitting enhancement. This defect engineering strategy provides a pathway for designing tunable valleytronic and spintronic devices based on vertical heterojunctions via precise atomic-scale defect control.

The non-Hermiticity of the system gives rise to a distinct knot topology in the complex eigenvalue spectrum, which has no counterpart in Hermitian systems. In contrast, the singular values of a non-Hermitian (NH) Hamiltonian are always real by definition, meaning that they can also be interpreted as the eigenvalues of some underlying Hermitian Hamiltonian. In this work, we demonstrate that if the singular values of an NH Hamiltonian are treated as eigenvalues of prototype translational invariant Hermitian models that undergo a topological phase transition between two distinct topological phases, the complex eigenvalues of the NH Hamiltonian will also undergo a first-order knot transition between different knot structures. Unlike the usual knot transition, this transition is not accompanied by an exceptional point (EP); in contrast, the real and complex parts of the eigenvalues of the NH Hamiltonian show a discrete jump at the transition point. We emphasize that the choice of an NH Hamiltonian whose singular values match the eigenvalues of a Hermitian model is not unique. However, our study suggests that this connection between the NH and Hermitian models remains robust as long as the periodicity in lattice momentum is the same for both. Furthermore, we provide an example showing that a change in the topology of the Hermitian model implies a transition in the underlying NH knot topology, but a change in knot topology does not necessarily signal a topological transition in the Hermitian system.

Machine learning offers a promising approach to addressing the unique challenges of non-Hermitian systems, particularly in classifying topological phases and overcoming the limitations of traditional methods. However, research remains sparse for complex non-Hermitian systems involving higher-order hopping terms. In this work, we employ uniform manifold approximation and projection (UMAP), an unsupervised machine learning technique, to identify phase transition points in systems exhibiting the non-Hermitian skin effect (NHSE). Conventionally, NHSE is analyzed using non-Bloch theory, which requires redefining the Brillouin zone as the generalized Brillouin zone and solving for the complex eigenvalue contours. In contrast, our UMAP-based approach can successfully identify NHSE phase transitions in a system featuring higher-order hopping terms without relying on prior knowledge. Beyond classification, we introduce a unified framework that integrates information from three major theoretical perspectives: numerical solutions under different boundary conditions, non-Bloch theory, and Bloch theory. This framework quantitatively connects these traditionally separate and sometimes incompatible analyses. UMAP's distance metric captures the topological phase structure in a way that bypasses the need for selecting specific analytical methods or performing multiple complex computations. This approach not only circumvents the limitations of detailed analytical methods but also offers physical insights into complex topological phenomena, representing a fundamental theoretical advancement in non-Hermitian physics. We anticipate that our work will further stimulate interdisciplinary research at the intersection of physics, photonics, and artificial intelligence.