Emergent magnetic fields exerted by topological spin textures of magnets lead to an additional Hall response of itinerant carriers called the topological Hall effect (THE). While THE as a bulk effect has been widely studied, THE driven by magnetic domain boundaries (DBs) has been elusive. Here, we report rich Hall responses characterized by multiple peak structures and a hysteresis loop in films of ${\mathrm{EuCd}}_2$, where Eu layers form a geometrically frustrated lattice of Heisenberg spins. We uncover a THE component sharply enhanced at magnetic transition fields, indicating a giant contribution from nontrivial spin textures possibly formed at the DBs.

The coherent control of wave absorption has important applications in areas such as energy harvesting, imaging, and sensing. However, most practical scenarios involve the absorption of partially coherent rather than fully coherent waves. Here we present a systematic theory of unitary control over the absorption of partially coherent waves by linear systems. Given an absorbing system and incident partially coherent wave, we provide analytical expressions for the range of attainable absorptivity under arbitrary unitary transformations of the incident field. We also present an explicit algorithm to construct the unitary control scheme that achieves any desired absorptivity within that attainable range. As applications of our theory, we derive the conditions required for achieving two phenomena—partially coherent perfect absorption and partially coherent zero absorption. Furthermore, we prove a theorem relating the coherence properties of the incident field, as quantified by majorization, to the resulting absorption intervals. Our results provide both fundamental insights and practical prescriptions for exploiting unitary control to shape the absorption of partially coherent waves. The theory applies across the electromagnetic spectrum as well as to other classical wave systems such as acoustic waves.

Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a systematic theory for the unitary control of partially coherent wave transmission and reflection. For a linear time-invariant system with an incident partially coherent wave, we derive analytical expressions for the range of attainable total transmittance and reflectance under arbitrary unitary transformations. We also introduce an explicit algorithm to construct a unitary control scheme that achieves any desired transmission or reflection within the attainable range. As applications of our theory, we establish conditions for four phenomena: partially coherent perfect transmission, partially coherent perfect reflection, partially coherent zero transmission, and partially coherent zero reflection. We also prove a theorem that relates the degree of coherence of the incident field, quantified by the majorization order, to the resulting transmission and reflection intervals. Furthermore, we demonstrate that reciprocity (or energy conservation) imposes direct symmetry constraints on bilateral transmission (or transmission and reflection) of partially coherent waves under unitary control. Our results provide fundamental insights and practical guidelines for using unitary control to manipulate the transmission and reflection of partially coherent waves. This theory applies to various wave systems, including electromagnetic and acoustic waves.

In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. The latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form ${\text{Tr}}_{\omega }\text{ln}\left\{G_0^{-1}G\right\}$, where ${\text{Tr}}_{\omega }$ is the integration in frequency of the trace operator. Here, we show that using a sum-over-poles representation for the Green's functions and the algorithmic-inversion method one can obtain, in full generality, an explicit analytical expression for ${\text{Tr}}_{\omega }\text{ln}\left\{G_0^{-1}G\right\}$. Further, this allows us (1) to recover an explicit expression for the random phase approximation correlation energy in the framework of the optimized effective potential and (2) to derive a variational expression for the Klein functional valid in the presence of an embedding bath.

Encircling non-Hermitian exceptional points (EPs) leads to the swapping of eigenstates, which naturally corresponds to the different state permutations. Here, we find that non-Abelian permutations meet the $D_4$ group in a four-state non-Hermitian system. By encircling three different exceptional arcs within a three-dimensional parameter space, we present seven eigenvalue permutations and correlate them with seven nontrivial operations in the non-Abelian $D_4$ group. Furthermore, our theory reveals the topological properties of higher-order EPs, improves the understanding of EPs in non-Hermitian systems, and offers a robust methodology for examining non-Abelian properties in systems with multiple EPs.

A Josephson junction may be in a stable odd-parity state when a single quasiparticle is trapped in an Andreev bound state. Embedding such junction in an electromagnetic environment gives rise to a special quantum mechanics of the superconducting phase that we investigate theoretically. Our analysis covers several representative cases, from the lifting of the supercurrent quench due to quasiparticle poisoning for a low ohmic impedance of the environment, to a Schmid transition in a current-biased junction that for odd parity occurs at four times bigger critical impedance. For intermediate impedances, the supercurrent in the odd state is higher than in the even one.

We present the mean-field phase diagram of electrons in a kagome flat band with repulsive interactions. In addition to flat-band ferromagnetism, the Hartree-Fock analysis yields cascades of unconventional magnetic orders driven by on-site repulsion as filling changes. These include a series of antiferromagnetic (AFM) spin-charge stripe orders, as well as an evolution from ${120}^{\circ }$ AFM to intriguing noncoplanar spin orders with tetrahedral structures. We also map out the phase diagram under extended repulsion at half and empty fillings of the flat band. To examine the possibilities beyond the mean-field level, we conduct a projective symmetry group analysis and identify the feasible ${\mathbb{Z}}_2$ spin liquids and the magnetic orders derivable from them. The theoretical phase diagrams are compared with recent experiments on FeSn and FeGe, enabling a determination of the most likely magnetic instabilities in these and similar flat-band kagome materials.

We discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index $0<q\le 1$. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as $O(c{N}^{0}log\beta )$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.

The $R\mathrm{BaC}{\mathrm{o}}_4{\mathrm{O}}_7$ system is a prototype geometrically frustrated magnet in which kagome planes and triangular layers of Co-O tetrahedra interleave. For $R=\mathrm{Y}$, an antiferromagnetic ground state is realized due to a frustration-breaking trigonal-orthorhombic phase transition. For $R=\mathrm{Lu}$, however, a long-range ordered state has rarely, if ever, been reported despite a similar symmetry-breaking transition, albeit at a significantly lower temperature. To explore this dichotomy, we present a comprehensive magnetic and structural phase diagram for ${\mathrm{Y}}_{1–x}\mathrm{L}{\mathrm{u}}_x\mathrm{BaC}{\mathrm{o}}_4{\mathrm{O}}_7$, established through complementary neutron diffraction and magnetization measurements. Our results outline the phase evolution of the nuclear structures in response to changes in composition and temperature. The temperature of the trigonal ($P31c$) to orthorhombic ($Pbn{2}_1$) transition, $T_{\mathrm{s}1}$, decreases monotonically with increasing Lu content from 310 K for $x=0.0$ to 110 K for $x=1.0$. In Lu-rich compositions ($0.7\le x\le 1.0$), first-order structural transitions are observed with coexisting and competing orthorhombic $Pbn{2}_1$ and metastable monoclinic $\mathit{Cc}$ phases. For the magnetically ordered Y-rich compositions, $T$- and $x$-dependent refinements of the magnetic structure reveal an antiferromagnetic “ribbonlike” arrangement of Co spin pairs in both the triangular and the kagome layers. A gradual suppression of long-range magnetic order is observed with increasing the Lu content, accompanied by the development of short-range magnetic correlations present in all the samples.

${\mathrm{SrCo}}_2{\mathrm{P}}_2$ with a tetragonal structure is known to be a Stoner-enhanced Pauli paramagnetic metal being nearly ferromagnetic. Recently J. Schmidt et al. [Phys. Rev. B 108, 174415 (2023)] reported that a ferromagnetic ordered state is actually induced by a small Ni substitution for Co of $x=0.02$ in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2$ where an antiferromagnetic ordered phase also appears by further Ni substitution with $x=0.06–0.35$. Here, using nuclear magnetic resonance (NMR) measurements on ${}^{31}\mathrm{P}$ nuclei, we have investigated how the magnetic properties change by the Ni substitution in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2$ from a microscopic point of view, especially focusing on the evolution of magnetic fluctuations with the Ni substitution and the characterization of the magnetically ordered states. The temperature dependencies of the ${}^{31}\mathrm{P}$ spin-lattice relaxation rate divided by temperature $(1/T_{1}T)$ and Knight shift $\left(K\right)$ for ${\mathrm{SrCo}}_2{\mathrm{P}}_2$ are reasonably explained by a model where a double-peak structure for the density of states near the Fermi energy is assumed. Based on a Korringa ratio analysis using the $T_1$ and $K$ data, ferromagnetic spin fluctuations are found to dominate in the ferromagnetic $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2$ as well as the antiferromagnets where no clear antiferromagnetic fluctuations are observed. We also found the distribution of the ordered Co moments in the magnetically ordered states from the analysis of the ${}^{31}\mathrm{P}$-NMR spectra exhibiting a characteristic rectangular-like shape.

We investigate the magneto-optical properties of two-dimensional nonsymmorphic Dirac semimetals in the presence of antiferromagnetic order. Using the Kubo formula, we calculate the conductivity tensor of two-dimensional CuMnAs, a prototype antiferromagnetic Dirac material, as a function of light frequency. From the finite-frequency conductivity tensor, we derive the dynamic dielectric function and magnetic linear dichroism, demonstrating how they are influenced by the orientation of the Néel order parameter. Adjusting the Néel vector changes both the sign and amplitude of the system's magneto-optical response. We propose that magnetic linear dichroism spectroscopy is a powerful technique for determining the orientation of the Néel vector.

We studied the electrical transport properties of a classical spin triangular lattice antiferromagnet ${\mathrm{Ag}}_2{\mathrm{CrO}}_2$. In this material, a unique spin structure with a five-sublattice unit cell emerges below the Néel temperature $T_{\mathrm{N}}$, owing to frustration from strong further-neighbor interactions. The material also exhibits unique electrical transport properties coupled with its magnetism, due to a highly conductive layer of ${\mathrm{Ag}}_2$. Here, we report magnetoresistance and the Hall effect in ${\mathrm{Ag}}_2{\mathrm{CrO}}_2$ flake devices below and above $T_{\mathrm{N}}$ up to a magnetic field of 8 T. A large magnetoresistance and anomalous Hall effect were observed in the vicinity of $T_{\mathrm{N}}$, indicating that the fluctuation of the magnetic moments plays a key role. We propose possible scenarios in which the anomalous Hall effect is enhanced through thermal fluctuation.

A. bound state eigenfunction is defined here to be strictly localized within a subspace of the structure under study and has no decreasing behavior. Its eigenwavelength can be within state continua. Bound states in the continuum (BICs) and long-lived resonances have become a unique way to produce the extreme localization of electronic waves. We present a theoretical and numerical demonstration of semi-infinite bound states in the continuum (SIBICs) and long-lived resonances in a ringlike electronic microresonator coupled to a finite stub and to two electronic rib/ridge waveguides, together with their existence conditions. This structure is composed of a closed loop of length $L$, a finite stub of length $L_1$ and two semi-infinite leads. SIBICs localized in a semi-infinite subspace domain induce transmission zeros. Others induce transmission ones in the middle of long-lived resonances. The BICs correspond to localized resonances of infinite lifetime inside the structure, without any leakage into the surrounding leads. When BICs exist within state continua, they induce Fano resonances exhibiting sharp peaks in the transmission spectra and in the variation of the density of states for specific values of the stub length $L_1$. This enables one to regulate these resonances by means of this length. The obtained results take due account of the state number conservation between the final system and the reference one. This conservation rule enables one to find all the states of the final system and among them the bound in the continuum ones. The analytical results are obtained by means of the Green's function technique. The structures and the long-lived resonances presented in this paper may have potential applications due to their high sensitivities to weak perturbations, in particular in sensing, wave filtering, and microelectronic devices.

The existence of a flat band near the Fermi level can be a suitable platform for the emergence of interesting phenomena in condensed matter physics. Recently, ${\mathrm{NbOCl}}_2$ monolayer has been experimentally synthesized [Q. Guo et al., Nature (London) 613, 53 (2023)], which has a flat and isolated valence band. Motivated by the recent experiment, we investigate the origin of the flat band as well as the electronic, optical, photocatalytic, and magnetic properties of the monolayer by combining density functional theory and many-body quantum perturbation theory. Our results show that the flat and isolated band of this monolayer is caused by the interplay between the Peierls distortion and the electronic configuration of Nb atoms. We show that monolayers based on other elements of group 5 of the periodic table, including the V and Ta atoms, also have a flat band. The investigation of the bandwidth of the monolayer under the biaxial and uniaxial strains reveals that this material can be grown on substrates with a larger lattice constant by maintaining the flat band. Examining the material's response to the linearly polarized light not only reveals the presence of weak optical anisotropy, but also shows the existence of a bright exciton with a binding energy of about 0.94 eV. Hole doping can result in a flat-band-induced phase transition from semiconductor to ferromagnet. By adjusting the amount of doping, a bipolar magnetic semiconductor or a half metal can be created. The interaction between the nearest Nb atoms is ferromagnetic, while an antiferromagnetic interaction appears between the second neighbors, which grows significantly with increasing doping. Our results demonstrate that ${\mathrm{NbOCl}}_2$ monolayer has a suitable potential for spintronic applications in addition to electronic and optoelectronic applications.