Understanding the effect of disorder on the stabilization of topological textures is essential for future spintronic applications. A large body of work has been devoted to study the interplay between magnetic skyrmions and pinning. Here, we examined the impact of disorder in a ferromagnetic skyrmion lattice by introducing random-bond disorder based on two different models for both exchange and Dzyaloshinskii-Moriya interactions: Model I, where both interactions present the same disorder distribution and thus the same local distortion, and Model II, where both interactions have different disorder distributions. Through extensive Monte Carlo simulations, we explored the effect of bond disorder on the emergent phases induced by an external magnetic field at different temperatures, varying the disorder amplitude across a range from weak (10%) to strong (200%) regimes. Our study shows that for both models, moderate disorder at low magnetic fields breaks the helical order and induces a topologically nontrivial bimeron phase. We also found that the skyrmion lattice phase loses its periodicity, but surprisingly, the resulting phases retain topological characteristics up to high disorder amplitudes. Moreover, a significant difference between both disorder models is found at large magnetic fields: while in the first model, the high-field skyrmion phase is suppressed by disorder, in the second model, this phase is enhanced and expanded in temperature and magnetic field. Furthermore, for the second model, intermediate values of disorder induce a diluted skyrmion phase and chiral textures emerging from the ferromagnetic phase at low temperatures. Our results are relevant for layered magnets and provide valuable insights into the intricate behavior of skyrmion systems under varying disorder conditions.

We report on the observation of the linear anomalous Hall effect (AHE) in the nonmagnetic Weyl semimetal $\mathrm{TaIrT}{\mathrm{e}}_4$. This is achieved by applying a direct current $I^{\mathrm{dc}}$ and an alternating current $I^{\omega }$ ($I^{\omega }\ll I^{\mathrm{dc}}$) in $\mathrm{TaIrT}{\mathrm{e}}_4$, where the former induces time-reversal symmetry breaking and the latter probes the triggered AHE. The anomalous Hall resistance $V_H^{\omega }/I^{\omega }$ shows a linear dependence on $I^{\mathrm{dc}}$ and changes sign with the polarity of $I^{\mathrm{dc}}$. In temperature-dependent measurements, $V_H^{\omega }/I^{\omega }$ also experiences a sign reversal at $\sim 100$ K, consistent with the temperature-dependent nonlinear Hall effect (NLHE). Furthermore, in measurements involving only dc transport, the dc Hall voltage exhibits a quadratic relationship with $I^{\mathrm{dc}}$. When the $I^{\mathrm{dc}}$ direction is reversed, the Hall resistance changes sign, demonstrating a colossal nonreciprocal Hall effect (NRHE). Our theoretical calculations suggest that the observed linear AHE, NLHE, and NRHE all dominantly originate from the current-induced orbital magnetization compared to the minor spin contribution. This work provides deep insights into the orbital magnetoelectric effect and nonlinear Hall response, promising precise electric control of out-of-plane polarized orbit flow.

The $\alpha \text{−}{T}_3$ system undergoes a topological phase transition (TPT) between two distinct quantum spin-Hall phases across $\alpha =0.5$ when the spin-orbit interaction of Kane-Mele type is taken into consideration. As a hallmark of such a TPT, we find that the Berry curvature and the orbital magnetic moment change their respective signs across the TPT. We also find the trails of the TPT in another physical observable, namely, the orbital magnetization (OM) that can, in principle, be detected experimentally through the circular dichroism associated with optical absorption. The topological features of the OM are understood in terms of valley and spin physics. The valley-resolved OM (VROM) and the spin-resolved OM (SROM) exhibit interesting characteristics related to the valley and the spin Chern number when the chemical potential is tuned in the forbidden gap(s) of the energy spectrum. In particular, we find that the slope of the VROM versus the chemical potential in the forbidden gap changes its sign abruptly across the TPT, which is also consistent with the corresponding change in the valley Chern number. Moreover, the slope of the SROM demonstrates a sudden jump by one unit of $e/h$ (where $e$ is the electronic charge and $h$ is the Planck's constant) across the TPT, which is also in agreement with the corresponding change in the spin Chern number. It is further seen that a definite spin-valley optical selection rule governs the circular dichroism. The $k$-resolved degree of the optical polarization and the low-frequency differential optical absorbance manifest sign change across the TPT. We discuss experimentally viable signatures of various quantum spin-Hall phases in the optical absorbance.

The most salient feature of electronic topological states of matter is the existence of exotic electronic modes localized at the surface or interface of a sample. In this work, in an electronic topological system, we demonstrate the existence of localized phonon modes at the domain wall between topologically trivial and nontrivial regions, in addition to the localized interfacial electronic states. In particular, we consider a theoretical model for the Dirac semimetal with a gap opened by external strains and study the phonon dynamics, which couples to electronic degrees of freedom via strong electron-phonon interaction. By treating the phonon modes as pseudogauge fields, we find that the axion type of terms for phonon dynamics can emerge in gapped Dirac semimetal model and lead to interfacial phonon modes localized at the domain wall between trivial and nontrivial regimes that possess the axion parameters 0 and $\pi$, respectively. We also discuss the physical properties and possible experimental probe of such interfacial phonon modes.

Collinear dipole orders such as ferroelectricity and antiferroelectricity have developed rapidly in recent decades, while the noncollinear dipole orders are rarely touched in solids. Noncollinear dipole orders can provide a route to realize ferrielectricity. Based on first-principles calculations, an inorganic molecular crystal ${\mathrm{MnO}}_3\mathrm{Cl}$ has been demonstrated to own intrinsic noncollinear ferrielectricity, which originates from the stereo orientations of polar molecules. The large negative piezoelectricity effect ($d_{33}\sim -27$ pC/N) is also predicted. A strong light absorption and moderate optical anisotropy are found for this molecular crystal in the ultraviolet-light window. Additionally, by electron doping via hydrogen intercalation, a ferromagnetic polar half-metal can be obtained. This study provides a material platform to explore the intriguing physics of noncollinear ferrielectricity and potential applications in devices.

Electrides have attracted increasing interest due to their diversely physical properties, including low work function, high catalytic activity, as well as potential superconductivity. In this work, using first-principles crystal structure prediction method in combination with first-principles calculations, we uncovered seven thermodynamically stable electrides in the electron-rich Li-Si system at a pressure range of 25–100 GPa, namely $C2/c{\mathrm{Li}}_5\mathrm{Si}, Cmcm{\mathrm{Li}}_6\mathrm{Si}, P{2}_1/m{\mathrm{Li}}_7\mathrm{Si}, Imma{\mathrm{Li}}_7\mathrm{Si}, C2/c{\mathrm{Li}}_8\mathrm{Si}, Cmcm{\mathrm{Li}}_9\mathrm{Si}$, and $I222{\mathrm{Li}}_{10}\mathrm{Si}$. Among these predicted structures, five of them are superconductor. In particular, the superconducting critical temperature $T_{\text{c}}$ of $I222{\mathrm{Li}}_{10}\mathrm{Si}$ was estimated to be approximately 15 K at 95 GPa. Our in-depth analysis shows that this high superconductivity is attributed to the strong coupling between the Li-$p$ electrons and the Li-dominated phonon softening at low frequencies. Additionally, ${\mathrm{Li}}_{10}\mathrm{Si}$ undergoes a phase transition from solid state to superionic state at 60 GPa and 850 K, where Si atoms remain fixed to form the lattice, allowing for the diffusion of Li atoms within the interstitial position. Our results reveal the emergence of two distinct dynamic states of superconducting and superionic in this particular system, and the further experimental studies are thus stimulated.

Quantum heat machines, encompassing heat engines, refrigerators, heaters, and accelerators, represent the forefront of quantum thermodynamics, offering a novel paradigm for converting heat energy into useful mechanical work. Leveraging quantum mechanical principles, these machines promise superior efficiency and performance compared to classical counterparts, with potential applications in renewable energy and quantum computing. This paper investigates a quantum Otto engine operating in both ideal and finite-time scenarios, employing a two-level system interacting with a harmonic oscillator within the framework of the anisotropic quantum Rabi-Stark model (AQRSM) as the working medium. This model is notable for exhibiting both first-order and continuous quantum phase transitions. By focusing on quantum heat engines, our study reveals that these phase transitions critically modulate the efficiency and power of AQRSM-based engines, outperforming quantum engines fueled by working medium with harmonic spectrum. Additionally, we explore the impacts of quantum friction and conduct limit cycle analysis in finite-time operations, providing insights into optimizing quantum heat engines for practical implementation.

The nondegenerate energy bands along a specific path of altermagnet enable the realization of magnetic tunnel junctions (MTJs) with high tunnel magnetoresistance (TMR). Herein, we propose a MTJ based on insulated altermagnet/ferromagnetic $\mathrm{MTJ}-\mathrm{Mn}{\mathrm{F}}_2/\mathrm{Cr}{\mathrm{O}}_2$. In addition to effectively simplifying the device configuration, high TMR is attained in the $\left[110\right]$ and $\left[111\right]$ crystal directions due to the spin-dependent tunneling effect in the real space of $\mathrm{Mn}{\mathrm{F}}_2$. The increase in the thickness of the $\mathrm{Mn}{\mathrm{F}}_2$ layer leads to an increase in electron spin filtering efficiency (SFE). When the thickness of the $\mathrm{Mn}{\mathrm{F}}_2$ layer is three layers, the SFE is as high as 85.65% and the TMR is as high as ${10}^4\%$. In addition, we find that the interface type has a significant impact on the magnetoresistance performance of the tunnel junction. Compared with F interface, the O interface leads to a further increase in the SFE of $\mathrm{Mn}{\mathrm{F}}_2$ (99.56%) and conductance of MTJ, and thus a significant enhancement of the TMR (up to ${10}^5\%$). The analysis of electronic states in real space reveals that the coordination of oxygen atoms with magnetic atoms in the current direction gives rise to the endowed electronic states and an increase in spin polarizability in the vicinity. The results provide insight into the development of ultrafast and efficient spintronic devices with altermagnet.

We present the magnetic excitation spectrum of the quantum magnet ${\mathrm{NiPS}}_3$ near the zig-zag ground state of a minimal honeycomb spin Hamiltonian that includes bilinear and biquadratic spin interactions. Our analysis, using a multiboson generalized spin wave theory suited for spin S = 1 systems, revealed two normal modes at the linear level. The one at lower energy corresponds to a single magnon mode, consistent with results from spectroscopy experiments. Without single-ion anisotropy, this mode features a Goldstone mode at the corner of the Brillouin zone. When single ion anisotropy is introduced, the zig-zag phase's global U(1) invariance is broken, resulting in a gap. The higher energy mode corresponds to two-magnon fluctuations, which appear at the harmonic level in the generalized spin wave theory. This mode forms a gapped flat band due to bilinear spin interactions and becomes dispersive when biquadratic interactions are considered. The higher energy dispersion is related to quadrupolar fluctuations, which are feasible in magnets where the order parameter fluctuates in the SU(3) space. The spectrum analysis yielded quantum corrections to the order parameter and detected instabilities in the ${\mathrm{NiPS}}_3$ dipolar phases. Identifying the highest energy branch in experiments could provide insight into hidden nematic orders in ${\mathrm{NiPS}}_3$ and other van der Waals magnets.

Superconductor/ferromagnet/superconductor Josephson junctions with anomalous phase shift ${\phi }_0$ (${\phi }_0$-S/F/S JJs) implement a coupling between the superconducting phase and the spin degrees of freedom. Here we investigate the dynamics of voltage-biased coupled chains of ${\phi }_0$-S/F/S JJs and predict that the presence of ${\phi }_0$ makes the conventional regime corresponding to the linear growth of the superconducting phase at each of the junctions and oscillating Josephson current unstable. New stable regimes are found and investigated. The changes of the dynamic behavior are clearly seen in the $\mathit{IV}$ characteristics of the system and can serve as a fingerprint of the presence of the magnetoelectric coupling ${\phi }_0$. Moreover, the collective magnetic excitations of the chains of ${\phi }_0$-S/F/S JJs, which were reported by G. A. Bobkov et al. [JETP Lett. 119, 251 (2024)], also manifest themselves in the $\mathit{IV}$ characteristics. This provides a method for their experimental detection and direct measurement of the constant quantifying the strength of the coupling between the superconducting phase and the spin degrees of freedom.

We explore the Dirac spin liquid (DSL) as a candidate for the ground state of the Mott insulating phase of fermions with six flavors on the kagome lattice, particularly focusing on realizations using ${}^{173}\mathrm{Yb}$ atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the DSL has the lowest variational energy among SU(6) symmetry-preserving trial wave functions with a periodicity of a 12-site unit cell, as well as uniform chiral states with larger unit cells. It remains a local minimum even when small second-nearest neighbor and ring-exchange interactions are introduced. To characterize the DSL, we calculate the static and dynamic structure factor of the Gutzwiller projected wave function and compare it with mean-field calculations. The static structure factor shows triangular-shaped plateaus around the $\mathrm{K}$ points in the extended Brillouin zone, with small peaks at the corners of these plateaus. The dynamical structure factor consists of a gapless continuum of fractionalized excitations. Our study also presents several complementary results, including bounds for the ground-state energy, methods for calculating three-site ring-exchange expectations in the projective mean field, the boundary of ferromagnetic states, and the nontopological nature of flat bands in the DSL band structure.

${\mathrm{RbMnF}}_3$ is a cubic antiferromagnet with a very small anisotropy field, so that it can be considered a prototype of a three-dimensional Heisenberg antiferromagnet. In this paper, we present a theoretical investigation of the spin Seebeck effect (SSE) in the spin-flop phase of ${\mathrm{RbMnF}}_3$. The analysis begins with the formulation of a quantum theory for spin waves in antiferromagnetic systems exhibiting cubic anisotropy, considering both the antiferromagnetic and spin-flop phases. Subsequently, we develop a magnon diffusion theory for the SSE in antiferromagnetic materials with cubic anisotropy in the spin-flop phase. The theoretical predictions are in good agreement with the experimental data, supporting the validity of the bulk magnon diffusion theory for describing spin transport in antiferromagnetic materials in the spin-flop phase.

In the study of van der Waals–layered magnetic materials, the properties of ${\mathrm{CrCl}}_3$ continue to attract attention. This compound is reported to undergo antiferromagnetic ordering below $\sim 14$ K, with a ferromagneticlike region proposed to exist between 14 and 17 K. Ideally, the crystal structure is rhombohedral (R) below $\sim 235$ K, separated from a higher-temperature monoclinic (M) phase by a layer-sliding structural phase transition. However, the structural transition is often inhibited even in bulk single crystals, allowing M-type layer stacking, reported to have a 10-fold greater interlayer magnetic coupling than R-type stacking, to be present at low temperature. To clarify the effect of stacking defects on ${\mathrm{CrCl}}_3$, we report magnetization measurements on samples of varying crystalline quality. At low applied magnetic field, some crystals predominantly show the $T_N=14$ K peak, but other crystals show hysteretic behavior and a magnetization enhancement at a slightly higher temperature ($14<T\lesssim 17$ K.) Samples with anomalous behavior exhibit a transition around $\sim 2$ T in isothermal magnetization-field data, evidence that M-type stacking defects are the source of these anomalies. Ground powder samples are especially likely to show strongly anomalous behavior. We suggest that the anomalous behavior arises from few-layer magnetic domains that form just above $T_N$ in an environment of mixed interlayer magnetic coupling strength. We argue that the influence of M-type stacking boundaries on sublattice magnetization is already observable in reported neutron scattering data, and may be responsible for an enhancement near 17 K in reported specific heat data.

In this article, the Curie-Weiss type behavior and the appearance of an “interaction” or “ordering” temperature for a collection of magnetic nanoparticles is explored theoretically. We show that some systems where an interaction temperature is reported are too dilute for dipolar interactions to play a role unless at least some of the particles are clumped together. We then show using the most simple type of clumps (particle pairs) that positive and negative interaction temperatures are possible due to dipolar interactions. The clump orientation dramatically changes this result. Finally, we show that an apparent interaction temperature can be measured in magnetic nanoparticle systems that have no interactions between particles, due to some alignment of anisotropy easy axes. These results show that nanoscale physical structures affect the measured magnetic response of nanoparticles.

Modulating exchange-coupling interaction at ferromagnet (FM)/antiferromagnet (AFM) interfaces is essential for constructing low-power magnetic random memories, logic devices, and topological electronic devices. Currently, most effective tunability focuses on the regulation of uncompensated magnetic moments by controlling the attributes of AFM materials, such as component, roughness, texture, or stress state. Here, we report a method of oxygen-tuned uncompensated magnetic moments to tailor the exchange-coupling interaction. By inserting an ultrathin oxide (MgO, $\mathrm{Hf}{\mathrm{O}}_2$, or ${\mathrm{Al}}_2{\mathrm{O}}_3$) into the NiFe/IrMn interface to regulate the chemical state of NiFe, both the magnetic anisotropy of NiFe and uncompensated magnetic moments of AFM were effectively modified. The oxidation product strongly depended on the metal-O dissociation energy of these oxides, leading to various tunability effect of exchange-coupling interaction. By appropriate formation of antiferromagnetic FeO, obvious enhancement of exchange-coupling interaction was achieved by boosting the uncompensated magnetic moments, accompanied by a maximal 60% increment in exchange bias. These findings provide insights for regulating exchange-coupling interaction and constructing efficient spintronic (topological) devices.

We explore the effect of decoherence on many-body mixed states from a purification perspective. Here, quantum channels map to unitary transformations acting on a purified state defined within an extended Hilbert space. First, we exploit this approach to analyze the phenomenon of spontaneous strong-to-weak symmetry breaking (sw-SSB) triggered by strongly symmetric local quantum channels. We find that sw-SSB for mixed states relates to proximity to a symmetry-protected topological (SPT) order in the purified state. Remarkably, the measurement-induced long-range order in the purified SPT state, as characterized by the Rényi-2 correlator, mirrors the ensuing long-range order in the mixed state due to sw-SSB. Moreover, we establish a 1-to-1 correspondence between various sw-SSB order parameters for the mixed state, and strange correlators in the purification, which signify the SPT order. This purification perspective is further extended to explore intrinsic mixed-state topological order and decoherent symmetry-protected topological phases.

Transition metal dichalcogenide $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ hosts a $2\times 2\times 2$ charge density wave (CDW) that is known to form the state with localized domains separated by the domain walls upon Cu intercalation. The CDW state with the domain-wall network has attracted significant interest due to its coexistence with superconductivity. Here, we present a scanning tunneling microscopy, transport, and magnetic susceptibility study of $1T\text{−}\mathrm{T}{\mathrm{i}}_{1-x}\mathrm{T}{\mathrm{a}}_x\mathrm{S}{\mathrm{e}}_2$. Ta substitution for Ti atoms allows us to perform experiments over the wide range of doping ($0\le x\le 0.2$), providing access to a significantly broader phase diagram than Cu intercalation experiments. At $x=0.02$, we observe a complex network of domains and domain walls. We identify two distinct types of domain walls and show their structure with atomic resolution. Additionally, an elusive symmetry-breaking stripe CDW is found at the light substitution of $x=0.02$. We also measure highly substituted $x=0.2$ crystals that are superconducting despite the full collapse of the CDW order. Our results uncover rich CDW physics in Ta-substituted $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ crystals and illuminate the interplay between the CDW and superconductivity.

Complex oxides are at the heart of modern functional material developments. In particular, the perovskite $AB{\mathrm{O}}_3$ structure is seen in compounds used in oxide solar cells, resistive memories, fuel cell catalysts, superconducting tapes, quantum bits, and programmable magnets, making it one of the most studied material families. One important advantage of these systems is that their properties may be controlled in situ to change between various electronic states, usually by means of thermal or electric conditioning. In this work, we investigate the two-terminal resistive switching properties of the perovskitelike oxide ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ when the system is driven by electric current. We perform all-electrical switching to characterize and control low-amplitude resistance changes, and we implement finite-element modeling to explain how these effects can be properly accounted for by oxygen-vacancy counterflow induced by electric bias. The presented research sheds light on the bulk displacement of oxygen atoms in perovskite materials with potential for sensing and memory technologies.