By carrying out first-principles calculations, we studied the charge density waves (CDWs) in monolayer/few-layer $H\text{−}{\mathrm{NbS}}_2$. For monolayer ${\mathrm{NbS}}_2$, unstable phonon modes are found to develop at the $2/3\mathrm{\Gamma }\mathrm{M}$ point and its symmetric points in the whole Brillouin zone. By displacing the atoms along the unstable mode, a new dynamically stable $3\times 3$ structure with lower total energy is obtained, which corresponds well to the experimentally observed $3\times 3$ CDW phase. The symmetries are broken in the $3\times 3$ CDW phase, leading to gap opening and anisotropic properties. The $3\times 3$ CDW phase of ${\mathrm{NbS}}_2$ is found to be stable with respect to small strains. In comparison with ${\mathrm{NbSe}}_2$, it is found that the Se atoms are much more active in vibration than the S atoms, resulting in the different CDW behaviors in these two very similar materials. We explored the CDW phase tuning by electron doping, and a sequence of CDW phase transitions from $3\times 3$ to $2\times 2$ and to $4\surd 3\times 4\surd 3$ is found. The doping-dependent CDW phase provides insight into the inconsistent observation of CDW phases in ${\mathrm{NbS}}_2$/graphene and ${\mathrm{NbS}}_2$/Au(111) based on the difference in substrate charge doping. We further investigated the CDW phases of the bilayer and trilayer ${\mathrm{NbS}}_2$. With the decrease of the temperature, a series of instabilities occur in the phonon spectrum of bilayer ${\mathrm{NbS}}_2$, which correspond to $2\times 2, 3\times 3$, and $4\times 4$ CDW phases. For trilayer ${\mathrm{NbS}}_2$, in contrast, only a $2\times 2$ CDW phase is found, whereas the $3\times 3$ CDW phase, which exists in monolayer and bilayer, is not manifested even at ultralow temperature. The layer-dependent CDW phases indicate significant effects of interlayer interactions.

We employ the spin cluster perturbation theory to investigate the dynamical properties of the antiferromagnetic $J_1\text{−}{J}_2$ Heisenberg model on the honeycomb lattice. We obtain the excitation spectra for all possible phases in the phase diagram, including the Néel phase, plaquette valence-bond-solid phase, dimer valence-bond-solid phase, and stripe antiferromagnetic phase. In the Néel phase, besides the obvious renormalization of the magnon dispersion, we find that the spectrum exhibits a dome-shaped broad continuum around the second Brillouin zone (BZ) and the additional strong continuum close to the corner of the BZ. In the valence-bond-solid phases, the spectra are dominated by a strong broad continuum all the way down to below $J_1$ coexisting with the lowest-energy triplon modes characterizing the plaquette and dimer phases. We ascribe this strong broad continuum and the additional continuum close to the BZ corner in the Néel phase to the contributions of fractionalized spinon excitations. In the stripe phase, a clear difference from the linear-spin-wave approximation is that the spectrum is gapped at the $M$ point, while that obtained by the latter is gapless due to the strong quantum fluctuations. We point out that the features observed in the Néel phase are consistent with the recent neutron scattering experiments on ${\mathrm{YbCl}}_3$ and ${\mathrm{YbBr}}_3$.

Exploring novel two-dimensional multiferroic materials that can realize electric-field control of two-dimensional magnetism has become an emerging topic in spintronics. Using first-principles calculations, we demonstrate that nonmetallic bilayer transition-metal dichalcogenides can be an ideal platform for building multiferroics by intercalated magnetic atoms. Moreover, we unveil that with Co intercalated bilayer ${\mathrm{MoS}}_2, \mathrm{Co}{\left(\mathrm{Mo}{\mathrm{S}}_2\right)}_2$, two energetically degenerate states with opposite chirality of Dzyaloshinskii-Moriya interaction are the ground states, indicating electric-field control of the chirality of topological magnetic objects such as skyrmions can be realized in this type of materials by reversing the electric polarization. These findings pave the way for electric-field control of topological magnetism in two-dimensional multiferroics with intrinsic magnetoelectric coupling.

Hybrid magnon-photon systems are a promising candidate for quantum information applications, with the potential to store and transfer both amplitude and phase information. For the photon subsystem, both amplitude and phase can be detected via microwave transmission. However, for the magnon subsystem, current techniques, such as spin pumping, are only sensitive to the amplitude. Measurements of the magnon phase remain elusive. Here, we demonstrate electrical detection of the magnon phase in a hybrid magnon-photon system using spin rectification. Spin rectification can be used to characterize typical hybrid features, such as the distorted microwave frequency-magnetic field dispersion and the resonance linewidth evolution. With spin rectification we also observe the phase difference between high-frequency and low-frequency coupled modes, which allows us to identify the relative magnon phase in a straightforward manner. This unique phase-sensitive technique could play an important role in integrated magnon-photon hybrid devices, in particular at low cooperativity.

We report measurement of terahertz anomalous Hall conductivity and Faraday rotation in the magnetic Weyl semimetal ${\mathrm{Co}}_2\mathrm{MnGa}$ thin films as a function of the magnetic field, temperature, and thickness, using time-domain terahertz spectroscopy. The terahertz conductivity shows a thickness-independent anomalous Hall conductivity of around 600 ${\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ at room temperature, and it is also frequency-independent from 0.2–1.5 THz. The magnitude of the longitudinal and Hall conductivities, the weak spin-orbit coupling, and the very close positioning of Weyl points to the chemical potential all satisfy the criteria for intrinsic anomalous Hall conductivity. First-principles calculation also supports the frequency-independent intrinsic anomalous Hall conductivity at low frequency. We also find a thickness-independent Faraday rotation of 59 $(\pm 6)$ mrad at room temperature, which comes from the intrinsic Berry curvature contribution. In the thinnest 20 nm sample, the Faraday rotation divided by the sample thickness reaches around 3 mrad/nm due to Berry curvature, and is the largest reported at room temperature. The giant Verdet constant of the order of ${10}^6$ rad ${\mathrm{m}}^{-1} {\mathrm{T}}^{-1}$ at room temperature and the large Hall angle around $8.5\%$ from 0.2–1.5 THz indicate that ${\mathrm{Co}}_2\mathrm{MnGa}$ is promising for THz spintronics at room temperature.

Three-dimensional (3D) magnetic textures attract much attention from researchers due to their fascinating structures and dynamic behaviors. The magnetic hopfion is a prominent example of a 3D magnetic texture. Here, we numerically study the mutual conversion between a Néel-type hopfion and a Néel-type toron under an external magnetic field. We also investigate the excitation modes of hopfions and torons in a film with strong perpendicular magnetic anisotropy. It is found that the Néel-type hopfion could be a stable state in the absence of the external magnetic field, and its diameter varies with the out-of-plane magnetic field. The Néel-type hopfion may transform into a Néel-type toron at an out-of-plane magnetic field of about 20 mT, where the cross-section structure is a Néel-type skyrmion. The hopfion and toron show different excitation modes in the presence of an in-plane microwave magnetic field. Our results provide a method to realize the conversion between a Néel-type hopfion and a Néel-type toron, which also opens a path to distinguish between a Néel-type hopfion and a Néel-type toron based on their excitation modes.

We present results from ramp compression experiments on high-purity Zr that show the $\alpha \to \omega , \omega \to \beta$, as well as reverse $\beta \to \omega$ phase transitions. Simulations with a multiphase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic $\alpha \to \omega$ transition occurs $\sim 9\mathrm{GPa}$ above the equilibrium phase boundary, the $\omega \to \beta$ transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium $\omega \text{−}\beta$ line at $P=29.2\mathrm{GPa}$, and $T=490\mathrm{K}$. The thermodynamic path in the interior of the sample lies $\sim 100\mathrm{K}$ above the isentrope at the point of the $\omega \to \beta$ transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the nonequilibrium $\alpha \to \omega$ transition. The inferred rate of the $\alpha \to \omega$ transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress $s_{ji}$ has the same effect on the nucleation rate as a pressure increase $\delta P=c{\epsilon }_{ij}{s}_{ji}/(\mathrm{\Delta }V/V),$ where $c$ is a geometric constant $\sim 1$ and ${\epsilon }_{ij}$ are the transformation shear strains. The small fractional volume change $\mathrm{\Delta }V/V\approx 0.1$ at the $\alpha \to \omega$ transition amplifies the effect of shear stress, and we estimate that for this case $\delta P$ is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

${\mathrm{K}}_{1\text{−}x}{\mathrm{Li}}_x\mathrm{Ta}{\mathrm{O}}_3$ ($x=0.043$, 0.08) crystals, characterized by pyroelectric current with calculated spontaneous polarization and zero-field second-harmonic generation, have been studied by broadband dielectric spectroscopy, including time-domain terahertz transmission and infrared (IR) reflectivity, and by polarized Raman spectroscopy in the 10–300 K temperature range. This multiexperimental approach has proven the percolative nature of the ferroelectric (FE) transition at low temperatures and demonstrated that the FE phase is inherently inhomogeneous and displays coexistence of FE and relaxor regions. Thanks to the very broad frequency range studied (from 1 Hz to 20 THz), the relevant excitations were identified and fitted in the dielectric response of both crystals: three relaxations, a central mode (CM), and a soft mode (SM) that splits into three components on cooling. Two Cole-Cole relaxations (assigned to flipping of polar nanoregions around the ${\mathrm{Li}}^{+}$ ions by $\pi /2$ and π, in agreement with the known literature), thermally activated below $\sim 150\mathrm{K}$, but staying in the gigahertz range at higher temperatures, do not show any frequency anomaly at the FE transition and are therefore related to the non-FE parts of the sample volume. A third thermally activated relaxation of unusually slow dynamics was revealed at low frequencies and preliminary assigned to an expected critical relaxation connected with the percolative nature of the FE phase transition. The IR SM, which undergoes much less softening than in the undoped ${\mathrm{KTaO}}_3$, splits into three components below the FE transition. Two higher-frequency components correspond to the FE volume part of the crystals assigned to the split $A_1$ and $E$ modes due to the cubic-tetragonal transition. The third low-frequency component is assigned to the non-FE (relaxor) volume part. Our assignment was confirmed by modeling the terahertz-IR response of the SM using the Bruggeman model within the effective medium approach. Below the SM response, an additional CM in the ${10}^{11}\mathrm{Hz}$ range in the whole temperature range is inferred from the fits.

Magnetic noise spectroscopy provides a noninvasive probe of spin dynamics in magnetic materials. We consider two-dimensional magnetically ordered insulators with magnon excitations, especially those supporting long-distance magnon transport, where nitrogen-vacancy (NV) centers enable the access to (nearly) ballistic transport regime of magnons. We develop a generalized theory to describe the magnon transport across a wide range of length scales. The longitudinal dynamic spin susceptibility is derived from the Boltzmann equation and extended to a Lindhard form, which is modified by both the spin-conserving magnon collisions and spin relaxation. Our result is consistent with the diffusive (ballistic) model for the length scale much larger (smaller) than the magnon mean free path, and provides a description for the intermediate regime. We also give a prediction for the NV transition rate in different magnon transport regimes.

Quantum anomalous valley Hall effect (QAVHE), which combines both the features of QAHE and AVHE, is both fundamentally intriguing and practically appealing, but is experimentally challenging to realize in two-dimensional (2D) intrinsic magnetic materials to date. Here, based on first-principles calculations with the density functional theory $+U$ approach, we predicted the electronic correlation-driven valley-dependent quantum phase transition from ferrovalley (FV) to half-valley-semiconductor (HVS) to QAVHE to HVS to FV phase in single-layer RuClBr. Remarkably, the QAVHE phase with an integer Chern number ($C=1$) and chiral spin-valley locking, which is induced by sign-reversible Berry curvature or band inversion between $d_{xy}/d_{x^2-y^2}$ and $d_{z^2}$ orbitals, can achieve complete spin and valley polarizations for low-dissipation electronics devices. We also find that the electron valley polarization can be switched by reversing magnetization direction, providing a route of magnetic control of the valley degree of freedom. An effective $k·p$ model is proposed to clarify valley-dependent quantum phenomena. Additionally, electronic correlation has an important effect on the variations of the Curie temperature of single-layer RuClBr. These findings shed light on the possible role of correlation effects on valley-dependent physics in 2D materials and open alternative perspectives for multifunctional spin-valley quantum devices in valleytronics.

The behavior of three-dimensional semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for potentially uncovering phases of matter that combine nontrivial band topology and interactions. While electronic instabilities of such semimetals at strong magnetic fields have been explored theoretically and experimentally, the role of electron-phonon interactions therein has been largely neglected. In this paper, we study the interplay of electron-electron and electron-phonon interactions in a minimal two-node model of Weyl semimetal. Using a Kadanoff-Wilson renormalization group approach, we analyze lattice (Peierls) instabilities emerging from chiral and nonchiral Landau levels as a function of the magnetic field. We consider both the adiabatic and nonadiabatic phonon regimes, in the presence or absence of improper symmetries that relate Weyl nodes of opposite chirality. We find that (i) the Cooper channel, often neglected in recent studies, can prevent purely electronic instabilities while enabling lattice instabilities that are not Bardeen-Cooper-Schrieffer-like; (ii) breaking the improper symmetry that relates the two Weyl nodes suppresses the Cooper channel, thereby increasing the critical temperature for the lattice instability; (iii) in the adiabatic phonon regime, lattice instabilities can preempt purely electronic instabilities; and (iv) pseudoscalar phonons are more prone to undergo a Peierls instability than scalar phonons. In short, our study emphasizes the importance of taking electron-phonon interactions into account for a complete understanding of interacting phases of matter in Dirac and Weyl semimetals at high magnetic fields.

We present an experimental and theoretical study of the longitudinal electron spin relaxation ($T_1$) of shallow donors in the direct band-gap semiconductor ZnO. $T_1$ is measured via resonant excitation of the Ga donor-bound exciton. $T_1$ exhibits an inverse-power dependence on magnetic field $T_1\propto B^{-n}$, with $4\le n\le 5$, over a field range of 1.75 T to 7 T. We derive an analytic expression for the donor spin-relaxation rate due to spin-orbit (admixture mechanism) and electron-phonon (piezoelectric) coupling for the wurtzite crystal symmetry. Excellent quantitative agreement is found between experiment and theory suggesting the admixture spin-orbit mechanism is the dominant contribution to $T_1$ in the measured magnetic field range. Temperature and excitation-energy dependent measurements indicate a donor density dependent interaction may contribute to small deviations between experiment and theory. The longest $T_1$ measured is 480 ms at 1.75 T with increasing $T_1$ at smaller fields theoretically expected. This work highlights the extremely long longitudinal spin-relaxation time for ZnO donors due to their small spin-orbit coupling.

Organic charge transfer complexes (CTCs) can be grown as thin films on intercalated graphene (Gr). Deciphering their precise film morphologies requires global ab initio structure search, where configurational sampling is computationally intractable unless we reconsider the model for the complex substrate. In this study, we employ charged freestanding Gr to approximate an intercalated Gr/O/Ir(111) substrate, without altering the adsoption properties of deposited molecules. We compare different methods of charging Gr and select the most appropriate substitute model for Gr/O/Ir(111) that maintains the adsorption properties of fluorinated tetracyanoquinodimethane (${\mathrm{F}}_4\mathrm{TCNQ}$) and tetrathiafulvalene (TTF), prototypical electron acceptor/donor molecules in CTCs. Next, we apply our model in the Bayesian optimization structure search method and density-functional theory to identify the stable structures of ${\mathrm{F}}_4\mathrm{TCNQ}$ and TTF on supported Gr. We find that both molecules physisorb to Gr in various configurations. The narrow range of adsorption energies indicates that the molecules may diffuse easily on the surface and molecule-molecule interactions likely have a central role in film formation. Our study shows that complex intercalated substrates may be approximated with charged freestanding Gr, which can facilitate exhaustive structure search of CTCs.

We report a comparative study of the bulk electronic structure of two Al-based complex metallic alloys (CMAs), $\beta -{\mathrm{Al}}_3{\mathrm{Mg}}_2$ and ${\mathrm{Al}}_{13}{\mathrm{Fe}}_4$ using hard x-ray photoemission spectroscopy (HAXPES) interpreted on the basis of density functional theory (DFT) calculations. An experimental confirmation of the role of the Hume-Rothery mechanism for the stability of the $\beta -{\mathrm{Al}}_3{\mathrm{Mg}}_2$ phase is established by identification of a shallow pseudogap near $E_F$ from HAXPES that is corroborated by DFT. An almost parabolic shape of the density of states (DOS), a large $n$($E_F$), and plasmon loss features that are similar to Al metal show its nearly free-electron-like nature. In the case of ${\mathrm{Al}}_{13}{\mathrm{Fe}}_4$ the total DOS exhibits a shallow pseudogap due to Al $s$ – Fe $d$ hybridization, which results in the DOS at $E_F$ [$n$($E_F$)] being large due to Fe $d$ states. However, the Al $s$ states show a deep pseudogap and this is revealed in HAXPES because of the large photoemission cross section of the $s$ states at high photon energies. The overall shape of the valence band is in excellent agreement with DFT for both the CMAs. The larger width of the Al core-level main peak and the plasmon loss peaks as well as the suppression of the intensities of the latter with respect to $\beta -{\mathrm{Al}}_3{\mathrm{Mg}}_2$ further underline the importance of $sp\text{−}d$ hybridization in ${\mathrm{Al}}_{13}{\mathrm{Fe}}_4$.

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel ground-state wave-function Ansätze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretraining modern RNNs on even small amounts of data significantly reduces the convergence time for a subsequent variational optimization of the wave function. This suggests that essentially any amount of measurements obtained from a state prepared in an experimental quantum simulator could provide significant values for neural-network-based VMC strategies.

Patterns formed in monolayer graphene (Gr) and hexagonal boron nitride (h-BN) upon ion irradiation in the temperature range from 950 to 1530 K using 500 eV ${\mathrm{He}}^{+}$ at normal or 500 eV ${\mathrm{Xe}}^{+}$ at grazing incidence and fluences up to $2.5\times {10}^{19}$ $\mathrm{ions}/{\mathrm{m}}^2$ are investigated by room-temperature scanning tunneling microscopy. Subnanometer pores are created and are distributed with the periodicity of the moiré which results from the interaction of the monolayers with their Ir(111) substrate. The moiŕe contains trapping sites for vacancies within each moiré unit cell as is investigated in detail for the case of h-BN with the help of ab initio calculations. The density of the nanopores is extremely high in the order of ${10}^{17}$ $\mathrm{pores}/{\mathrm{m}}^2$ and their size distribution is limited by the size of the vacancy traps causing excess vacancies to be expelled from the array and to anneal at preexistent defects. Successful delamination of a perforated Gr monolayer from the substrate is demonstrated and makes the material accessible for membrane research.

The study of thermal transport in low-dimensional materials has attracted a lot of attention recently after discovery of high thermal conductivity of graphene. Here we study numerically phonon transport in low-dimensional carbon structures being interested in the hydrodynamic regime revealed through the observation of second sound. We demonstrate that correct numerical modeling of such graphene systems (such as nanotubes and nanoribbons) requires semiquantum molecular dynamics simulations of temperature waves that, using classical molecular dynamics, allows us to take into account quantum statistics of thermalized phonons. We reveal that second sound can be attributed to the maximum group velocity of bending optical oscillations of carbon structures, and the hydrodynamic effects disappear for $T>200\mathrm{K}$, being replaced by diffusive dynamics of thermal waves. Our numerical results suggest that the velocity of second sound in such low-dimensional structures is about 6 km/s, and the hydrodynamic effects are manifested stronger in carbon nanotubes rather than in carbon nanoribbons.

The community currently lacks a complete understanding of how resonant inelastic x-ray scattering (RIXS) experiments probe the electron-phonon interaction in solids. For example, most theoretical models of this process have focused on dispersionless Einstein phonons. Using a recently developed momentum average variational approximation for computing RIXS spectra of band insulators, we examine the influence of both electron and phonon dispersion in the intermediate state of the scattering process. We find that the inclusion of either, and their mutual interplay, introduces significant momentum variations in the RIXS intensity, even for momentum-independent electron-phonon coupling. The phonon dispersion also induces nontrivial changes in the excitation line shapes, which can have a quantitative impact on the data analysis. These results highlight the considerable challenges of interpreting RIXS data in actual materials.

In this study, we have performed the magnetocaloric effect and the specific heat measurements of chromium spinel oxide $\mathrm{Hg}{\mathrm{Cr}}_2{\mathrm{O}}_4$, wherein the magnetic ${\mathrm{Cr}}^{3+}$ ions form a highly frustrated pyrochlore lattice with significant spin-lattice coupling. In addition to the known magnetic-field-induced phases, our thermodynamic measurements detect a quantum phase just before the saturation of the magnetization, which has not been expected from the classical theories of the pyrochlore lattice antiferromagnet with spin-lattice coupling. Based on recent theoretical model calculation, we discuss the possibility of a spin nematic state appearing for this quantum phase.