We report on the charge-ordered structure of $\mathrm{Li}{\mathrm{Rh}}_2{\mathrm{O}}_4$ arising below the metal-insulator transition at 170 K. Structural studies using synchrotron x rays have revealed that the charge-ordered states of ${\mathrm{Rh}}^{3+}$ and ${\mathrm{Rh}}^{4+}$ with dimerization are realized in the low-temperature phase below 170 K. Although the low-temperature ground state resembles that of $\mathrm{Cu}{\mathrm{Ir}}_2{\mathrm{S}}_4$, a charge-ordering pattern satisfying the Anderson condition is realized in $\mathrm{Li}{\mathrm{Rh}}_2{\mathrm{O}}_4$. Based on structural information such as the short-range order of dimers appearing above the transition temperature and the weakening of the correlation between rhodium one-dimensional chains appearing in the crystal structure, we argue that the Coulomb interaction plays an important role in determining the charge-ordering patterns.

Perovskite solid solutions ${\mathrm{PbHfO}}_3\text{−}{\mathrm{PbSnO}}_3$ offer valuable opportunities for studying the formation mechanisms of incommensurate phases, owing to the presence of an intermediate (between cubic and incommensurate) phase, which is stabilized in ${\mathrm{PbHfO}}_3$ upon ${\mathrm{PbSnO}}_3$ admixture. Here, an x-ray diffuse scattering signal is used to quantify the evolution of susceptibilities related to different modes of distortion (ferroelectric, incommensurate, antiferrodistortive) as a function of temperature and the results are critically compared to the predictions of a minimal symmetry-based Landau-like model with two coupled order parameters (ferroelectric and antiferrodistortive) and an incommensurate order parameter being interpreted as inhomogeneous polarization. Experimentally, we observe a Curie-Weiss-like linear dependence of ferroelectric stiffness (inverse of susceptibility related to homogeneous polarization fluctuations) in the cubic phase down to about 50 K above the transition to the intermediate phase, where this dependence nearly saturates. Upon cooling down to the intermediate phase, the maximum of susceptibility shifts gradually to the nonzero wave vector, where another Curie-Weiss-like linear stiffness trend is established, but with respect to the incommensurate order parameter. Symmetry of diffuse scattering distributions indicates an orthorhombic symmetry of the intermediate phase. A notable temperature dependence of the constant that describes the energy of polarization inhomogeneities is observed experimentally, which is in disagreement with the model expectations. The specifics of this dependence suggest the presence of a nearly temperature-independent characteristic length scale for inhomogeneities across several phases. Other differences with the model suggest that the incommensurate order parameter cannot be straightforwardly identified with weakly inhomogeneous ferroelectric polarization.

We theoretically investigate the microscopic conditions for emergent nonreciprocal magnons toward a unified understanding on the basis of a microscopic model analysis. We show that the products of the Bogoliubov Hamiltonian obtained within the linear spin-wave approximation are enough to obtain the momentum-space functional form and the key ingredients in the nonreciprocal magnon dispersions in an analytical way even without solving the eigenvalue problems. We find that the odd order of an effective antisymmetric Dzyaloshinskii-Moriya interaction and/or the even order of an effective symmetric anisotropic interaction in the spin rotated frame can be a source of the antisymmetric dispersions. We present possible kinetic paths of magnons contributing to the antisymmetric dispersions in the one- to four-sublattice systems with the general exchange interactions. We also test the formula for both ferromagnetic and antiferromagnetic orderings in the absence of spatial inversion symmetry.

We report the magnetic properties of the layered heavy-fermion antiferromagnet ${\mathrm{CePdGa}}_6$ and their evolution upon tuning with the application of magnetic field and pressure. ${\mathrm{CePdGa}}_6$ orders antiferromagnetically below $T_{\mathrm{N}}$ = 5.2 K, where there is evidence for heavy-fermion behavior from an enhanced Sommerfeld coefficient. Our results are best explained by a magnetic ground state of ferromagnetically coupled layers of Ce $4f$ moments orientated along the $c$ axis, with antiferromagnetic coupling between layers. At low temperatures, we observe two metamagnetic transitions for fields applied along the $c$ axis corresponding to spin-flip transitions, where the lower transition is to a different magnetic phase with a magnetization one-third of the saturated value. From our analysis of the magnetic susceptibility, we propose a crystalline electric field level scheme which accounts for the Ising anisotropy at low temperatures, and we find that the evolution of the magnetic ground state can be explained considering both antiferromagnetic exchange between nearest neighbor and next-nearest neighbor layers, indicating the influence of long-range interactions. Meanwhile, we find little change of $T_{\mathrm{N}}$ upon applying hydrostatic pressures up to 2.2 GPa, suggesting that significantly higher pressures are required to examine for possible quantum critical behaviors.

Recently, a theoretical study [Z.-X. Li et al., npj Quantum Mater. 6, 36 (2021)] investigated a model of a disordered $d$-wave superconductor, and reported local time-reversal symmetry breaking current loops for sufficiently high disorder levels. Since the pure $d$-wave superconducting state does not break time-reversal symmetry, it is surprising that such persistent currents arise purely from nonmagnetic disorder. Here, we perform a detailed theoretical investigation of such disorder-induced orbital currents, and show that the occurrence of the currents can be traced to the emergence of local (extended) $s$-wave order coexisting with underlying disordered $d$-wave pairing, making it favorable to generate local $s\pm id$ regions. We discuss the energetics leading to such regions of $s\pm id$ order, which support spontaneous local current loops in the presence of inhomogeneous density modulations.

An atomistic first-principles-based effective Hamiltonian is used to investigate energy storage in $\mathrm{Ba}\left({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ relaxor ferroelectrics, both in their bulk and epitaxial films' forms, for electric fields applied along different crystallographic directions. We find that the energy density linearly increases with temperature for electric fields applied along the pseudocubic [001], [110], and [111] directions in $\mathrm{Ba}\left({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ bulk. For films at room temperature, the energy density adopts different behaviors (i.e., increase versus decrease) with strain depending on the direction of the applied electric fields. We also predicted ultrahigh energy densities (basically larger than 100 J/${\mathrm{cm}}^3$) with an ideal efficiency of 100% in all these $\mathrm{Ba}\left({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ systems. In addition, a phenomenological model is used to reveal the origin of all the aforementioned features, and should be applicable to other relaxor ferroelectrics.

We investigate the behavior of the frustrated $J_1-J_2$ Ising model on a square lattice under the influence of random dilution and spatial anisotropies. Spinless impurities generate a random-field type disorder for the spin-density wave (stripe) order parameter. These random fields destroy the long-range stripe order in the case of spatially isotropic interactions. Combining symmetry arguments, percolation theory, and large-scale Monte Carlo simulations, we demonstrate that arbitrarily weak spatial interaction anisotropies restore the stripe phase. More specifically, the transition temperature $T_c$ into the stripe phase depends on the interaction anisotropy $\mathrm{\Delta }J$ via $T_c\sim 1/|ln\left(\mathrm{\Delta }J\right)|$ for small $\mathrm{\Delta }J$. This logarithmic dependence implies that very weak anisotropies are sufficient to restore the transition temperature to values comparable to that of the undiluted system. We analyze the critical behavior of the emerging transition and find it to belong to the disordered two-dimensional Ising universality class, which features the clean Ising critical exponents and universal logarithmic corrections. We also discuss the generality of our results and their consequences for experiments.

The phonon dispersion relations of crystal lattices can often be well described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in the case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with machine-learning force fields of near-first-principles accuracy. Through large-scale molecular dynamics simulations the projected velocity autocorrelation function (PVACF) is obtained. We apply this approach to the inorganic perovskite $\mathrm{Cs}\mathrm{Pb}{\mathrm{Br}}_3$. Imaginary modes in the harmonic picture of this perovskite are absent in the PVACF, indicating a dynamic stabilization of the crystal. The anharmonic nature of the potential makes a decoupling of the system into a weakly interacting phonon gas impossible. The phonon spectra of $\mathrm{Cs}\mathrm{Pb}{\mathrm{Br}}_3$ show the characteristics of a phonon liquid. Rattling motions of the ${\mathrm{Cs}}^{+}$ cations are studied by self-correlation functions and are shown to be nearly dispersionless motions of the cations with a frequency of $\sim 0.8\mathrm{THz}$ within the lead-bromide framework.

We calculate the dynamic structure factor $S(\mathit{k},\omega )$ in the paramagnetic regime of quantum Heisenberg ferromagnets for temperatures $T$ close to the critical temperature $T_c$ using our recently developed functional renormalization group approach to quantum spin systems. In $d=3$ dimensions, we find that for small momenta $\mathit{k}$ and frequencies $\omega$ the dynamic structure factor assumes the scaling form $S(\mathit{k},\omega )=\left(\tau TG\right(\mathit{k})/\pi )\mathrm{\Phi }(k\xi ,\omega \tau )$, where $G\left(\mathit{k}\right)$ is the static spin-spin correlation function, $\xi$ is the correlation length, and the characteristic timescale $\tau$ is proportional to ${\xi }^{5/2}$. We explicitly calculate the dynamic scaling function $\mathrm{\Phi }(x,y)$ and find satisfactory agreement with neutron scattering experiments probing the critical spin dynamics in EuO and EuS. Precisely at the critical point where $\xi =\infty$, our result for the dynamic structure factor can be written as $S(\mathit{k},\omega )={\left(\pi {\omega }_k\right)}^{-1}{T}_{c}G\left(\mathit{k}\right){\mathrm{\Psi }}_c(\omega /{\omega }_k)$, where ${\omega }_k\propto k^{5/2}$. We find that ${\mathrm{\Psi }}_c\left(\nu \right)$ vanishes as ${\nu }^{-13/5}$ for large $\nu$, and as ${\nu }^{3/5}$ for small $\nu$. While the large-frequency behavior of ${\mathrm{\Psi }}_c\left(\nu \right)$ is consistent with calculations based on mode-coupling theory and with perturbative renormalization group calculations to second order in $\epsilon =6-d$, our result for small frequencies disagrees with previous calculations. We argue that until now, neither experiments nor numerical simulations have been sufficiently accurate to determine the low-frequency behavior of ${\mathrm{\Psi }}_c\left(\nu \right)$. We also calculate the low-temperature behavior of $S(\mathit{k},\omega )$ in one- and two-dimensional ferromagnets and find that it satisfies dynamic scaling with exponent $z=2$ and exhibits a pseudogap for small frequencies.

Transition metals Fe, Co, and Ni are the canonical systems for studying the effect of external perturbations on ferromagnetism. Among these, Ni stands out as it undergoes no structural phase transition under pressure. Here we have investigated the long-debated issue of the pressure-induced magnetization drop in Ni from first principles. Our calculations confirm an abrupt quenching of magnetization at high pressures not associated with any structural phase transition. We find that the pressure substantially enhances the crystal-field splitting of Ni-$3d$ orbitals, driving the system toward a new metallic phase violating the Stoner Criterion for ferromagnetic (FM) ordering. Analyzing the charge populations in each spin channel, we show that the next-nearest-neighbor interactions play a crucial role in quenching FM ordering in Ni and materials alike.

The influence of the anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI) on the structure of magnetic domains in thin Co/Pt films is investigated using magnetic force microscopy. The iDMI anisotropy is induced via application of strong (0.08%) in-plane uniaxial mechanical strain. We observe transformation of an isotropic labyrinth domain structure to oriented stripe domains and zigzag domain structures. According to theoretical considerations, such a transformation appears due to strain-induced strong iDMI anisotropy and change of iDMI sign along the direction perpendicular to the deformation axis.

We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion}\text{boundary}\text{area}}{\text{subregion}\text{volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigenoperators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is cut off around the order of subregion volume, and some of their EHSM eigenoperators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly as a power law if the system is integrable, with the exponent $s\approx 1$ $(s\approx 1.5–2)$ if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigenoperators of which correspond to the identity and the subregion Hamiltonian.

We propose an approach concerning the derivation of the spin-resolved orbital magnetization in ferromagnets with spin-orbit interaction. An approach is presented in full detail based on non-Abelian Keldysh formalism. The self-consistency and reliability of results are examined through verifications of the equilibrium thermodynamic relation and nonequilibrium thermal transport. The study of equilibrium thermodynamic features reveals the nontransport spin-resolved properties. Meanwhile, the nonequilibrium spin thermal transport with the incorporation of SU(2) structures offers a route to explore the nature of correlations in the charge-spin response.

The honeycomb superlattice model from the nearly commensurate charge-density-wave phase of $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$ has been shown to host multiple robust flat bands that depends on the number $\left(m\right)$ of extra atoms residing on each edge of the hexagon [Lee et al., Phys. Rev. Lett. 124, 137002 (2020)]. In this work we numerically study the transport phenomenon of the single-valley Dirac electrons around the band center $E=0$ where a flat band crosses. A super-Klein tunneling (SKT) phenomenon is found for $m=1$ that the Dirac electrons can tunnel through a rectangle barrier with a unity transmission irrespective of the incident angle of electrons. For the case of $m=3$, a super electron-beam collimation instead of the SKT phenomenon is identified that the Dirac electrons are allowed to tunnel through the barrier only within nearly zero incident angle, and such perpendicular transmission probability is optimal in the low-energy regime but suppressed in the high-energy regime.

It is generally believed that the intrinsic properties of glasses are intimately related to potential-energy landscapes (PELs). However, little is known about the PELs of glasses below the glass transition temperature $\left(T_g\right)$. Taking advantage of lower potential-energy barriers in nanosystems, we have systematically investigated the dynamics behavior of two nanoglasses, ${\mathrm{Al}}_{43}$ and ${\mathrm{Al}}_{46}$. Structure transformation is identified in our pure molecular-dynamics simulation far below $T_g$, which manifests the existence of metabasins in PELs, at least for nanoglasses. Surprisingly, we find that the distribution of potential energies shows a paired Gaussian and long-tailed distribution at temperatures below and approaching $T_g$; correspondingly, the distribution of the α-relaxation time exhibits an exponential-like decay. In contrast to the Gaussian distribution of energy in typical liquids and solids, the unexpected distribution may reflect the intrinsic feature of nanoglasses. Associated with the exponential-like distribution of the α-relaxation time, the stretched-exponential structural relaxation is found, and the maximum stretched behavior appears around $T_g$. Despite our studies focused on nanoglasses, the current finding may shed light on future studies of bulk glasses.

Two-dimensional transition-metal dichalcogenides appear as good candidates for gas sensing and catalysis. Here, by means of density functional theory, we characterize the adsorption and dissociation of selected diatomic molecules $(\mathrm{CO}, {\mathrm{H}}_2$, ${\mathrm{O}}_2, \mathrm{and} \mathrm{NO})$ on the ${\mathrm{MoSe}}_2$ monolayer. We consider that these processes occur on the pristine $1H\text{−}{\mathrm{MoSe}}_2$ monolayer and in the vicinity of an isolated Se vacancy. The presence of a single Se vacancy both enhances the molecular adsorption and reduces the energy needed for dissociation, making it energetically favorable for the case of ${\mathrm{O}}_2$ and NO molecules. Moreover, the presence of a second Se vacancy makes the dissociation process energetically favorable for all the molecules that are studied here. For each case we evaluate the effect that each adsorbate has on the electronic structure of the ${\mathrm{MoSe}}_2$ monolayer and the charge transfer that takes place between the adsorbate and the surface. Remarkably, adsorption of either CO or NO at the Se vacancy induces a finite spin-magnetization in the system that is spatially well localized around the adsorbate and the three closest Mo atoms.

Auxiliary field quantum Monte Carlo simulations of interacting fermions require sampling over a Hubbard-Stratonovich field $h$ introduced to decouple the interactions. The weight for a given configuration involves the products of the determinant of matrices $M_{\sigma }\left(h\right)$, where $\sigma$ labels the species, and hence is typically not positive definite. Indeed, the average sign $\langle \mathcal{S}\rangle$ of the determinants goes to zero exponentially with increasing spatial size and decreasing temperature for most Hamiltonians of interest. This statement, however, does not explicitly separate two possible origins for the vanishing of $\langle \mathcal{S}\rangle$. Does $\langle \mathcal{S}\rangle \to 0$ because randomly chosen field configurations have $\det \left[M\right(h\left)\right]<0$, or does the sign problem arise because the specific subset of configurations chosen by the weighting function have a greater preponderance of negative values? In the latter case, the process of weighting the configurations with $\left|\det \right[M\left(h\right)\left]\right|$ might steer the simulation to a region of configuration space of $h$ where positive and negative determinants are equally likely, even though randomly chosen $h$ would preferentially have determinants with a single dominant sign. In this paper, we address the relative importance of these two mechanisms for the vanishing of $\langle \mathcal{S}\rangle$ in quantum simulations.

We present a microscopic study of quasiholes in bosonic fractional quantum Hall (FQH) liquids at filling factor $\nu =1/2$ in the lowest Landau level with anisotropic band mass tensors. We use the spatial density profile to characterize the shape of a quasihole and analyze its anisotropy. We then compare the quasihole's anisotropy with the intrinsic geometric metric of the system that is extracted from the maximal overlap between the numerically obtained quasihole ground state and a set of model wave functions of anisotropic quasiholes. For a static system, we find that the quasihole's anisotropy, similar to the intrinsic metric, grows with the anisotropy of the band mass tensor. When the quasihole develops well, we observe a correspondence between the anisotropy of the quasihole and the intrinsic metric of the underlying anisotropic FQH state. We also drive the system out of equilibrium by suddenly changing the band mass tensor. In this case, the shape of the quasihole evolves with time and shows similar dynamics with the intrinsic metric of the postquench state. The evolving frequency matches the energy of a spin-2 quadrupole degree of freedom in the system. Our results suggest that the density profile of a quasihole is a useful tool to estimate the intrinsic metric and capture the dynamics of an FQH system.