We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, $J_{\mathrm{A}}, J_{\mathrm{B}}$, and $J_{\mathrm{C}}$, that is realized in a distorted honeycomb-lattice antiferromagnet ${\mathrm{Cu}}_2{\left(\mathrm{pymca}\right)}_3\left({\mathrm{ClO}}_4\right)$. We remeasured the magnetic susceptibility of its polycrystalline sample with special care and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the $J_{\mathrm{A}}/J_{\mathrm{C}}\text{−}{J}_{\mathrm{B}}/J_{\mathrm{C}}$ plane. The phase diagram consists of a small $\mathrm{N}\acute{\mathrm{e}}\mathrm{el}$ phase and a gapped quantum paramagnetic phase surrounding the $\mathrm{N}\acute{\mathrm{e}}\mathrm{el}$ phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continua near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground state of ${\mathrm{Cu}}_2{\left(\mathrm{pymca}\right)}_3\left({\mathrm{ClO}}_4\right)$ by future neutron scattering measurements.

We investigate the motion of magnetic domain walls driven by magnetic fields and current-driven spin-orbit torques in an exchange-biased system with perpendicular magnetization. We consider ${\mathrm{Cr}}_2{\mathrm{O}}_3/\mathrm{Co}/\mathrm{Pt}$ trilayers as a model system, in which the magnetization of the Co layer can be exchanged biased out-of-plane or in-plane depending on the field-cooling direction. In field-driven experiments, the in-plane exchange bias favors the propagation of the domain walls with internal magnetization parallel to the exchange-bias field. In current-driven experiments, the domain walls propagate along the current direction, but the domain wall velocity increases and decreases symmetrically (antisymmetrically) for both current polarities when the exchange bias is parallel (perpendicular) to the current line. At zero external field, the exchange bias modifies the velocity of current-driven domain wall motion by a factor of 10. We also find that the exchange bias remains stable under external fields up to 15 kOe and nanosecond-long current pulses with current density up to $3.5\times {10}^{12}$ A/m. Our results demonstrate versatile control of the domain wall motion by exchange bias, which is relevant to achieve field-free switching of the magnetization in perpendicular systems and current-driven manipulation of domain walls velocity in spintronic devices.

Controlling the magnetic anisotropy of two-dimensional (2D) ferromagnets (FMs) is of great importance for the development of next generation spintronics. Here, by combining the 2D FM chromium trihalides $\mathrm{Cr}{X}_3 (X=\mathrm{I},\mathrm{Br},\mathrm{Cl})$ monolayer (ML) with the fully hydrogenated bilayer AlN (AlN-2L) together, the electronic and magnetic properties, especially the magnetic anisotropies, of $\mathrm{Cr}{X}_3\text{/}\mathrm{AlN}$ heterostructures ($\mathrm{Cr}{X}_3$ HSs) are systematically investigated based on first-principles calculations. When the polarization direction of AlN-2L reverses, the magnetic easy axis of $\mathrm{Cr}{X}_3$ MLs can be switched between out-of-plane and in-plane directions. Particularly the magnetic anisotropic energy is tuned by a maximum of 200% variation in $\mathrm{Cr}{\mathrm{I}}_3$/AlN. It is shown that the different effects of AlN-2L on the modulation of the magnetic easy axis of $\mathrm{Cr}{X}_3$ MLs are related to their different interfacial charge transfer/redistribution across their interfaces. In addition, a transition from FM semiconductor to half-metal is found in all $\mathrm{Cr}{X}_3$ MLs when the polarization direction points toward $\mathrm{Cr}{X}_3$ MLs. Our results suggest a feasible avenue for the design of van der Waals HSs to realize the control of magnetic anisotropy in 2D FMs.

We demonstrate the occurrence of a topological phase transition induced by an effective magnetic field in a two-dimensional electron gas with spin-orbit coupling and in proximity to an $s$-wave superconductor. The effective, perpendicular magnetic field is generated by an in plane, off-resonant ac-magnetic field or by circularly polarized light. The conditions for entering the topological phase do not rely on fine parameter tuning: For fixed frequency, one requires a minimal amplitude of the effective field which can be evaluated analytically. In this phase, chiral edge states generally emerge for a system in stripe geometry unless the Rashba and Dresselhaus coupling have the same magnitude. In this special case, for magnetic field driving the edge states become Majorana flat bands, due to the presence of a chiral symmetry; the light irradiated system is a trivial superconductor.

The cluster expansion (CE) method has seen continuous and increasing use in the study of configuration-dependent properties of crystalline materials. The original development of the CE method along with the underlying mathematical formalism and assumptions was focused on the study of metallic alloys. Since then the methodology has been actively and successfully used in the study of ionic materials as well. In this work, we present a cohesive reformulation of the mathematical formalism underlying the CE method based on a synthesis of its original formulation, several additions and extensions that have been proposed since, and a revised representation of its constituent mathematical objects. We then proceed to describe some of the formal implications of using the methodology for charge-neutral configurations in ionic systems. In particular, we discuss the reduction of the size of configuration spaces and the resulting linear dependencies that arise among correlation functions that span the larger unconstrained configuration space. Additionally, we explore the effects of long-range electrostatic interactions. We also demonstrate how the previously proposed use of a point electrostatic term successfully accounts for the majority of the longer-range electrostatic interactions, and leaves the cluster expansion terms to capture mostly short-range interactions. Finally, we present and discuss a variety of recently developed methodologies, including training structure selection, oxidation state assignment, structure mapping, and regression algorithms, that are necessary to address these formal mathematical notions for a practical implementation of the CE method in the study of multicomponent ionic materials.

The study of spin dynamics in artificial spin ice (ASI) has in recent years become a vibrant research field for reconfigurable magnonics. We present experimental and theoretical studies of magnetization dynamics in disconnected kagome ASI lattices using broadband ferromagnetic resonance and micromagnetic simulations. By systematically varying the field strength and orientation, the dynamical coupling effects between different ASI sublattices have been distinguished for the field along the symmetric axes. For the field parallel to one sublattice bar, the mode hybridization with an avoided-crossing gap is identified, and a special dynamical magnon mode emerges. But, for the field perpendicular to one sublattice bar, the magnon modes from the other two sublattice bars merge into a single mode, which is attributed to the static dipolar interactions between the sublattice bars. Our research shows a detailed investigation of magnetization dynamics in kagome ASIs, which is of great significance to further understand collective spin-dynamics behavior in nanomagnet systems.

The anomalous Hall effect (AHE) is an electronic transport phenomenon with rich physics. In thin magnetic films and multilayers, an unusual peak observed in AHE is often identified as the topological Hall effect (THE), induced by topologically nontrivial spin textures. However, it is a challenge to determine whether this unusual peak truly originates from such spin textures or is an artifact due to inhomogeneities. In this work, we systematically study the Pd thickness and temperature dependence of the Hall effect in ${\mathrm{Mn}}_2\mathrm{CoAl}$/Pd thin films. We observe an unusual peak in the Pd thickness dependence and rule out that the origin of the peak is from the topologically nontrivial spin textures by directly imaging the magnetic domain structures. We also build a model for the AHE based on the sum of contributions from ${\mathrm{Mn}}_2\mathrm{CoAl}$ and an intermixed CoPd alloy. These materials have opposite signs of the AHE and different coercive fields, which successfully explains the thickness and temperature behaviors of the unusual peak. Our results show that the interface mixing layer can play an important role in the interpretation of the AHE in ferromagnet/heavy metal systems.

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a “real” charge density wave (rCDW), but also time-reversal symmetry breaking, typical of loop currents described by an “imaginary” charge density wave (iCDW). Here, we combine density-functional theory, group theory, and phenomenological modeling to investigate the complex charge-ordered states that arise from interactions between the low-energy van Hove singularities present in the electronic structure of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$. We find two broad classes of mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, triple-$\mathbf{Q}$ rCDW order, dubbed $3\mathbf{Q}\text{−}3\mathbf{Q}$, and double-$\mathbf{Q}$ iCDW, single-$\mathbf{Q}$ rCDW order, dubbed $2\mathbf{Q}\text{−}1\mathbf{Q}$. Moreover, we identify seven different types of iCDW order, stemming from the different vanadium-orbital and kagome-sublattice structures of the two pairs of van Hove singularities present above and below the Fermi level. While the $2\mathbf{Q}\text{−}1\mathbf{Q}$ states trigger an orthorhombic distortion that breaks the threefold rotational symmetry of the kagome lattice, the $3\mathbf{Q}\text{−}3\mathbf{Q}$ states induce various types of subsidiary uniform magnetic orders, from conventional ferromagnetism to magnetic octupolar, magnetic toroidal, and even magnetic monopolar order. We show that these exotic orders display unique magnetostriction, magnetoelectric, and magnetoelectrostriction properties that can be probed experimentally to identify which iCDW state is realized in these compounds. We briefly discuss the impact of an out-of-plane modulation of the charge order and the interplay between these complex charge-ordered states and superconductivity.

Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of nonlocal interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transition in this interaction regime.

Controllable topological phase transitions in low-dimensional materials allows for unconventional optical selection rules and exciton series. We show that the broad mixing of single-particle contributions to the exciton states occurring across a ${\mathbb{Z}}_2$ phase transition in one-dimensional polyacene polymers leads to an extreme tunability of optical properties, with exciton dispersions ranging from gigantic bandwidth ($\approx 1.5$ eV) to practically zero. The acene length transversal to the periodic axis controls the exciton localization, allowing for a crossover from Mott-Wannier to Frenkel-like excitons and large changes in optical gaps, singlet-triplet splittings and the orbital structure of the real-space exciton states. Our work opens appealing perspectives for the design of novel optoelectronic devices.

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbor interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a “spin-locked” cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a “polarized holonic” phase, and a crystalline phase at the filling 2/5, that we address via a semiclassical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.

Minimally entangled typical thermal states are a construction that allows one to solve for the imaginary time evolution of quantum many-body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrix product states. We generalize these ideas to arbitrary variational wave functions and we focus, as an illustration, on the particular case of restricted Boltzmann machines. The imaginary time evolution is carried out using stochastic reconfiguration (natural gradient descent) combined with Monte Carlo sampling. Since the time evolution takes place on the tangent space, deviations between the actual path in the Hilbert space and the trajectory on the variational manifold can be important, depending on the internal structure and expressivity of the variational states. We show how these differences translate into a rescaled temperature and demonstrate the application of the method to quantum spin systems in one and two spatial dimensions.

The orientation-dependent conduction polarity, e.g., $p$-type conduction along one direction and $n$-type conduction along another direction, namely “goniopolarity,” observed in highly anisotropic materials brought us an alternative concept for novel electronic devices. But goniopolarity has hardly been utilized due to the rarity of goniopolar materials. Here, we associate goniopolarity with the saddle points in electronic band structure and the hyperbolic Fermi surface of materials and highlight the potential of layered metal diboride ($M{\mathrm{B}}_2$) materials in achieving this interesting phenomenon using first-principles calculations. We demonstrate that the electron-doped ${\mathrm{MgB}}_2$, ${\mathrm{CaB}}_2$, and ${\mathrm{SrB}}_2$ can exhibit remarkable orientation-dependent conduction polarity with opposite Seebeck coefficients which are detectable in verifying goniopolarity. We attribute the goniopolarity with the $p_{x,y}$ orbitals of the boron layers of these materials which constitute anisotropic electronic states along in-plane and out of plane directions. Moreover, their anisotropic Seebeck coefficients can be efficiently enhanced by applying tensile strain. This work offers a promising strategy for design of goniopolar materials and regulation of goniopolarity.

The moiré potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum ${\mathrm{\Phi }}_0$ for experimentally accessible magnetic field strengths. Close to rational fractions of ${\mathrm{\Phi }}_0$, $p/q·{\mathrm{\Phi }}_0$, magnetotranslation invariance is restored giving rise to Brown-Zak fermions featuring the same dispersion relation as in the absence of the field. Employing a highly efficient numerical approach we simulate the magnetoconductance of bulk graphene on hexagonal boron nitride. The resulting Hofstadter butterfly is analyzed in terms of a novel half-integer Wannier diagram for Landau spectra of Dirac particles. This complex diagram can account for many features observed in the simulation and in experiment on a single-particle level, such as spin and valley degeneracy lifting and a nonperiodicidy in ${\mathrm{\Phi }}_0$.

We study the kagome antiferromagnet for quantum spin-1/2 with first $J_1$, second $J_2$, and third $J_3$ neighbor exchanges, along the $J_2=J_3\equiv J$ line. We use Schwinger boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at $J=0$ remains essentially stable over a large window, up to $J\approx 1/3$, because it is only weakly frustrated by the $J$ term. Then, at $J\approx 1/2$, the intermediate $Z_2$ spin liquid condenses into a long-range chiral order because of the change of nature of the local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.

We investigate numerically the time evolution of wave packets incident on one-dimensional semi-infinite lattices with mosaic modulated random on-site potentials, which are characterized by the integer-valued modulation period $\kappa$ and the disorder strength $W$. For Gaussian wave packets with the central energy $E_0$ and a small spectral width, we perform extensive numerical calculations of the disorder-averaged time-dependent reflectance, $\langle R\left(t\right)\rangle$, for various values of $E_0, \kappa$, and $W$. We find that the long-time behavior of $\langle R\left(t\right)\rangle$ obeys a power law of the form $t^{-\gamma }$ in all cases. In the presence of the mosaic modulation, $\gamma$ is equal to 2 for almost all values of $E_0$, implying the onset of the Anderson localization, while at a finite number of discrete values of $E_0$ dependent on $\kappa , \gamma$ approaches 3/2, implying the onset of the classical diffusion. This phenomenon is independent of the disorder strength and arises in a quasiresonant manner such that $\gamma$ varies rapidly from 3/2 to 2 in a narrow energy range as $E_0$ varies away from the quasiresonance values. We deduce a simple analytical formula for the quasiresonance energies and provide an explanation of the delocalization phenomenon based on the interplay between randomness and band structure and the node structure of the wave functions. We explore the nature of the states at the quasiresonance energies using a finite-size scaling analysis of the average participation ratio and find that the states are neither extended nor exponentially localized, but critical states.

Out-of-equilibrium effects provide an elegant pathway for probing and understanding the underlying physics of topological materials. In particular, controlling electronic band structure properties using ultrafast optical pulses has shown promise for creating exotic states of matter. Of recent interest is band renormalization in Dirac and Weyl semimetals as it leads to direct physical observables through the enhancement of the effective mass or in the shift of resonant energies. Here we provide experimental and theoretical signatures of photoinduced renormalization of the electronic band structure in the topological nodal-line semimetal ZrSiS. Specifically, we show how the change in the transient reflectivity spectra under femtosecond optical excitations is induced by out-of-equilibrium effects that renormalize the kinetic energy of electrons. We associate the observed spectral features with an enhancement of the effective mass and to a redshift of the resonant frequency as a function of pump field strength. Finally, we show that the transient relaxation dynamics of the reflectivity is primarily an electronic effect with a negligible phononic contribution. Our study presents conclusive modifications of electronic properties in ZrSiS using ultrashort pulses and demonstrates the potential of this approach in creating photoinduced phases in topological quantum matter through an all-optical route.