We investigate the ground state and critical temperature ($T_c$) phase diagrams of the classical and quantum $S=\frac{1}{2}$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange interaction as well as direct and indirect DMI. At the classical level, three ground states are found: all-in/all-out, ferromagnetic, and a locally ordered $XY$ phase, known as ${\mathrm{\Gamma }}_5$, which displays an accidental classical U(1) degeneracy at the mean-field level. Quantum zero-point energy fluctuations computed to order $1/S$ are found to lift the classical ground-state degeneracy and select the so-called ${\psi }_3$ state out of the degenerate manifold in most parts of the ${\mathrm{\Gamma }}_5$ regime. Likewise, thermal fluctuations treated classically at the Gaussian level entropically select the ${\psi }_3$ state at $T=0^{+}$. In contrast to this low-temperature state-selection behavior, classical Monte Carlo simulations find that the system orders at $T_c$ in the noncoplanar ${\psi }_2$ state of ${\mathrm{\Gamma }}_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from ${\psi }_2$ to ${\psi }_3$ at a temperature $T_{{\mathrm{\Gamma }}_5}<T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the ${\psi }_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=\frac{1}{2}$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground state of the model, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=\frac{1}{2}$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. Interestingly, we find that a combined ferromagnetic Heisenberg and indirect DMI, near the boundary of ferromagnetism and ${\mathrm{\Gamma }}_5$ antiferromagnetism, may potentially realize a $T=0$ quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same long-range ordered phases (all-in/all-out, ferromagnetic, and ${\mathrm{\Gamma }}_5$) as in the classical model.

We theoretically analyze Josephson dynamics of superconducting weak links with transmissions $\mathcal{T}$ not much smaller than unity at subgap bias voltages $V$. Employing the effective action approach combined with the Keldysh technique, we develop a regular perturbation theory in $\mathcal{R}=1-\mathcal{T}$ and derive the first-order correction to the current across the weak link, which consists of two different contributions. One of them is negative, effectively corresponding to a decrease of the excess current at small $V$ due to breaking of the multiple Andreev reflection cycle by normal reflection for some subgap quasiparticles. These quasiparticles, in turn, generate the second (Josephson-like) contribution to the current, which increases with decreasing $V$ down to very small voltages, where the perturbation theory in $\mathcal{R}$ ceases to be valid. Some of the above features are not reproduced within the physical picture involving Landau-Zener tunneling between subgap Andreev states.

Recently, Heusler ferromagnets have been found to exhibit unconventional anomalous electric, thermal, and thermoelectric transport properties. In this study, we employed first-principles density functional theory calculations to systematically investigate both intrinsic and extrinsic contributions to the anomalous Hall effect (AHE), anomalous Nernst effect (ANE), and anomalous thermal Hall effect (ATHE) in two Heusler ferromagnets: ${\mathrm{Fe}}_2\mathrm{CoAl}$ and ${\mathrm{Fe}}_2\mathrm{NiAl}$. Our analysis reveals that the extrinsic mechanism originating from disorder dominates the AHE and ATHE in ${\mathrm{Fe}}_2\mathrm{CoAl}$, primarily due to the steep band dispersions across the Fermi energy and corresponding high longitudinal electronic conductivity. Conversely, the intrinsic Berry phase mechanism, physically linked to nearly flat bands around the Fermi energy and gapped by spin-orbit interaction band crossings, governs the AHE and ATHE in ${\mathrm{Fe}}_2\mathrm{NiAl}$. With respect to ANE, both intrinsic and extrinsic mechanisms are competing in ${\mathrm{Fe}}_2\mathrm{CoAl}$ as well as in ${\mathrm{Fe}}_2\mathrm{NiAl}$. Furthermore, ${\mathrm{Fe}}_2\mathrm{CoAl}$ and ${\mathrm{Fe}}_2\mathrm{NiAl}$ exhibit tunable and remarkably pronounced anomalous transport properties. For instance, the anomalous Nernst and anomalous thermal Hall conductivities in ${\mathrm{Fe}}_2\mathrm{NiAl}$ attain giant values of 8.29 A/Km and 1.19 W/Km, respectively, at room temperature. To provide a useful comparison, we also thoroughly investigated the anomalous transport properties of ${\mathrm{Co}}_2\mathrm{MnGa}$. Our findings suggest that Heusler ferromagnets ${\mathrm{Fe}}_2\mathrm{CoAl}$ and ${\mathrm{Fe}}_2\mathrm{NiAl}$ are promising candidates for spintronics and spin caloritronics applications.

We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the 2D infinite projected entangled-pair state (iPEPS) calculation provides more accurate values of transition points. Near the phase boundary, moreover, our iPEPS results indicate that it is more difficult to pin down the orientation of magnetic easy axes, and we interpret it as the easy-axis softening. This phenomenon implies an emergence of continuous $U\left(1\right)$ symmetry, which is indicated by the low-energy effective model and has been analytically shown by the field theory. Our model and study provide a concrete example for utilizing iPEPS near the critical region, showing that the emergent phenomenon living on the critical points can already be captured by iPEPS with a rather small bond dimension.

A model of nonequilibrium thermodynamics of erbium orthoferrite is presented. The quantum-mechanical effects in arbitrary magnetic fields, related both to the direction of a general quantization axis and an influence of anisotropic exchange interactions on the magnetic structure, spin-reorientation phase transition, spin reversals, and hysteresis, are considered. Based on recent experimental data on temperature-induced spin switching [Phys. Rev. B 105, 094424 (2022)], a possible mechanism for the exchange bias of magnetic hysteresis loops is proposed. The main parameters of the model Hamiltonian are determined, which point out a strongly competitive character of exchange interactions in erbium orthoferrite.

We investigate the ultrafast demagnetization in ${\mathrm{Co}}_2\mathrm{Mn}{\mathrm{Si}}_{1\text{–}x}{\mathrm{Al}}_x$ quaternary Heusler compounds induced by terahertz (THz) and infrared (IR) pulses. Adjusting the alloy's composition allows us to tailor the spin polarization at the Fermi energy from $97\%\pm 3\%$ $\left({\mathrm{Co}}_2\mathrm{MnSi}\right)$ due to its minority spin gap around 0.6 eV, down to $63\%\pm 3\%$ $\left({\mathrm{Co}}_2\mathrm{MnAl}\right)$ without a spin gap. Here we experimentally compare the cases of ultrafast demagnetization, when the material is excited with the help of laser pulses with photon energies below and above the minority spin gap, respectively. More particularly, the pump-photon energies were tuned from 1.02 eV (IR) down to 4.1 meV (THz). We found that the ultrafast demagnetization time decreases upon substitution of Si by Al and thus destroys the minority spin gap. Moreover, a decrease of the pump-photon energies in the near-infrared spectral range results in a slight increase of the demagnetization time. Nevertheless, further decrease of the photon energy by a factor of 250 hardly changes the characteristic time of ultrafast demagnetization. Both THz and IR pulses cause very similar ultrafast magnetization dynamics in our ${\mathrm{Co}}_2\mathrm{Mn}{\mathrm{Si}}_{1\text{–}x}{\mathrm{Al}}_x$ Heusler compounds.

The role of quantum correction such as weak localization in anomalous Hall effects (AHEs) is an important issue. In this work, we have investigated the robust quantum correction to the AHE in magnetic PtMnGe (PMG) thin films of high crystalline quality. The PMG films have not shown long-range magnetic order. The observed temperature and magnetic field dependence of the sheet conductivities in the ultrathin PMG films are explained based on the perturbation theory, where the interplay of spin-dependent scattering and the spin Zeeman splitting effect are taken into consideration. It is found that, as long as the magnetic scattering time is comparable to the spin-orbit scattering time, the conductivity correction due to the Cooperons between antiparallel spins that involves spin-flip scattering can be negligible in the two dimensions. Therefore, even when the spin-dependent scattering exists, the quantum correction to the transport behavior is robust in the two-dimensional PMG system. Our work makes a significant step toward clarifying the role of quantum correction in the AHE of the magnetic materials.

The ferrimagnet ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ attracts attention because of a recently discovered colossal magnetoresistance (CMR) with unique magnetic field properties. An improved magnetic structure for the material has emerged from a neutron diffraction study linked to understanding the CMR. A deeper theoretical investigation of the magnetic structure has now revealed anapole, chiral, and orbital states of manganese ions not previously mentioned. Moreover, it is shown that existence of these states in the low temperature form of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$, with a magnetic field applied, can be tested by neutron and resonant x-ray diffraction.

Using first-principles $\mathit{GW}$ plus Bethe-Salpeter equation calculations, we identify exceptionally strong excitonic effects in several vacancy-ordered double perovskites ${\mathrm{Cs}}_2{MX}_6$ ($M$ = Ti, Zr; $X=\mathrm{I},\mathrm{Br}$). Giant exciton binding energies of about 1 eV are found in these moderate-gap, inorganic bulk semiconductors, pushing the limit of our understanding of the electron-hole interaction and exciton formation in solids. Not only are the exciton binding energies extremely large compared with any other moderate-gap bulk semiconductors, but they are also larger than typical two-dimensional semiconductors with comparable quasiparticle gaps. Our calculated lowest bright exciton energies agree well with the measured optical band gaps. The low-energy excitons closely resemble the Frenkel excitons in molecular crystals, as they are highly localized in a single ${\left[{MX}_6\right]}^{2-}$ octahedron and extended in the reciprocal space. The weak dielectric screening effects and the nearly flat frontier electronic bands, which are derived from the weakly coupled ${\left[{MX}_6\right]}^{2-}$ units, together explain the significant excitonic effects. Spin-orbit coupling effects play a crucial role in redshifting the lowest bright exciton by mixing up spin-singlet and spin-triplet excitons, while exciton-phonon coupling effects have minor impacts on the calculated exciton binding energies.

Studies of Hamiltonians modeling electron-electron (e-e) and electron-phonon (e-ph) coupling have been fundamental in capturing the novel ordering seen in many quasi-one-dimensional condensed matter systems. Extending such studies to quasi-two-dimensional (2D) systems is of great current interest, as e-ph couplings are predicted to play a major role in the stabilization or enhancement of novel phases in 2D material systems. In this work, we study model systems that describe the interplay between the Hubbard coupling and the phonon modes in the Holstein and Su-Schrieffer-Heeger (SSH) Hamiltonians using the functional renormalization group. For both types of e-ph couplings, we find the predicted charge density wave phases in competition with antiferromagnetic ordering. As the system is doped, the transition shifts, with both orders showing incommensurate peaks. We compare the evolution of the quasiparticle weight for the Holstein model with that of the SSH model as the systems transition from antiferromagnetic to charge-ordered ground states. Finally, we calculate the self-energy of the phonon and capture the impact of charge ordering on the phonon modes.

Magnetoresistance, that is, the change of the resistance with the magnetic field, is usually a quadratic function of the field strength. A linear magnetoresistance usually reveals extraordinary properties of a system. In the quantum limit where only the lowest Landau band is occupied, a quantum linear magnetoresistance was believed to be the signature of the Weyl fermions with 3D linear dispersion. Here, we comparatively investigate the quantum-limit magnetoresistance of systems with different band dispersions as well as different types of impurities. We find that the magnetoresistance can also be linear for the quadratic energy dispersion. We show that both longitudinal and transverse magnetoresistance can be linear if long-range-Gaussian-type impurities dominate, but Coulomb-type impurities can only induce linear transverse magnetoresistance. Our findings well explain some of the linear magnetoresistance observed in the experiments and provide insights to the understanding of quantum-limit magnetoresistance.

We propose that a spin-dependent second-order topological insulator can be realized in a monolayer FeSe/GdClO heterostructure, in which substrate GdClO helps to stabilize and enhance the antiferromagnetic order in FeSe. The second-order topological insulator is free from spin-orbit coupling and in-plane magnetic field. We also find that two types of distinct corner modes residing in the intersections of two ferromagnetic edges and two antiferromagnetic edges exist. The underlying physics for the ferromagnetic corner mode follows a sublattice-chirality-kink picture. More interestingly, the ferromagnetic corner mode shows a spin-dependent property, which is also robust against spin-orbit coupling. Unexpectedly, the antiferromagnetic corner mode can be taken as a typical emergent and hierarchical phenomenon from an array of ferromagnetic corner modes. Remarkably, antiferromagnetic corner modes violate the general kink picture and can be understood as bound states of a one-dimensional Schrodinger equation under a connected potential well. Our findings not only provide a promising second-order topological insulator in electronic materials but also uncover some different properties of corner modes in high-order topological insulators.

Exciton binding energy and lifetime are the two most important parameters controlling exciton dynamics, and the general consensus is that the larger the former, the larger the latter. However, our first-principles study of monolayer ferroelectric ${\mathrm{TiOCl}}_2$ shows that this is not always the case. We find that ferroelectric polarization tends to weaken exciton binding but enhance exciton lifetime. This stems from the different effects of the induced built-in electric field and structural distortion by the spontaneous polarization: the former always destabilizes or even dissociates the exciton while the latter leads to a relaxation of the selection rule and activates excitons that are otherwise not optically active. Their combined effect leads to a halving of the exciton binding energy but a substantial increase in lifetime by 40 times. Our results deepen the understanding of the interaction of light with ferroelectric materials and provide new insights into the use of ferroelectricity to control exciton dynamics.

Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one- and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite $LC$ circuits. Through the method of images, we study how resonance modes in a multidimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally reduced expressions for the impedance in three dimensions and above.

Over the last decade, the spin-$1/2$ Heisenberg antiferromagnet on the square-kagome (SK) lattice has attracted growing attention as a model system of highly frustrated quantum magnetism. A further motivation for theoretical studies of this model comes from the recent discovery of SK spin-liquid compounds ${\mathrm{KCu}}_6{\mathrm{AlBiO}}_4{\left({\mathrm{SO}}_4\right)}_5\mathrm{Cl}$ [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)] and ${\mathrm{Na}}_6{\mathrm{Cu}}_7{\mathrm{BiO}}_4{\left({\mathrm{PO}}_4\right)}_4{[\mathrm{Cl},(\mathrm{OH}\left)\right]}_3$ [O. V. Yakubovich et al., Inorg. Chem. 60, 11450 (2021)]. The SK antiferromagnet exhibits two nonequivalent nearest-neighbor bonds $J_1$ and $J_2$. One may expect that in SK compounds $J_1$ and $J_2$ are of different strength. Here, we present a numerical study of finite systems of $N=30$, 36, and $N=42$ sites by means of the finite-temperature Lanczos method. We discuss the temperature dependence of the Wilson ratio $P\left(T\right)$, the specific heat $C\left(T\right)$, the entropy $S\left(T\right)$, and of the susceptibility $X\left(T\right)$ of the $J_1-J_2$ SK Heisenberg antiferromagnet varying $J_2/J_1$ in a range $0\le J_2/J_1\le 4$. We also discuss the zero-field ground state of the model. We find indications for a magnetically disordered singlet ground state for $0\le J_2/J_1\lesssim 1.65$. Beyond $J_2/J_1\sim 1.65$ the singlet ground state gives way for a ferrimagnetic ground state, which becomes a stable Lieb ferrimagnet with magnetization $M=N/6$ (UUD state) for $J_2/J_1\gtrsim 1.83$. In the region $0.77\lesssim J_2/J_1\lesssim 1.65$ the low-temperature thermodynamics is dominated by a finite singlet-triplet gap filled with low-lying singlet excitations leading to an exponentially activated low-temperature behavior of $X\left(T\right)$. On the other hand, the low-lying singlets yield an extra maximum or a shoulderlike profile below the main maximum in the $C\left(T\right)$ curve. For $J_2/J_1\lesssim 0.7$ the low-temperature thermodynamics is characterized by a large fraction of $N/3$ weakly coupled spins leading to a sizable amount of entropy at very low temperatures. In an applied magnetic field the magnetization process features plateaus and jumps in a wide range of $J_2/J_1$.

Intrinsic magnetic topological insulators categorized by bulk-boundary correspondence are of significant fundamental and technological importance in topotronics. Yet the topological phase transition with variation of the bulk-boundary correspondence remains elusive. Here, using a tight-binding model and first-principles calculations, we demonstrate that $2H\text{−}M{\mathrm{Br}}_2$ $(M=\mathrm{Ru} \text{and} \mathrm{Os})$ monolayers are intrinsic ferromagnetic (FM) second-order topological insulators (SOTIs) distinguished by the emergence of well-localized nontrivial corner states. Remarkably, with giant valley polarization, we point out the possibilities of the two-dimensional FM SOTIs for displaying a rich topological phase diagram; that is, topological phase transitions from FM SOTIs to quantum anomalous Hall insulators and then to normal insulators emerge by engineering the valleys. The obtained quantum anomalous Hall effect is characterized by a nonzero Chern number $\mathcal{C}=\pm 1$ and one chiral edge state. Our results not only uncover a general framework to tune the bulk-boundary correspondence but also motivate a technological avenue to bridge valleytronics and magnetic topology with potential applications in topotronics and valleytronics.

We investigated the electronic structure and superconducting properties of single-crystalline ${\mathrm{LaCuSb}}_2$. The resistivity, magnetization, and specific heat measurements showed that ${\mathrm{LaCuSb}}_2$ is a bulk superconductor. The observed Shubnikov–de Haas oscillation and magnetic field dependence of the Hall resistivity can be reasonably understood assuming a slightly hole-doped Fermi surface. An electron-phonon coupling calculation clarified the difference from the isostructural compound ${\mathrm{LaAgSb}}_2$, indicating that (i) low-frequency vibration modes related to the interstitial layer sandwiched between the Sb square nets significantly contribute to the superconductivity and (ii) carriers with sizable electron-phonon coupling distribute isotropically on the Fermi surface. These are assumed to be the origin of the higher superconducting transition temperature compared with ${\mathrm{LaAgSb}}_2$. We conclude that the superconducting properties of ${\mathrm{LaCuSb}}_2$ can be understood within the framework of the conventional phonon-mediated mechanism.

The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an “orthogonality column” of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (${\mathrm{iTEBD}}^2$) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.