We report a magnetic and neutron diffraction study on the ground state magnetism and field evolution of single-crystal van der Waals multiferroic ${\mathrm{CuCrP}}_2{\mathrm{S}}_6$. The ordered moments align along the $b$ axis in the “$A$-type” antiferromagnetic configuration with a spin-flop transition along the same direction. Field application along $a$ introduces a smooth transition to a fully polarized ferromagnetic state via in-plane spin rotation. These findings resolve the ambiguity of the ground state magnetization direction in ${\mathrm{CuCrP}}_2{\mathrm{S}}_6$ and uncover its field responses, providing a firm basis for future magnetoelectric study. A magnetoelastic coupling effect connecting the interlayer spacing and the magnetic order was further revealed, highlighting the out-of-plane strain as an effective control knob for tuning magnetism both in this system and in related van der Waals magnets.

We report a quantitative calorimetric study of ${\mathrm{UTe}}_2$ under pressure with a direct measurement of the Sommerfeld $\gamma$ coefficient, showing a threefold enhancement of electronic effective mass when approaching the critical pressure where superconductivity is suppressed and ordered states occur. We analyze the evolution of $\gamma$ with the amplitude of the jumps in the specific heat at the two superconducting transitions, and the superconducting critical temperature with pressure. This analysis would suggest that the high pressure superconducting phase nucleates only on a fraction of the Fermi surface. It also points to the possible major role of a quantum critical point of the unidentified phase that has been called weak magnetic order, rather than to the critical pressure of the antiferromagnetic phase. Just at the border of long-range antiferromagnetic order, where superconductivity emerges from the weak magnetic order phase, a significant increase in the specific heat jump for both superconducting transitions is found, accompanied by a noticeable change of their shapes.

The discovery of fractional quantum anomalous Hall (FQAH) states in two-dimensional heterostructures has opened the door to realizing phases of dispersing anyons. Here, we develop an analytically controlled theory of anyon dispersion in FQAH states realized in ideal or Aharonov-Casher (AC) bands by projecting interactions onto the space of Laughlin quasiholes. Constructing quasihole momentum eigenstates allows efficient evaluation of the single-quasihole dispersion using Monte Carlo. We find that the quasihole bandwidth grows with increasing quantum-geometry inhomogeneity of the AC band and with increasing interaction screening length. For realistic parameters relevant to the bands of twisted $\mathrm{MoTe}{}_2$, the quasihole bandwidth is of order 1 meV and increases with increasing displacement field, suggesting that itinerant-anyon physics may play an important role in sufficiently clean samples. Furthermore, we develop a microscopic Lagrangian framework in terms of a quasihole guiding-center coordinate, which reproduces the momentum-space formula for the dispersion. This approach reveals that quasihole dispersion originates from the combined effects of an interaction-generated periodic potential, arising from nonuniform quantum geometry of the single-particle bands, and the quasihole many-body Berry phase arising from the background magnetic field. The latter endows the guiding-center coordinate with a noncommutative structure, converting the periodic potential into a finite dispersion. Finally, we outline how this framework generalizes to multiple quasiholes, enabling a microscopic theory of charged excitations in FQAH systems that retains only the anyon degrees of freedom.

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet ${\mathrm{CeRh}}_6{\mathrm{Ge}}_4$ has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the $4f$ electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the $4f$ shell in ${\mathrm{CeRh}}_6{\mathrm{Ge}}_4$ using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce $4f$ with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the noncrossing approximation. The Kondo effect mixes higher-lying crystal-field states into a resulting multiorbital ground state with $4f$ occupancy, $n_f\sim 0.9$. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in ${\mathrm{CeRh}}_6{\mathrm{Ge}}_4$.

By laser pump-probe time-resolved coherent magnetic x-ray diffraction imaging, we have measured the migration velocity of antiferromagnetic domain walls in the Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ at 100 K. Coherent diffraction patterns, recorded at the 106 pure-magnetic Bragg peak, showed fringes, which responded distinctly to the excitation laser. These patterns could not be inverted with current phasing algorithms, but could be modeled as four domains with phase shifts consistent with the antiferromagnetic structure. During the laser-induced demagnetization, we observed these domains and their domain walls moving at $3\times {10}^6\mathrm{m}/\mathrm{s}$, significantly faster than acoustic velocities. This is understood to arise from a purely electronic spin contribution to the magnetic structure without any role for coupling to the crystal lattice.

Following recent intensive studies on altermagnetism (ALM) characterized by nonrelativistic even-parity spin splitting, realizing unconventional odd-parity magnetism has also attracted increasing interest. Here, using symmetry arguments based on spin-group analyses, we elucidate necessary conditions for the emergence of odd-parity spin splitting in collinear antiferromagnetic systems, which is further established as the standard odd-parity ALM. It is derived that the odd-parity ALM arises from the following criteria: (i) the breaking nonmagnetic time reversal symmetry (TRS), i.e., the breaking real-space TRS; (ii) the long-range collinear compensated magnetism; (iii) the symmetry $\left[C_2\right|\left|\overline{E}\right]$ or $\left[C_2\right|\left|M\right]$ connecting opposite-spin sublattices, where $C_2, \overline{E}$, and $M$, respectively, represent a ${180}^{\circ }$ rotation around the axis perpendicular to spins, the inversion, and the mirror reflection separating opposite-spin sublattices, directly reflecting the high-order harmonic ($l\ge 3$) and the $p$-wave ($l=1$) odd-parity ALM, respectively. Moreover, we utilize the well-known Haldane-Hubbard model to identify odd-parity spin splitting in the collinear ALM ground state, where (i) the nonmagnetic TRS is broken by opposite sublattice currents coming from the Haldane hopping; (ii) the symmetry $\left[C_2\right|\left|\overline{E}\right]$ is ensured because the currents flowing on opposite-spin sublattices are reversed.

Band flattening has been identified as a key ingredient to correlation phenomena in Moiré materials and beyond. Here, we examine strongly repulsive fermions on a ladder—a minimal platform for unconventional $d$-wave pairing—and show that flattening of the lower band through an additional diagonal hopping term produces non-Fermi-liquid behavior, evidenced by the violation of Luttinger's theorem, as well as axial $d$-wave pairing correlations. Alternatively, a plaquette ring exchange can also generate pairing, albeit with a distinct diagonal $d$-wave pairing symmetry. Hence, our finding showcases a competition of different unconventional pairing channels, and demonstrates via a simple model how band geometry can induce fermionic pairing. This offers broadly relevant insights for correlated flat-band systems, ranging from ultracold atoms to strongly interacting electrons in solids.

We report a strong coupling between a Love surface acoustic wave (SAW) and a spin wave in epitaxial FeRh as analyzed from their anticrossing dispersion relationships obtained by Brillouin light scattering. Reproducing the results using a numerical model that solves the coupled Landau-Lifshitz and Christoffel equations reveals that this effect stems from both the large magnetoelastic coupling coefficient in this material, $|B_2|$ = $17\mathrm{MJ}{\mathrm{m}}^{-3}$, and the strength of the Love-wave magnetoacoustic effective field when the magnetization vector $\mathbf{M}$ is parallel to the SAW wave vector $\mathbf{k}$. We also observe a substantial, albeit weaker, coupling in the unusual configuration of the Sezawa surface wave crossing the pseudo Damon-Eshbach mode, i.e., when the angle between M and k is $\pi /4$. These findings identify the optimal acoustic modes and magnetic geometries for achieving strong phonon–magnon hybridization, paving the way for coherent information transfer via elastic waves in magnetoacoustic nanodevices.

The magnetic properties and crystal electric field (CEF) scheme of ${\mathrm{BiErGeO}}_5$ are investigated via magnetization, heat capacity, inelastic neutron scattering (INS) and muon spin relaxation ($\mu \mathrm{SR}$) experiments on a polycrystalline sample. The ${\mathrm{Er}}^{3+}$ ions form a quasi-two-dimensional distorted honeycomb network with a Kramers doublet ground state. Magnetic susceptibility and heat capacity reveal short-range antiferromagnetic correlations, manifested as a broad maximum around 1.4 K and 1.1 K, respectively. Heat-capacity data further confirm the onset of a magnetic long-range order at $T_{\mathrm{N}}\simeq 0.4\mathrm{K}$. The INS spectra exhibit eight CEF excitations, and the CEF analysis yields the $g$-factor anisotropy with $g_{xy}/g_z\simeq 1.38$ and exchange anisotropy with ${\mathcal{J}}_{xy}\simeq 2.96\mathrm{K}$ and ${\mathcal{J}}_z\simeq 1.56\mathrm{K}$. The experimental temperature and field-dependent magnetization and heat capacity are also reproduced by the simulation using the CEF energy scheme. Zero-field $\mu \mathrm{SR}$ measurements down to 30 mK do not exhibit coherent oscillations or a static $1/3$ tail. The spectra are well described by two exponential relaxation components, indicating two magnetically inequivalent muon environments. The relaxation rates display a nearly temperature-independent plateau below $T_{\mathrm{N}}$ and follow an Orbach-type activated behavior at higher temperatures involving excited CEF levels, consistent with the INS results. Longitudinal-field $\mu \mathrm{SR}$ measurements reveal only weak decoupling up to 1.5 T, indicating the presence of slow spin fluctuations that persist well below $T_{\mathrm{N}}$. Overall, ${\mathrm{BiErGeO}}_5$ emerges as an anisotropic spin-orbit-coupled honeycomb magnet in which strong CEF-driven anisotropy and reduced dimensionality give rise to unconventional low-temperature magnetic behavior distinct from its Yb counterpart ${\mathrm{BiYbGeO}}_5$.

Since the prediction of a time-reversal symmetry breaking (TRSB) $d+i{d}^{\prime }$ state in twisted bilayer cuprate superconductors by Can et al. [Nat. Phys. 17, 519 (2021)], several experiments have attempted to detect this state, yielding conflicting results. At present, it is not clear which differences in samples or experimental conditions might explain these discrepancies. In this work, we perform a tight-binding lattice model calculation with phenomenological interlayer tunneling, examining the order parameter as a function of twist angle, interlayer tunneling, doping, and temperature. We observe the TRSB state to be correlated to the position of the Van Hove singularity in the normal state, which changes not only as a function of doping but also the tunneling strength. Two such phases are identified as nominally consistent with in-plane $d+i{d}^{\prime }$ and $d+is$ order, but with unexpected transformation properties under bilayer symmetry operations. We calculate the Josephson critical current, in particular examining the angle dependence for various tunneling strengths. Finally, we discuss the existing experiments in the context of our results.

Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic potential does not consider the possibility of soft modes, such as those due to an effective quartic potential. In this work, we show that such quartic potentials arise under very general conditions in a broad class of isotropic spin systems without a fine-tuning of the interaction parameters. Considering models with spin-spiral ground states in two and three spatial dimensions, we numerically demonstrate that quartic amplitude spin oscillations produce a fluctuation-induced spin-wave gap which grows with temperature according to a characteristic power-law. In conjunction with a phenomenological theory, the present work provides a general theoretical framework for describing soft spin modes. This framework generalizes earlier treatments of soft-spin dynamics and gap generation in order-by-disorder systems arising from accidental classical ground-state degeneracies, and highlights the important role of finite-size effects relevant to numerical studies. Our predictions of a temperature-dependent gap in spiral spin systems could be tested in inelastic neutron scattering experiments, providing direct spectroscopic evidence for thermal effects arising from soft spin modes in magnetic materials.

We introduce $\mathrm{\Sigma }$-Attention, a transformer-based operator-learning framework for approximating the self-energy operator of strongly correlated electronic systems. By creating a batched dataset that combines results from three complementary approaches, i.e., many-body perturbation theory, strong-coupling expansion, and exact diagonalization, each effective in specific parameter regimes, $\mathrm{\Sigma }$-Attention is applied to learn an accurate approximation for the self-energy operator that is valid across a wide range of parameter regimes. This hybrid strategy leverages the strengths of existing methods while relying on the transformer's ability to generalize beyond individual limitations. More importantly, the scalability of the transformer architecture allows the learned self-energy to be extended to systems with larger sizes, leading to much improved computational scaling. Using the one-dimensional Hubbard model, we demonstrate that $\mathrm{\Sigma }$-Attention can accurately predict the Matsubara Green's function of large systems with a wide range of coupling strength. Our framework offers a promising and scalable pathway for studying strongly correlated systems with many possible generalizations.

The Gilbert damping of magnetic materials is an important magnetic parameter that determines the switching speed and energy dissipation of spintronic devices. In simple metals, the intrinsic Gilbert damping increases with temperature and diverges near the Curie temperature as a result of spin fluctuations. Here we present atomistic simulations and experimental measurements showing surprising and opposite behavior in Py/Nd bilayers, where the Gilbert damping decreases with increasing temperature. The effect arises because of the enhanced damping at the interface as a result of spin pumping, where elevated temperatures cause a dynamic separation of the interfacial and bulk magnetization during relaxation. Furthermore, the temperature dependence of the damping can be controlled by varying the thickness of the Nd capping layer. Our findings present a spintronic effect that can be used to modify the dynamic properties of nanoscale materials and devices for enhanced energy efficiency or with improved switching dynamics.

Spintronic, spin caloritronic, and magnonic phenomena arise from complex interactions between charge, spin, and structural degrees of freedom that are challenging to model and even more difficult to predict. This situation is compounded by the relative scarcity of magnetically ordered materials with relevant functionality, leaving the field strongly constrained to work with a handful of well-studied systems that do not encompass the full phase space of phenomenology predicted by fundamental theory. Here we present an important advance in this coupled theory-experiment challenge, wherein we extend existing theories of the spin Seebeck effect (SSE) to explicitly include the temperature-dependence of magnon nonconserving processes. This expanded theory quantitatively describes the low-temperature behavior of SSE signals previously measured in the mainstay material yttrium iron garnet (YIG) and predicts another regime for magnonic and spintronic materials that have low saturation magnetization, $M_S$, and ultralow damping. Finally, we validate this prediction by directly observing the spin Seebeck resistance in the molecule-based ferrimagnetic semiconductor vanadium tetracyanoethylene $(\mathrm{V}{\left[\mathrm{TCNE}\right]}_x, x\sim 2)$. Our results yield spin Seebeck resistance signals comparable in magnitude to YIG, identify magnon diffusion lengths $({\lambda }_m>1\mu \mathrm{m})$ and determine magnon lifetimes for $\mathrm{V}{\left[\mathrm{TCNE}\right]}_x$ $({\tau }_{\mathrm{th}}\approx 1-10\mu \mathrm{s})$ that exceed those of YIG $({\tau }_{\mathrm{th}}\sim 10\mathrm{ns})$. Surprisingly, these properties persist to room temperature despite relatively low spin wave stiffness (exchange). This identification of another regime for highly efficient SSE-active materials opens the door to another class of magnetic materials for spintronic and magnonic applications.

The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory successfully explains the melting mechanism of two-dimensional isotropic lattices as a two-step process driven by the unbinding of topological defects. By considering the elastic theory of the square lattice, we extend the KTHNY theory to melting of square-lattice solids. In addition to the familiar elastic constants that govern the theory—the Young's modulus and the Poisson ratio—a third constant controlling the anisotropy of the medium emerges. This modifies both the logarithmic and angular interactions between the topological defects. Despite this modification, the extended theory retains the qualitative features of the isotropic case, predicting a two-step melting with an intermediate tetratic phase. However, some subtle differences arise, including a modified bound on the translational correlation exponent and the absence of universal values for the Young's modulus at the solid-to-tetratic phase transition.

We investigate the effect of interparticle interactions on the quantized Thouless pump in the bosonic quasiperiodic Aubry–André model and find that the quantization of the pumped charge breaks down already for weak interactions. Furthermore, the pumped charge undergoes sharp changes as a function of interaction strength that we can attribute to the closing of specific doublon channels. As expected, the quantization revives in the hard-core limit at very large interaction strengths where the bosons are subject to a hard-core constraint. Interestingly, the stability of isolated doublons under the pump depends on the band they are in. For repulsive interactions and a suitably fixed pump period, doublons in the lowest band are pumped stably while doublons in higher bands dissociate during the pump with one particle decaying into a lower band. This asymmetry leads to the decay of the total energy over time, in stark contrast to the typical Floquet heating expected for a driven many-body system.

In the past two decades, enormous efforts have been made to search for possible platforms and schemes to implement topological quantum computation (TQC). In exploring the Fu-Kane scheme of TQC based on Josephson trijunctions constructed on topological insulators, the predicted Majorana phase diagram of an individual trijunction has already been verified experimentally. If Majorana zero modes indeed exist in this kind of trijunction, coupling between them in multiple trijunction devices should be further expected. In this study, we fabricated Josephson devices containing two adjacent Josephson trijunctions on the surface of $\mathrm{Sn}\text{−}{\left(\mathrm{Bi},\mathrm{Sb}\right)}_2{\left(\mathrm{Te},\mathrm{S}\right)}_3$ and observed a possible signature of the coupling effect manifesting as the reopening of a minigap in both trijunctions where a closure would otherwise be expected if the trijunctions existed individually. While alternative interpretations cannot be fully ruled out, our findings provide experimental support for the validity of the Fu-Kane theory and provide further motivation for advancing the TQC scheme proposed by Fu and Kane.

We present a systematic construction of non-Hermitian tight-binding lattices whose Bloch spectra are $n\mathrm{th}$ roots of those of Hermitian parent two-dimensional lattices, namely, graphene and the Lieb lattice. The $n$ roots of these models are constructed from connecting loop modules of unidirectional couplings whose geometrical arrangements match those of the corresponding parent system. Their energy spectrum is shown to consist of $n$-rotated and equivalent branches in the complex energy plane, each matching the real spectrum of the parent model when raised to the $n\mathrm{th}$ power, together with extra zero-energy flat bands accounted for by the generalized index theorem. We show how the low-energy Dirac cones of the parent models translate, for an appropriate choice of phase configuration for the couplings of the $n$-root lattices, as what we call an “exceptional horn” appearing at each branch, with the central Dirac point converted into zero-energy exceptional points (EPs) of order $n$ or higher at high-symmetry momenta. These exceptional horns reflect the behavior of low-lying excitations that scale with momentum as $E\sim {\left|\mathbf{q}\right|}^{\frac{1}{n}}$, with $n\ge 3$, as opposed to the linear massless modes that characterize a Dirac cone. Moreover, we derive analytic expressions for the associated Landau levels (LLs), whose energies scale with magnetic flux as $E\sim {\varphi }^{\frac{1}{2n}}$. For the case of the $n$-root Lieb lattice, the zeroth LL is shown to be exceptional. These results are analytically derived for both $n$-root models and numerically demonstrated for certain values of $n$. Finally, we propose a realistic photonic implementation based on coupled ring resonators with a split configuration of optical gain and loss. This distribution yields strongly asymmetric couplings nearing unidirectionality, and appropriate positioning of the rings allows for fine tuning of the coupling phases. We also discuss the impact of experimental imperfections on the EP signatures, modeling them through tight-binding simulations.

We present a comprehensive experimental investigation of the temperature evolution of magnetic states in triangular-lattice delafossite ${\mathrm{YbCuSe}}_2$. Magnetization measurements on high-quality single crystals reveal easy-plane anisotropy. Specific heat, magnetization, and muon spin relaxation ($\mu \mathrm{SR}$) establish the absence of magnetic order or spin freezing down to 0.03 K ($\le J_{\mathrm{avg}}/250$), demonstrating a dynamically fluctuating quantum spin liquid (QSL) ground state. Thermodynamic measurements uncover multiple characteristic energy scales at $T_H\approx 4.5\mathrm{K}, T_L\approx 1.8\mathrm{K}$, and $T^{*}\approx 0.7\mathrm{K}$. Below $T^{*}, \mu \mathrm{SR}$ detects a dynamical phase separation in which the majority of the spins are forming a QSL state whereas the remaining spins form a sporadic, disorder-induced state decoupled from the dominant QSL component. Remarkably, the unconventional temperature dependence of the $\mu \mathrm{SR}$ relaxation rate indicates roton-like excitations emerging between $T_H$ and $T_L$, a feature not previously observed in any QSL system, preceding the stabilization of the low-temperature QSL at 0.3 K. These findings identify ${\mathrm{YbCuSe}}_2$ as a unique QSL platform, providing valuable insights for further experimental and theoretical exploration.

In twisted bilayer graphene, a unified understanding of the mechanisms governing temperature-dependent electronic spectra and thermodynamic properties remains controversial despite extensive theoretical efforts. Here, we present a comprehensive theoretical framework that quantitatively accounts for scanning tunneling spectroscopy, quantum twisting microscopy, and thermodynamic properties of magic angle twisted bilayer graphene. We demonstrate that the observed behavior arises from the interplay between electron correlations and external symmetry breaking induced by strain and lattice relaxation. These effects act cooperatively to shape the emergent electronic behavior, leaving characteristic signatures across spectroscopy, compressibility, and entropy.