The dispersion of topological surface states in three-dimensional topological insulators (TIs) is commonly attributed to the atomic spin-orbit coupling (SOC) of the constituent elements. Whether the observable surface-state dispersion reflects this bare atomic value, or instead an effective SOC renormalized by surface–bulk hybridization, remains an open question. Here, we investigate this issue for the occupied and unoccupied surface-state dispersion in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ by combining angle-resolved photoemission (ARPES) and time-resolved (tr-ARPES) at a fixed 1 ps delay time with ab initio one-step photoemission calculations. Comparison between experimental and calculated spectra indicates that the SOC governing the surface-state dispersion deviates from the atomic expectation, with this effect more clearly resolved in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ than in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The calculations, which explicitly include hybridization between topological surface states and bulk-derived surface resonance states, provide a microscopic framework for this behavior. These results indicate that the spin-orbit interaction governing topological surface states is effectively shaped by surface–bulk hybridization and can vary significantly across materials.

We study two-dimensional fermionic systems, displaying quadratic band touching in the normal state, in the presence of vortices and skyrmions of insulating and superconducting masses in the ordered phase. A prototypical example of such systems is the Bernal bilayer graphene that supports eight zero-energy modes in the presence of a mass vortex with the requisite U(1) symmetry. Near the vortex core, additional ten masses that close an SO(5) algebra can develop local expectation values by splitting the manifold of zero modes in five and ten different ways by lifting its SO(4) and SU(2) chiral symmetries, respectively. In particular, each SU(2) chiral symmetry can be broken by three distinct copies of chiral-triplet mass orders, giving rise to the notion of the color degeneracy among the competing orders near the vortex core. By contrast, a skyrmion of three anticommuting masses supports additional six masses in its core, and possesses an SU(2) isospin quantum number, aside from the usual generalized U(1) charge. Consequently, charge $4e$ Kekulé pair density waves can develop in the skyrmion core of Néel layer antiferromagnet, while a skyrmion of quantum spin Hall insulator in addition supports an $s$-wave pairing. We also analyze the internal algebra of competing orders in the core of these defects on checkerboard or kagome lattice that supports only a single copy of quadratic band touching in the normal state.

We investigate the stability of topological phases in Kitaev-Heisenberg ladders under local charge fluctuations by studying the competition with itinerant electrons in a Hubbard model on a honeycomb ribbon geometry. We analyze the evolution of string order parameters, spin correlations, and charge fluctuations as functions of hopping amplitude and interaction strength in a half-filled band. Our results from density matrix renormalization group calculations show that increasing electron bandwidth progressively suppresses the topological phases, shifting and narrowing their stability regions in the phase diagram. We identify the critical values of hopping where string order vanishes and characterize the interplay between magnetic order and charge fluctuations. These findings provide insight into the robustness of topological phases against doping and charge dynamics, with implications for candidate Kitaev materials and engineered quantum systems.

Anisotropic intersite exchange interactions in frustrated rare-earth magnets are difficult to assess both theoretically and experimentally. Here, we propose an ab initio force-theorem framework combining the quasiatomic Hubbard-I approach to $4f$ correlations with a static mean-field treatment of the on-site intershell Coulomb interaction between rare-earth $4f$ and $5d$ states to simultaneously capture both $4f$ superexchange and $5d$-mediated indirect exchange. Applying it to the triangular lattice Ce delafossites ${\mathrm{CsCeSe}}_2, {\mathrm{KCeS}}_2$, and ${\mathrm{RbCeO}}_2$, we find that the indirect exchange dominates in the selenide, the superexchange in the oxide, while both mechanisms contribute almost equally in the sulfide. The magnetic exciation spectra of ${\mathrm{CsCeSe}}_2$ and ${\mathrm{KCeS}}_2$ evaluated from the calculated spin Hamiltonains are in good qualitative and quantitative agreement with experimental data.

The mechanical properties of a solid, which relate its deformation to external applied forces, are key factors in enabling or disabling the use of an otherwise optimal material in any application, strongly influencing also its service lifetime. Intrinsic crystal deformation mechanisms, investigated experimentally on single crystals with low dislocation densities, have been studied theoretically through atomistic simulations, mainly focusing on lattice-induced instabilities. Here, instead, we employ density functional theory and a thermodynamic analysis to probe and analyze the way in which the electronic charge of crystalline solids (Cu, Al and diamond) respond to uniaxial strain and affects their mechanical properties. Indeed, despite the very simple nature of our models, and in the presence of minimal atomic displacements, we find that the stress strain curves of Cu and Al deviate from a simple linear elastic behavior. Within a thermodynamics perspective, the features of such curves can be interpreted in terms of first- and second-order phase transitions, which originate from Van Hove singularities of the electronic density of states crossing the Fermi level and electron redistribution within the solid.

The past decade has witnessed a spectacular development of machine-learned interatomic potentials (MLIPs), to the extent that they are already the approach of choice for most atomistic simulation studies not requiring an explicit treatment of electrons. Typical MLIP usage guidelines emphasize the need for exhaustive training sets and warn against applying the models to situations not considered in the corresponding training space. This restricts the scope of MLIPs to interpolative calculations, essentially denying the possibility of using them to discover new phenomena in a serendipitous way. While there are reasons to be cautious, here we adopt a more sanguine view and challenge the predictive power of two representative and widely available MLIP approaches. We work with minimalist training sets that rely on little prior knowledge of the investigated materials. We show that the resulting models—for which we adopt modest/default choices of the defining hyperparameters—are very successful in predicting nontrivial structural effects (competing polymorphs, energy barriers for structural transformations, occurrence of nontrivial topologies) in a way that is qualitatively and quasiquantitatively correct. Our results thus suggest an expanded scope of modern MLIP approaches, evidencing that somewhat trivial—and easy to compute—models can be an effective tool for the discovery of complex physical phenomena.

Herein, we report spectroscopic, electronic, and magnetic investigation of the mixed-cation pyrochlores $\mathrm{C}{\mathrm{a}}_3{R}_3\mathrm{T}{\mathrm{a}}_2\mathrm{T}{\mathrm{i}}_7{\mathrm{O}}_{26.5}$ ($R={\mathrm{Dy}}^{3+}, {\mathrm{Nd}}^{3+}$), elucidating key signatures of A- and B-site cation disorder and oxygen nonstoichiometry. Structural characterization, Raman and infrared spectroscopy, complemented by lattice dynamical analysis, reveal disorder-induced distortions of the pyrochlore lattice and relaxation of the vibrational selection rules. The ab initio density-functional theory computations using LDA+$U$ and LDA−1/2 approaches reproduce experimentally observed wide optical band gaps (≈3 eV), highlighting the sensitivity of the electronic states near band edges to oxygen rearrangements and cation mixing. Crystal-field (CF) calculations employing the exchange charge model reproduce UV-visible and photoluminescence spectra, yielding reliable CF energy levels and wavefunctions for $R^{3+}$ ions. $\mathrm{D}{\mathrm{y}}^{3+}$ ions in $\mathrm{C}{\mathrm{a}}_3\mathrm{D}{\mathrm{y}}_3\mathrm{T}{\mathrm{a}}_2\mathrm{T}{\mathrm{i}}_7{\mathrm{O}}_{26.5}$ retain a well-isolated $〈111〉$ Ising-like Kramers doublet with large magnetic moment. The dc and ac magnetic susceptibility measurements reveal absence of long-range spin-ice freezing, with only slow spin dynamics and short-range correlations persisting arising from disorder-induced disruption of exchange interactions. $\mathrm{N}{\mathrm{d}}^{3+}$ ions in $\mathrm{C}{\mathrm{a}}_3\mathrm{N}{\mathrm{d}}_3\mathrm{T}{\mathrm{a}}_2\mathrm{T}{\mathrm{i}}_7{\mathrm{O}}_{26.5}$ exhibit pronounced CF-induced $J$ mixing, reduced Ising anisotropy, and dominant antiferromagnetic interactions, leading to short-range ‘‘all-in, all-out’’ correlations that are enhanced under applied magnetic fields. Mean-field modeling incorporating CF effects, anisotropic exchange, and long-range dipolar interactions quantitatively accounts for the magnetic response of both compounds. Electrical resistivity measurements on Nd-based compound reveal thermally activated hopping transport, consistent with a wide-gap insulating state and disorder-induced electronic localization. Our results establish chemical disorder as an effective tuning factor controlling the spectroscopic, electronic, magnetic, and transport properties of rare-earth pyrochlores and provide a robust platform for exploring emergent phenomena in frustrated materials.

Coherent two-state oscillations are observed in numerical simulations of the one-dimensional transverse-longitudinal-field Ising model within false-vacuum decay regimes. Starting from the false vacuum (a nearly fully polarized ferromagnetic state), we show that in moderate-size systems, at resonances $h\approx 2J/n$ (with longitudinal field $h$, transverse field $J$, and an integer $n$), the expected decay can give way to coherent oscillations between the false vacuum and a symmetric resonant state. The oscillation frequency, i.e., the tunneling splitting, is notably observed to exhibit a $\sqrt{L}$ collective enhancement, as confirmed by a Schrieffer-Wolff analysis. In large chains, coherence remains for $n\gtrsim L/2$ due to bubble-size blockade and is robust against stronger transverse fields; for small $n$, long-range interactions can stabilize the oscillations by lifting multibubble degeneracies, establishing a robust many-body coherence mechanism beyond perturbative and finite-size limits.

Faithfully simulating the dynamics of open quantum systems requires efficiently addressing the challenge of an infinite Hilbert space. Inspired by the shifted boson operator technique used in ground-state studies of the spin-boson model (SBM), we develop an algorithm that integrates a shifted optimized boson basis with the time-evolving block decimation method. We validate our approach by accurately reproducing the polarization dynamics of the sub-Ohmic SBM at a significantly reduced computational cost. For the Ohmic SBM, we demonstrate that the time-evolved final state converges precisely to the variational prediction at both zero and finite temperatures. Furthermore, our method confirms the aperiodic pseudocoherent phase in the super-Ohmic SBM with an initially polarized bath. This work establishes an efficient and powerful approach for simulating the real-time dynamics of open quantum systems.

We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behavior at finite size, we conjecture that in the large-$n$ limit, the ratios between consecutive Lanczos coefficients should have specific scalings with the size of the lattice that we make precise and that depend on the hydrodynamic tail of the autocorrelation function. The scaling associated with strong or approximate zero modes is also discussed. We support our conjecture with a numerical study of different models.

We perform time-resolved magneto-optical Kerr effect measurements and record the magnetization dynamics for external magnetic fields along various symmetry axes of the chiral magnet MnSi. The different orientations of the magnetic field result in very different magnetization dynamics. For magnetic fields along the $a\text{−}b$ plane, we observe rapid oscillations assigned to magnon modes. These oscillations are detected for various external magnetic fields and are well reproduced by our theoretical spin-wave calculations. When applying magnetic fields at ${45}^{\circ }$ with respect to the $a\text{−}b$ plane and along the $c$ axis, changes in the net magnetization are instead observed. In the absence of external magnetic fields, the net magnetization is zero, and light-induced magnetization is observed. First-principles calculations identify the inverse Faraday effect as the mechanism leading to the observed light-induced magnetization. When sufficiently strong external magnetic fields are applied off the $a\text{−}b$ plane, the MnSi crystal is brought into a ferromagnetic phase, where the laser pulse's demagnetizing effect is observed. This observation suggests that by changing the strength or orientation of the external magnetic field the MnSi crystal can be magnetized or demagnetized using a laser pulse.

Using density functional theory, we revisit the magnetic properties of a recently proposed family of noncentrosymmetric two-dimensional magnetic materials, chromium chalcohalide monolayers, $\mathrm{Cr}XY$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$; $Y=\mathrm{Cl},\mathrm{Br},\mathrm{I}$). These systems consist of three atomic planes stacked in the $X$–Cr–$Y$ sequence, which breaks inversion symmetry, giving rise to their designation as Janus monolayers. We consider both $1T$ and $1H$ structural polymorphs of $\mathrm{Cr}XY$, beginning with an assessment of their dynamical stability via phonon spectra calculations. All systems, except for the $1H\text{−}\mathrm{CrTe}Y$ variants, are found to be dynamically stable. Among the two polymorphs, the $1T$ phase is consistently more favorable, with energy gains exceeding 0.55 eV per formula unit. Our total-energy calculations reveal that all dynamically stable $\mathrm{Cr}XY$ monolayers exhibit ferromagnetic coupling. However, robust out-of-plane magnetic anisotropy is observed only in the CrSI and CrSeI compositions for both $1T$ and $1H$ structures. The perpendicular magnetic anisotropy results from a constructive interplay between single-ion and anisotropic exchange contributions that overcome the dipole–dipole interaction. We further quantify the Dzyaloshinskii-Moriya interaction (DMI) in CrSI and CrSeI for both polymorphs and reveal a weak-to-moderate DMI strength as compared to the isotropic exchange interaction term. Finally, for systems exhibiting ferromagnetic coupling and perpendicular magnetic anisotropy, the exchange and anisotropy parameters derived from density functional theory calculations are employed as inputs for large-scale atomistic spin dynamics simulations to probe the temperature evolution of real-space magnetic structures. The calculated Curie temperatures are at least 210 K for $1T\text{−}\mathrm{CrSI}$, 235–260 K for $1H\text{−}\mathrm{CrSeI}$, and 370–410 K for $1H\text{−}\mathrm{CrSI}$. In contrast, the sizable DMI in $1T\text{−}\mathrm{CrSeI}$ results in a wormlike domain ground state at zero external field and enables the stabilization of skyrmions under a perpendicular magnetic field. We then discuss and illustrate how $\mathrm{Cr}XY$ monolayers can be used to tune the Bychkov-Rashba split surface state of BiTeI or to enhance magnetism of thin films of the intrinsic antiferromagnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

Artificial spin-vortex ice (ASVI) is a reconfigurable nanomagnetic metamaterial consisting of magnetic nanoislands tailored to support both Ising macrospin and vortex textures. ASVI has recently shown functional applications including reconfigurable magnonics and neuromorphic computing, where the introduction of vortex textures broadens functionality beyond conventional artificial spin ice, which only supports macrospin states. However, local control of writing vortex states in ASVI remains an open challenge. Here, we demonstrate techniques for field-free local magnetic vortex writing. We expand ASVI to support metastable macrospin, single-vortex, and double-vortex states. All-optical writing via focused laser illumination can write double-vortex textures, and surface-probe writing using an MFM tip can write single-vortex states. We leverage this writing to tailor and explore the reconfigurable energy landscape of ASVI, demonstrating programmable local seeding of avalanche-like reversal events. The writing techniques reported here expand the suite of nanomagnetic control techniques, with a host of future applications including fundamental studies of avalanche dynamics, physical memory, and direct writing of nanomagnetic ‘‘weights’’ in physical neuromorphic neural networks.

We report a comprehensive NMR study of the chiral square-cupola antiferromagnet $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ and compare its microscopic hyperfine and local-field parameters with the Ba/Sr analogs in the $A\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ family. Above $T_{\mathrm{N}}\simeq 6.7\mathrm{K}$, the ${}^{31}\mathrm{P}$ Knight shift tracks the bulk susceptibility and yields nearly isotropic transferred hyperfine couplings $H_{\mathrm{hf}}^{\left[010\right]}=6.77\left(3\right)$ and $H_{\mathrm{hf}}^{\left[001\right]}=6.19\left(3\right)$ kOe/${\mu }_{\mathrm{B}}$. Below $T_{\mathrm{N}}$, the frequency-swept ${}^{31}\mathrm{P}$ spectrum splits into three lines, in contrast to the four-line pattern reported for BaTCPO. The line separation tracks the onset of the static ${}^{31}\mathrm{P}$ internal field with a power-law exponent $\beta \simeq 0.23$, consistent with quasi-two-dimensional criticality. Crystal-rotation ${}^{31}\mathrm{P}$ NMR in the ordered state resolves all eight symmetry-related P sites and their site-dependent anisotropy. In the ordered state, zero-field ${}^{63,65}\mathrm{Cu}$ NMR gives a Cu-site internal field $B_{\mathrm{int}}=14.50\left(6\right)\mathrm{T}$ and a quadrupole frequency ${\nu }_Q=32.72\left(5\right)\mathrm{MHz}$, while point-charge electric-field-gradient calculations including Sternheimer corrections yield an on-site Cu hole occupancy $n_d=0.20\left(4\right)$, consistent with a ligand-hole–dominated charge-transfer character. Comparing PbTCPO with BaTCPO and SrTCPO, we find that the transferred hyperfine coupling $H_{\mathrm{hf}}$ varies across the series, reflecting changes in local Cu-O-P covalency, whereas the ordered-state ${}^{31}\mathrm{P}$ internal field in PbTCPO is 69.5 mT, considerably higher than in BaTCPO (35.6 mT) and SrTCPO (34.6 mT). This enhancement is not captured by dipolar terms alone and points to the combined effects of transferred contributions and stacking-dependent cancellation.

Rare earth-transition metal compounds $R{\mathrm{Mn}}_2{\mathrm{Ge}}_2$ ($R$=rare earth element) exhibit rich magnetic structures and intriguing physical phenomena, which have attracted sustained research interest. Different from the reported family members with light $R$ elements exhibiting noncoplanar magnetic structures, ${\mathrm{GdMn}}_2{\mathrm{Ge}}_2$ and ${\mathrm{TbMn}}_2{\mathrm{Ge}}_2$ exhibit collinear magnetic structures. In this work, single crystals of ${\mathrm{GdMn}}_2{\mathrm{Ge}}_2$ and ${\mathrm{TbMn}}_2{\mathrm{Ge}}_2$ are synthesized and their electrical transport properties are systematically investigated for the first time. Both compounds undergo two magnetic transitions, from paramagnetic (PM) to antiferromagnetic (AFM) and subsequently to ferrimagnetic (FiM), and exhibit uniaxial anisotropy. The magnetoresistance (MR) also manifests three distinct features: low-temperature positive MR, butterfly-shaped low-field MR, and high-field negative MR. A distinct anomalous Hall signal emerges below the Curie temperature, with anomalous Hall conductivity (AHC) reaching 262 ${\mathrm{\Omega }}^{-1}{\text{cm}}^{-1}$ for ${\mathrm{GdMn}}_2{\mathrm{Ge}}_2$ and 177 ${\mathrm{\Omega }}^{-1}{\text{cm}}^{-1}$ for ${\mathrm{TbMn}}_2{\mathrm{Ge}}_2$. Scaling analysis within the TYJ model indicates the intrinsic Berry curvature is the dominant mechanism. Our findings provide important insights into the intricate magnetism and transport properties in $R{\mathrm{Mn}}_2{\mathrm{Ge}}_2$ systems, underscoring their potential for spintronic applications.

CrRhAs was theoretically proposed to be a kagome metal with unusual magnetic ground states; however, little is known about its magnetic structure and physical properties experimentally. Here, we present an experimental investigation of CrRhAs with ZrNiAl-type structure and a distorted Cr kagome lattice. CrRhAs is an antiferromagnet with $T_N=149\mathrm{K}$. Powder neutron diffraction analysis reveals a noncollinear antiferromagnetic structure with propagation vector $k=(1/3,1/3,1/2)$, which features a ferromagnetic second nearest neighbor coupling in the kagome plane that is different from the prediction in previous density functional theory calculations. Furthermore, CrRhAs exhibits anomalous electrical transport properties which are possibly related to multiband effects and strong spin fluctuations. For the temperature-dependent longitudinal resistivity ${\rho }_{xx}$, it is semiconductinglike above $T_N$ and becomes metallic below $T_N$. The Hall coefficients exhibit two sign changes near 70 and 300 K. Combined with the results of heat capacity measurements, a large Kadowaki-Woods ratio $\alpha =33.9\mu \mathrm{\Omega }\mathrm{cm}{\mathrm{mol}}^2{\mathrm{K}}^2/{\mathrm{J}}^2$ is obtained. The above results suggest CrRhAs is a strongly correlated kagome metal with multiband and noncollinear magnetic structure features.

Surface magnetoelectric (ME) coupling is conventionally attributed to strong spin-orbit coupling (SOC) or interface-induced polarization and is therefore considered strongly limited in centrosymmetric antiferromagnets. Here we show, theoretically, that rutile-type transition-metal fluorides ${M\mathrm{F}}_2$ ($M=\mathrm{V}$, Mn, Fe, Co, Ni) can exhibit a linear ME response at the (110) surface even in the absence of SOC, enabled by the interplay between bulk magnetic octupolar order and surface symmetry breaking. Our first-principles calculations reveal that ferroically ordered bulk magnetic octupoles in ${M\mathrm{F}}_2$ provide the symmetry prerequisite for a linear surface ME effect. The magnitude of this surface ME coupling is primarily governed by the magnetic exchange energy scale and the extent of interfacial electronic reconstruction. Specifically, in ${\mathrm{VF}}_2$ and ${\mathrm{CoF}}_2$, relatively weak exchange splitting generates pronounced $d$-orbital surface states near the Fermi level, yielding large displacement-induced surface magnetoelectric coefficients ${\lambda }^{\mathrm{surf}}$. In contrast, the strong exchange splitting in ${\mathrm{MnF}}_2$ and ${\mathrm{FeF}}_2$ maintains an insulating surface character and substantially suppresses ${\lambda }^{\mathrm{surf}}$. ${\mathrm{NiF}}_2$, featuring nearly degenerate $d^8$ spin configurations (i.e., an electronic configuration with eight electrons occupying the Ni $3d$ orbitals), further displays nonlinear magnetic reconstruction under small perturbations. These findings establish a general mechanism of “exchange-controlled surface magnetoelectricity” in rutile ${M\mathrm{F}}_2$ compounds, clarify that bulk octupoles act as a symmetry prerequisite rather than the primary determinant of the response amplitude, and render this ${M\mathrm{F}}_2$ family a promising platform for designing tunable, multipole-driven surface ME functionalities.