We introduce methods of characterizing entanglement on the example of the quantum skyrmion Hall effect, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over subsets of a system's degrees of freedom, yielding reduced density matrices useful in computing various measures of entanglement, which also preserve the observable expectation value. We focus here on applying these methods to compute observable-enriched entanglement spectra, unveiling bulk-boundary correspondences of canonical four-band models for topological skyrmion phases and their connection to simpler forms of bulk-boundary correspondence. Given the fundamental roles entanglement signatures and observables play in the study of quantum systems and the fundamental generalization of the interpretation and treatment of spin within the framework of the quantum skyrmion Hall effect, concepts of observable-enriched entanglement introduced here are broadly applicable to myriad problems of quantum systems.

Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as fractional Chern insulators (FCIs). Most TFB models are established in two-dimensional Euclidean lattices with zero curvature. In this paper, we systematically explore TFBs in a class of two-dimensional non-Euclidean lattices with constant negative curvature, i.e., the hyperbolic analogs of the kagome lattice. Based on Abelian hyperbolic band theory, TFBs have been respectively found in the heptagon-kagome, the octagon-kagome, the nonagon-kagome, and the decagon-kagome lattices by introducing staggered magnetic fluxes and next-nearest-neighbor hoppings. The flatness ratios of all hyperbolic TFB models are more than 15, which suggests that hyperbolic FCIs can be realized in these TFB models. We further demonstrate the existence of a $\nu =1/2$ FCI state with open boundary conditions when hard-core bosons fill into these hyperbolic TFB models.

Spin fluctuations in two-dimensional ferromagnets in the presence of crystalline lattice dislocations are investigated. We show the existence of topologically protected nonpropagative modes that localize at dislocations. These in-gap states, termed magnonic dislocation modes, are characterized by the $Z_2$ topological invariant that derives from broken parity symmetry induced by sublattice magnetic anisotropy. We uncover that bulk topology existing in the perfect crystal is robust under the influence of lattice defects, which is monitored by the real-space Bott index. It is also revealed that the topology of magnonic dislocation modes remains unaffected when bulk topology becomes trivial and is remarkably resilient against magnetic disorder. Our findings point to the intriguing relationship between topological lattice defects and the spectrum of topological spin excitations.

The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are nonanalytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of $\mathrm{SU}\left(n\right)$ models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.

Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective measure to study dissipative quantum chaos. Motivated by the rich properties of non-Hermitian power-law banded random matrices and their promise as a platform to study localized and delocalized phases in non-Hermitian systems, we make an in-depth study to assess different spectral phases of these matrices through the lens of both complex eigenvalues and singular values. Remarkably, the results from complex spectra and singular value analysis are seemingly different, thereby necessitating caution while identifying different phases. We also exemplify our findings by studying a non-Hermitian Hamiltonian with a complex on-site disorder. Our work indicates that systems where disorder is present in both the Hermitian and non-Hermitian segments of a Hamiltonian are sensitive to the specific diagnostic tool that needs to be employed to study quantum chaos.

The high pressure equation of state for the ${\mathrm{W}}_{0.75}\mathrm{R}{\mathrm{e}}_{0.25}$ alloy is experimentally determined up to 183 GPa with synchrotron angle-dispersive powder x-ray diffraction in the diamond-anvil cell and to ∼925 GPa with density-functional theory. W-Re alloys are used in many industrial high-temperature applications and as a confining gasket material in high-pressure diamond-anvil cell research. The inclusion of 25 wt. % Re achieves the highest performance in terms of strength and ductility while also maintaining the body-centered-cubic (bcc) crystal structure, yet to date there has been no investigation into its elastic behavior at high pressure. We present the experimentally and theoretically determined volumetric and elastic pressure response and systematically compare these results to other W-Re alloys, finding that the bulk modulus of W-Re alloys varies nonlinearly with Re content and ${\mathrm{W}}_{0.75}{\mathrm{Re}}_{0.25}$ becomes less incompressible than W at 85 GPa.

Nitrogen allotropes, especially under extreme conditions, play a crucial role in understanding atomic configurations and driving innovations in high-energy materials. The phase composition of layered polymeric nitrogen (LP-N) remains unresolved, with Pba2, $C2$/c, and Pccn structures proposed as candidates. However, their relative stabilities and ambiguous x-ray-diffraction (XRD) patterns—consistent with experimental data but not definitely—along with multiple possible explanations, have been topics of ongoing debate, particularly under varying pressures. In this study, we present an unexpected orthorhombic phase, $o-{\mathrm{N}}_{16}$, predicted using machine-learning driven swarm-intelligence approach. Gibbs free-energy calculations, kinetic barrier analysis during decompression, and simulated XRD patterns reveal $o-{\mathrm{N}}_{16}$ and Pba2 as dominant LP-N phases at elevated pressures, with a partial transition from $o-{\mathrm{N}}_{16}$ to $C2$/c upon decompression. Notably, the relative stabilities of nitrogen allotropes cg-N, $o-{\mathrm{N}}_{16}, C2$/c, and Pccn are dictated by configurational and conformational isomerism of armchair chains and interchain bonding. These findings shed light on the evolution of atomic configurations under high-pressure conditions. Beyond its favorable energy density, $o-{\mathrm{N}}_{16}$ exceeds all polymeric nitrogen structures in terms of detonation velocity and detonation pressure.

The optical orientation of ${\mathrm{Mn}}^{2+}$ spins in the first excited state ${}^4\mathrm{T}_1$ was experimentally observed in bulk ${\mathrm{Zn}}_{0.99}{\mathrm{Mn}}_{0.01}\mathrm{Se}$ in an external magnetic field of up to $6\mathrm{T}$ in Faraday geometry at temperature 1.6 K. This occurred during quasiresonant continuous wave circularly polarized photoexcitation of the intracenter d-d transitions. A nonmonotonic dependence of the thermal circular polarization of the intracenter photoluminescence on the magnetic field was observed. A theoretical model is proposed to describe the selection rules for resonant optical d-d transitions of an isolated ${\mathrm{Mn}}^{2+}$ ion in a ZnSe cubic crystal. These rules are based on the analysis of the total angular momentum symmetry for the ground (${}^6\mathrm{A}_1$) and first excited (${}^4\mathrm{T}_1$) states of the ${\mathrm{Mn}}^{2+}$ ion. Additionally, the Jahn-Teller coupling of the excited state orbital parts with tetragonal ($e$-type) local distortions of the crystal lattice is considered. This coupling results in the segregation of cubic axes and energy splitting for spin states with their projections of $\pm 1/2$ and $\pm 3/2$ on each axis in the corresponding atomic potential minimum. By introducing two different times of relaxation to reach thermodynamic equilibrium for $\pm 1/2$ and $\pm 3/2$ states in each Jahn-Teller configuration, an angle dependent optical orientation contribution in photoluminescence polarization arises in the presence of a magnetic field.

We investigate the emergence of topological Hall-like signals in disordered multidomain ferromagnets. Nonmonotonic behavior in Hall resistivity, commonly attributed to topological spin textures such as skyrmions, is produced in a random resistor network model without any chirality. It arises from simple mechanisms of the anomalous Hall effect in combination with the domain wall scattering. By varying domain configurations and domain wall resistances, we explore the conditions under which the nonmonotonic resistivity can be enhanced. Our results emphasize the need for careful analysis in distinguishing between true topological Hall effects and artifacts caused by domain disorders.

Nonreciprocal spin-wave propagation in bilayer ferromagnetic systems has attracted significant attention due to its potential to precisely quantify material parameters as well as for applications in magnonic logic and information processing. In this paper, we investigate the nonreciprocity of spin-wave dispersions in heterostructures consisting of two distinct ferromagnetic materials, focusing on the influence of saturation magnetization and thickness of the magnetic layers. We exploit Brillouin light scattering to confirm numerical calculations which are conducted with the finite element software TetraX. An extensive numerical analysis reveals that the nonreciprocal behavior is strongly influenced by the changing material parameters, with asymmetry in the spin-wave propagation direction reaching several GHz under optimized conditions. Our findings demonstrate that tailoring the bilayer composition enables precise control over nonreciprocity, providing a pathway for engineering efficient unidirectional spin-wave devices. These results offer a deeper understanding of hybrid ferromagnetic systems and open avenues for designing advanced magnonic circuits.

Frustrated magnetism, driven by competing exchange interactions, remains a pivotal topic in modern condensed-matter physics. In frustrated systems, observation of a partially disordered (PD) state where long-range magnetic order coexists with disorder is a unique phenomenon. Here, we focus on the emergence of a PD state and its underlying mechanism in a Heusler alloy, $\mathrm{P}{\mathrm{d}}_2\mathrm{DySn}$. Our findings reveal that this alloy crystallizes in a cubic structure and undergoes a partial transformation to tetragonal phase at low temperatures. The static magnetization and heat capacity studies reveal three successive long-ranged antiferromagnetic transitions at ∼16, 12, and 6 K, respectively, while dynamic magnetization studies provide clear evidence for multiple cluster glass transitions, concomitant with the long-range ordering temperatures. This study demonstrates the coexistence between antiferromagnetic and glassy magnetic states, which is a relatively rare phenomenon in Heusler alloys. We propose that the emergence of the PD state stems from magnetic frustration induced by the structural distortion rather than geometrical frustration associated with triangular networks of magnetic ions as observed in other PD magnetic systems.

We report evidence for $p$-wave superconductivity at the dual topological insulator (BiTe)/$s$-wave superconductor (${\mathrm{NbSe}}_2$) heterojunction by performing electrical transport measurements. Four-terminal differential conductance measurements performed at low temperatures exhibit sharp V-shaped zero-bias dip and convex-shaped coherence peaks. The multiband two-dimensional Blonder-Tinkham-Klapwijk model employed to fit the differential conductance reveals two distinct superconducting gaps, with anisotropic $p$-wave and $s$-wave characters, respectively. Detailed out-of-plane magnetic-field-dependent spectra show that the anisotropic $p$-wave gap gets destroyed at much smaller fields as compared to the $s$-wave gap.

Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among these advances, DTCs were demonstrated in a hybrid spin register within diamond, comprising a processor spin and surrounding memory spins. However, in conventional strategies involving a bias magnetic field, the field application effectively restricts the controllability of the processor spin. This limitation can be a significant barrier to the next goal of DTCs: achieving multifunctionality through enhanced local controllability. In this study, we theoretically propose multiple DTC protocols through the design of specific single-site control within the entire system. To this end, we consider a concrete model of a diamond-based quantum simulator operating without a bias magnetic field, thereby eliminating the restrictions on the processor spin. Our findings demonstrate that single-site operations enable access to DTCs with multiple distinct features in terms of periodicity and lifetime. Therefore, this approach provides a promising platform for creating diverse DTCs induced by single-site operations.

Two-dimensional (2D) multiferroic heterostructures present a promising platform for advanced spin devices by leveraging the coexisting ferromagnetic and ferroelectric orders. Through first-principles calculations and atomistic simulations, we reveal nonvolatile control of metallicity and topological spin textures in the ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6/{\mathrm{Hf}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ (CGT/HGT) heterostructure. Notably, manipulating ferroelectric polarization in HGT significantly modulates the magnetic anisotropy energy and Dzyaloshinskii-Moriya interaction of CGT/HGT, reversing the easy magnetization axis from in plane to out of plane. By analyzing the atomic-resolved spin-orbit-coupling energy ($\mathrm{\Delta }{E}_{soc}$), it is found that the cause of the change comes from the Fert-Levy mechanism. Additionally, this polarization control enables the creation and annihilation of bimerons and skyrmions, with interlayer sliding further altering magnetic ordering. Our findings offer valuable insights into magnetoelectric coupling and spin texture manipulation in 2D magnets, highlighting their potential for next-generation spintronic and memory devices.

In this paper, we introduce an efficient, linear algebra-based method for optimizing supercell selection to determine Heisenberg exchange parameters from density functional theory (DFT) calculations. A widely used approach for deriving these parameters involves mapping DFT energies from various magnetic configurations within a supercell to the Heisenberg Hamiltonian. However, periodic boundary conditions in crystals constrain the number of extractable exchange parameters. To identify optimal supercell structures for extracting a target number of exchange parameters, we systematically generate supercells within a specified volume range using Hermite normal form matrices. Then, for each supercell, we perform a null space analysis on the coefficient matrix obtained by mapping magnetic configurations to the Heisenberg Hamiltonian. By analyzing the null space results for each supercell structure, we identify the optimal configuration for extracting a target number of exchange parameters. This optimal supercell selection approach significantly reduces computational time and resource requirements. This method, which involves generating and analyzing supercells before performing DFT calculations, has demonstrated a reduction in computational costs by one to two orders of magnitude in many cases.

We investigate magnetic properties of the $s=1/2$ compound ${\mathrm{K}}_2{\mathrm{Cu}}_3{\left({\mathrm{MoO}}_4\right)}_4$ by combining magnetic susceptibility, magnetization, specific heat, and electron spin resonance (ESR) with density functional calculations. Its monoclinic structure features alternating ${\mathrm{Cu}}^{2+}$ ($s=1/2$) monomers and edge-shared dimers linked by ${\mathrm{MoO}}_4$ units, forming a distorted diamond chain along the $a$ axis. Antiferromagnetic order occurs at $T_{\mathrm{N}}=2.3$ K, as evident from a $\lambda$-type anomaly in specific heat and magnetic susceptibility derivatives. Inverse magnetic susceptibility reveals coexisting ferro- and antiferromagnetic interactions. Specific heat and ESR data show two characteristic temperatures: one at 20 K, associated with spin-singlet formation in ${\mathrm{Cu}}_2{\mathrm{O}}_9$ dimers, and another at 3.68 K, indicating short-range correlations between dimers and monomers. Magnetization measurements reveal a metamagnetic transition at 2.6 T and a critical magnetic field ${\mu }_0{H}_c=3.4$ T, where a 1/3 magnetization plateau emerges with saturation near 0.35 ${\mu }_{\mathrm{B}}$. Low-temperature specific heat and magnetization data reveal the suppression of long-range order at ${\mu }_0{H}_c$, enabling the construction of a temperature-magnetic field phase diagram showing multiple magnetic phases near the ${\mu }_0{H}_c$. Density functional theory confirms a distorted diamond chain with $J_1$ dimers and competing $J_2, J_4, J_3$, and $J_5$ interactions with monomer spins as an effective low-temperature spin model.

Topological antiferromagnetic systems, which exhibit anisotropic band structures combined with complex relativistic spin structures in momentum space, have shown strong magnetoresistance effects driven by Dirac fermion characteristics. While these new antiferromagnets have been studied in transport experiments, very little is known about their spin-dependent electronic dynamics on ultrafast timescales and far-from-equilibrium behavior. This paper investigates theoretically the spin-dependent electronic dynamics due to electron-phonon scattering in a model electronic band structure that corresponds to a Dirac semimetal antiferromagnet. Following a spin-conserving instantaneous excitation we obtain a change of the antiferromagnetic spin polarization due to the scattering dynamics for the site-resolved spin expectation values. This allows us to identify fingerprints of the anisotropic band structure in the carrier dynamics on ultrashort timescales.

We present a comprehensive investigation of the kagome metal ${\mathrm{LuV}}_6{\mathrm{Sn}}_6$ through magnetotransport and torque magnetometry studies in magnetic fields up to 41 T and temperatures as low as 0.3 K. Magnetoresistance measurements up to 31 T reveal clear Shubnikov–de Haas (SdH) oscillations with two dominant frequency peaks: $F_{\alpha }=12 \mathrm{T}$ and $F_{\beta }=155 \mathrm{T}$. The Berry phase ${\mathrm{\Phi }}_{\mathbf{B}}$, calculated from Landau level fan diagrams, indicates a nontrivial topology for both the $\alpha$- and $\beta$-orbits. To explore the possibility of higher-frequency signals in ${\mathrm{LuV}}_6{\mathrm{Sn}}_6$, we employed another technique: torque magnetometry. Torque measured with applied fields up to 41 T reveals clear de Haas–van Alphen (dHvA) oscillations, with frequency signals as high as 10 kT. Angular and temperature-dependent quantum oscillation measurements allowed us to extract the effective mass of charge carriers and map the Fermi surface of ${\mathrm{LuV}}_6{\mathrm{Sn}}_6$. To complement the experimental findings, we performed electronic band structure and Fermi surface calculations. The electronic bands of ${\mathrm{LuV}}_6{\mathrm{Sn}}_6$ reveal intriguing features, including flat bands, van Hove singularities, and Dirac points near the Fermi level. Two bands cross the Fermi level, contributing a deformed cylindrical shape at the $\mathrm{\Gamma }$-point and small chainlike Fermi surfaces near the Brillouin zone boundaries. Theoretical quantum oscillation frequencies derived from Fermi surface cross-sectional areas align well with experimental SdH and dHvA results. These combined experimental and theoretical insights provide a deeper understanding of the electronic structure of ${\mathrm{LuV}}_6{\mathrm{Sn}}_6$ and establish the foundation for exploring electronic properties in other vanadium- and titanium-based kagome systems.

The recently discovered dipole-octupole pyrochlore magnet ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ is a promising three-dimensional quantum spin liquid candidate, which shows no signs of ordering at low temperature. The low-energy effective pseudospin-1/2 description in a magnetic field is characterized by the XYZ Hamiltonian and a Zeeman term where the dipolar local $z$ component of the pseudospin couples to the local $z$ component of the applied magnetic field, while the local $x$ and $y$ components of the pseudospin remain decoupled as a consequence of their octupolar character. Using effective Hamiltonian parameters determined in Poree et al., arXiv:2305.08261, remarkable experimental features can be reproduced, as for instance the specific heat and magnetization data as well as the continuum of states seen in neutron scattering. Here we investigate the thermodynamic response to magnetic fields applied along the global [110] direction using specific heat measurements and fits using numerical methods, and solve the corresponding magnetic structure using neutron diffraction. Specific heat data in moderate fields are reproduced well, however, at high fields the agreement is not satisfactory. We especially observe a two-step release of entropy, a finding that demands a review of both theory and experiment. We address it within the framework of three possible scenarios, including an analysis of the crystal field Hamiltonian not restricted to the two-dimensional single-ion doublet subspace. We conclusively rule out two of these scenarios and find qualitative agreement with a simple model of field misalignment with respect to the crystalline direction. We discuss the implications of our findings for [111] applied fields and for future experiments on ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ and its sister compounds.