Recent neutron scattering and thermodynamic measurements suggest that Weyl electrons in the emergent Weyl semimetal SmAlSi mediate unconventional magnetic interactions and induce spiral magnetic order. In this work, we investigate the nature of these interactions by modeling long-range f - f exchange mediated by itinerant d electrons via the Ruderman-Kittel-Kasuya-Yosida mechanism, employing a material-specific tightbinding Hamiltonian obtained from first-principles calculations. The magnetic susceptibility is derived from the spin-spin correlation function based on the random phase approximation. Our results demonstrate that Fermisurface nesting alone cannot account for the experimentally observed magnetic modulation at the wave vector (1/3, 1/3, 0); however, incorporating appropriate antiferromagnetic exchange interactions among the d electrons yields the correct propagation vector. The spin-texture analysis reveals a configuration that is close to a cycloidal spin structure, preserving combined glide and time-reversal symmetry, and reflecting an intricate competition between inter- and intrasublattice interactions in SmAlSi.

Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum metric of Bloch bands. Using a gauge-invariant formulation based on eigenprojectors, we construct the full Riemannian geometry of the quantum-state manifold and apply it to a two-dimensional two-band model. We find that the Gauss curvature is constant over regular regions, but the manifold inevitably develops a closed curve of singular points where the metric tensor degenerates. These singularities obstruct the conventional Gauss-Bonnet theorem. By introducing the notion of a front and a signed area form, we derive a generalized Gauss-Bonnet relation that includes a singular curvature term defined along the fold curve. This result establishes a direct, quantized link between the total signed Gauss curvature and the Chern number, providing a unified geometric interpretation of Berry curvature and quantum metric. This framework bridges differential geometry and topological band theory, revealing how singular folds mediate the discrepancy between quantum volume and topological charge.

protected edge states serve as direct evidence of nontrivial electronic topology in atomically thin materials. Finding these states in experimentally realizable single-phase materials presents a substantial challenge for their use in fundamental studies and developing functional nanoscale devices. Here, we show the presence of robust edge states in phosphorene and group-Va monolayers with puckered lattice structures. By carefully analyzing the symmetry of the atomic sites and edge mode properties, we demonstrate that these atomically thin monolayers realize recently introduced obstructed atomic insulator states with partially occupied edge modes. The obstructed edge modes attain a Rashba-type spin splitting with Rashba parameter (alpha) alpha ) of 1.52 eV & Aring; for arsenene. Under strain or doping effects, these obstructed insulators transition to a phase with substantial spin-Berry curvature, yielding a double quantum spin Hall state with a spin Hall conductivity approximate to 4 e 2 h . The experimental availability of phosphorene and other group-Va monolayers could enable verification of obstructed atomic states and enhanced spin-Berry curvature effects discussed in this study, offering the potential for in electronic and devices.

AbstractA polymorph of Cu2OSeO3 with the distorted kagome lattice is successfully obtained using the high‐pressure synthesis technique (Cu2OSeO3‐HP). The structural analysis using X‐ray and neutron powder diffraction suggests that the tetrahedral Cu2+ clusters [similar to those in Cu2OSeO3 ambient‐pressure phase (Cu2OSeO3‐AP)] exist in Cu2OSeO3‐HP but with three symmetry inequivalent sites. No structural change is observed between 1.5 K and the room temperature. The complex magnetic H‐T phase diagram is established based on the temperature‐ and field‐dependent magnetization data, indicating two distinct antiferromagnetic phases at low and intermediate temperatures, in addition to the higher‐temperature spin‐glass‐like phase. The low temperature phase is identified by neutron powder diffraction refinements as a canted noncollinear antiferromagnetic order with a weak ferromagnetic component along the b‐axis. Size of the refined ordered moment is ≈1.00(4) µB in Cu2OSeO3‐HP, indicating a large enhancement compared to that of Cu2OSeO3‐AP (≈0.61 µB). By applying a uniaxial stress, finite enhancement of weak ferromagnetic component in the noncollinear antiferromagnetic phase in Cu2OSeO3‐HP is observed, which is the clear evidence of the piezomagnetic effect. Interestingly, the sign of the induced magnetization changes on heating from the low‐temperature to the intermediate‐temperature phases, indicating a novel piezomagnetic switching effect in this compound.

Understanding the role of lattice geometry in shaping topological states and their properties is of fundamental importance to condensed matter and device physics. Here we demonstrate how an anisotropic crystal lattice drives a topological hybrid nodal line in transition metal tetraphosphides $Tm$P$_4$ ($Tm$ = Transition metal). $Tm$P$_4$ constitutes a unique class of black phosphorus materials formed by intercalating transition metal ions between the phosphorus layers without destroying the characteristic anisotropic band structure of the black phosphorous. Based on the first-principles calculations and $k \cdot p$ theory, we show that $Tm$P$_4$ harbor a single hybrid nodal line formed between oppositely-oriented anisotropic $Tm~d$ and P states unhinged from the high-symmetry planes. The nodal line consists of both type-I and type-II nodal band crossings whose nature and location are determined by the effective-mass anisotropies of the intersecting bands. We further discuss a possible topological phase transition to exemplify the formation of the hybrid nodal line state in $Tm$P$_4$. Our results offer a comprehensive study for understanding the interplay between structural motifs-driven mass anisotropies and topology in anisotropic lattice materials to realize hybrid semimetal states.

Weyl electrons are intensely studied due to novel charge transport phenomena such as chiral anomaly, Fermi arcs, and photogalvanic effect. Recent theoretical works suggest that Weyl electrons can also participate in magnetic interactions, and the Weyl-mediated indirect exchange coupling between local moments is proposed as a new mechanism to induce spiral magnetic ordering by involving chiral Weyl electrons. Here, we present evidence of Weyl-mediated spiral magnetism in SmAlSi from neutron diffraction, transport, and thermodynamic data. We show that the spiral order in SmAlSi results from the nesting between topologically nontrivial Fermi pockets and weak magnetocrystalline anisotropy, unlike related materials (Ce,Pr,Nd)AlSi, where a strong anisotropy prevents the spins from freely rotating. We map the magnetic phase diagram of SmAlSi and reveal an A phase where topological magnetic excitations may exist. Within the A phase, we find a large topological Hall effect whose variation with the magnetic field direction suggests a dominant helical instead of cycloidal character, as theoretically predicted for the Weyl-induced spiral order.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

The intersections of topology, geometry and strong correlations offer many opportunities for exotic quantum phases to emerge in condensed matter systems. Weyl fermions, in particular, provide an ideal platform for exploring the dynamical instabilities of single-particle physics under interactions. Despite its fundamental role in relativistic field theory, the concept of causality and the associated spacetime light cone and event horizon has not been considered in connection with interacting Weyl fermionic excitations in quantum matter. Here, by using charge-density wave (CDW) as an example, we unveil the behavior of interacting Weyl fermions and show that a Weyl fermion in a system can open a band gap by interacting only with other Weyl fermions that lie within its energy-momentum dispersion cone. In this sense, causal connections or interactions are only possible within overlapping dispersion cones and each dispersion cone thus constitutes a solid-state analogue of the more conventional `event horizon' of high-energy physics. Our study provides a universal framework for considering interacting relativistic quasiparticles in condensed matter by separating them into energy-like and momentum-like relationships in analogy with the time-like and space-like events in high-energy physics. Finally, we consider two different candidate materials for hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study greatly enriches the phenomenology and unveils new connections between condensed matter and high-energy physics.

Helical magnets are extremely promising, as they have fascinating magnetic, electric, and phononic properties. Here, we report a spectrum of simultaneously occurring and highly entangled intriguing phenomena induced by helical spin ordering in a noncentrosymmetric and spin-frustrated system ${\mathrm{Fe}}_{3}(\mathrm{P}{\mathrm{O}}_{4}){\mathrm{O}}_{3}$. These phenomena include magnetodielectric effect in the form of a frequency-independent pronounced dielectric peak, clear magnetostriction effect manifested as a dramatic downturn in the thermal variation of lattice parameters, and strong spin-phonon coupling (which displays a unique anomalous hardening and softening of various phonon modes) at temperatures as high as ${T}_{N}=163\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The observed dielectric peak is seemingly associated with a structural distortion via the strong magnetostriction effect.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state(1-13). Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids(5), magnets(6,7). the quantum Hall effect(3,8), topological insulators(9,10), Weyl semimetals(11-13) and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet(14-20). Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T-3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

Unlike a typical spin–phonon coupling, an exhibition of unconventional spin–phonon coupling, which is mediated via magnetostriction effect, is reported in a hole-doped double perovskite Pr1.5Sr0.5CoMnO6. Various investigations including electronic and crystal structures, spin structure, transport property, lattice dynamics, and theoretical density of states analysis by density-functional theory (DFT) have been performed. A substantial increase in the mean oxidation states of Co ions and a concurrent abrupt decrease in the resistivity upon Sr doping is observed, thus altering its underlying transport mechanism. An insulating and ferromagnetic (FM) ground state is predicted by DFT calculations. The neutron diffraction data analysis reveals a complex crystal structure of Pr1.5Sr0.5CoMnO6, which consists of B-site disordered monoclinic (P21/n) and orthorhombic (Pnma) structures, highlighting the presence of an anti-site disorder in the system. The analysis also suggests an overall FM ordering of Co/Mn spins below 150 K for the monoclinic phase, whereas no such magnetic ordering is found for the orthorhombic phase. More interestingly, the neutron powder diffraction study perceives the presence of a strong magnetostriction effect in the system. Raman spectroscopy unravels the presence of a spin–phonon coupling, which is essentially mediated by the magnetostriction effect.

Recently, the discovery of multiferroicity in pyrochlore-like compound Cu2OCl2 has generated significant interest, and several studies have been performed in this area. This transition metal oxychloride is unique because the divalent copper atoms create an S=1/2 correlated insulator and the pyrochlore lattice tends to frustrate spins. From neutron powder diffraction measurements, an incommensurate magnetic order of the ordering vector q=(0.827,0,0) emerges below the Néel temperature of 70 K. At this temperature or slightly above, ferroelectricity (FE) or antiferroelectricity, accompanying a lattice distortion, has been observed. Experimentally, some discrepancies remain. In this paper, we report our first-principles simulation results by evaluating the possible lattice and spin spiral states. We found that the Fddd structure is not more stable than Fdd2(a) , which is supported by our reexamination of the x-ray diffraction data. In addition, we find that after we include magnetism in the calculation, it predicts that the Fdd2(a) lattice with a helical (proper screw) spin structure is energetically more stable than other spin configurations. Our results indicate charge-order-driven FE that subsequently induces magnetism.

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solidstate systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the SrIn2As2 materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that SrIn2As2 is a dual topological insulator with Z(2) = (1; 000) and mirror Chern number C-m = -1. Its isostructural and isovalent antiferromagnetic cousin EuIn2As2 is found to be an axion insulator with Z(4) = 2. The broken timereversal symmetry via Eu doping in Sr1-xEuxIn2As2 results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic EuIn2P2 is a trivial insulator with Z(4) = 0, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with Z(4) = 1 with applied magnetic field. Our study identifies Sr1-xEuxIn2(As, P)(2) as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.

A study of the structural and magnetic properties of Bi0·5La0·5Fe0·45Co0·05Mn0·5O3 is presented in the article. We report the rare observations of two glassy transitions below the long-range ordering temperature along with the metamagnetic transitions at low temperatures. Frequency and DC field dependence of AC susceptibility and isothermal relaxation of remnant magnetization studies have all shown the slow spin dynamics for the compound. Interestingly, in the glass phase of the materials, metamagnetic transitions of the antiferromagnetic spins were found which indicate the coexistence of the long-range ordered phase along with the short-range ordered glassy phase. The double cluster glass phases can be comprehended, from the relaxations of the spin clusters arising from the competing magnetic interactions present in the system. Moreover, the roles of additional exchange interactions which are brought to the system by Co doping are also considered in explaining the observed double cluster glass transitions.

The study of crystal structure, electronic structure, transport, and magnetic properties of heterovalent Sr2+ doped Pr2-xSrxCoFeO6 (x = 0.0 to 1.0) system have been done. Crystal structure study reveals an occurrence of structural change from orthorhombic (Pnma) to tetragonal (I4/m) phase above x = 0.6. A sudden transformation of the Griffiths-like to non-Griffiths-like magnetic phase is observed as the system changes its crystal structure from Pnma to I4/m. The X-ray photoemission spectroscopy (XPS) study suggests for the existence of mixed oxidation states of the B-site ions viz., Co3+/Co4+ and Fe3+/Fe4+, and it also indicates an increase in the mean oxidation states owing to the hole substitution (Sr2+). The temperature variation of the electrical resistivity of the studied systems follows two different transport mechanisms, such as the variable range hopping (VRH) (in the lower temperature region) and small polaron hoping (SPH) (in the higher temperature region) models. Dc magnetization study shows that a local competing ferromagnetic (FM) exchange interaction increases with Sr doping. Finally, the ac susceptibility study reveals breaking of the long-range-ordering in the system x = 1.0, which appears to be related to the structural change and enhanced spin frustration due to increased competing local FM exchange interactions. In addition, electronic density of states (DOS) calculations of PrSrCoFeO6 (i.e. x = 1.0) using the density functional theory (DFT) have been performed for various Co/Fe atomic distributions. For most of the Co/Fe atomic distributions studied, the calculations show that the total energy of the system with FM coupling among spins has slightly lower energy than that for antiferromagnetic (AFM) coupling.

Dielectric anomaly observed in cubic Mn1.5Cr1.5O4 around ferrimagnetic ordering temperature (TN) suggests a possible magneto-dielectric coupling in the system. This report confirms the presence of a weak but significant magneto-dielectric coupling in the system. The ab initio calculations show a band gap of around 1.2 eV, with fermi-level closer to the conduction band. The major features of conduction band nearest to the Fermi-level correspond to dxz and d3z2-r2 orbitals of Mn3+ ion. Temperature-dependent neutron diffraction results show a rapid decay in structural parameters (lattice-striction and transition metal-oxygen bond length) around TN. We confirmed that these changes in structural parameters at TN are not related to structural transition but the consequences of orbital-ordering of Mn3+. The rapid decay in transition metal-oxygen bond length under internal magnetism of the system shows that magnetism could certainly manipulate the electric dipole moment and hence the dielectric constant of the system. Magneto-striction acts as a link between magnetic and dielectric properties.

Ternary transition metal chalcogenides (TTMCs) have attracted interest due to the discovery of their Weyl semimetallic property and the recent synthesis of layered TTMCs which are regarded as potential candidates for two-dimensional (2D) topological insulators. Here, employing first-principles calculations, we predicted the emergence of non-trivial band topologies in the monolayer MM'X4 family (M= V, Nb, or Ta; M' = Co, Rh, or Ir; and X = Se or Te) within hybrid functional calculations. Five of eighteen 2D materials were found to be topological insulators, while four of them are magnetic thin films. The nontrivial topologies were verified via the calculated Z2 topological invariant and topologically protected edge states. Further calculations showed a strain-induced phase transition in VCoTe4 from a magnetic phase to a nonmagnetic topological insulating phase. Our comprehensive study revealed a diverse family of monolayer ternary transition metal chalcogenides adding new members to the current catalog of 2D topological insulators and 2D magnetic materials.

Probing the effects of thin-film thickness on transition metal dichalcogenides offer novel insights into their electronic properties and tunability, which leads to a new avenue of research and applications. A comprehensive first-principles study on thickness-dependent structural stabilities and electronic properties of ZrX2 (X = S, Se, or Te) thin films from 1 layer (L) to 6L and bulk was performed. The calculated formation energies show that ZrX2 adopts the 1T phase as the most stable structure. Furthermore, 1T-ZrS2 and ZrSe2 thin films and bulk are indirect semiconductors and their band gaps decrease as the number of layers is increased up to 6L, while 1T-ZrTe2 thin films and bulk are semimetallic. Interestingly, we demonstrate that the surface band structure of bulk and monolayer ZrTe2 under generalized gradient approximation + U and HSE06 methods is in excellent agreement with the angle-resolved photoelectron spectroscopy measurement. Finally, we discover the existence of van Hove singularities in strained 2L and unstrained 3L 1T-ZrS2 thin films, implying the existence of superconductivity in these thin films. These results showcase the tunable electronic properties of ZrX2 thin films because of thickness dependence and strain.