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Two-dimensional (2D) materials with nontrivial band crossings, namely linear or double Weyl points, have been attracting tremendous attention.

Rechargeable ion batteries require anode materials with excellent performance, presenting a key challenge for researchers. This paper explores the potential of using two-dimensional dumbbell silicene as an anode material for alkali metal ion batteries through density functional theory (DFT) calculations. Our findings demonstrate that alkali metal ions have negative adsorption energies on dumbbell silicene, and the energy barriers for Li/Na/K ion diffusion are as low as 0.032/0.055/0.21 eV, indicating that metal ions can easily diffuse across the entire surface of dumbbell silicene. Additionally, the average open circuit voltages of dumbbell silicene as anode for Li-ion, Na-ion, and K-ion batteries are 0.42 V, 0.41 V, and 0.60 V, respectively, with corresponding storage capacities of 716, 622, and 716 mAh/g. These results suggest that dumbbell silicene is an ideal anode material for Li-ion, Na-ion, and K-ion batteries, with high capacity, low open circuit voltage, and high ion diffusion kinetics. Moreover, our calculations show that the theoretical capacities obtained using DFT-D2 are higher than those obtained using DFT-D3, providing a valuable reference for subsequent theoretical calculations.

Electrides are a unique class of electron-rich materials where excess electrons are localized in interstitial lattice sites as anions, leading to a range of unique properties and applications. While hundreds of electrides have been discovered in recent years, magnetic electrides have received limited attention, with few investigations into their fundamental physics and practical applications. In this work, 51 magnetic electrides (12 antiferromagnetic, 13 ferromagnetic, and 26 interstitial-magnetic) were identified using high-throughput computational screening methods and the latest Material Project database. Based on their compositions, these magnetic electrides can be classified as magnetic semiconductors, metals, or half-metals, each with unique topological states and excellent catalytic performance for N2 fixation due to their low work functions and excess electrons. The novel properties of magnetic electrides suggest potential applications in spintronics, topological electronics, electron emission, and as high-performance catalysts. This work marks the beginning of a new era in the identification, investigation, and practical applications of magnetic electrides.

Centrosymmetric AB2 (A = Cr, Mo; B = Si, Ge) compounds host movable triple degenerate points without SOC and Dirac points with SOC.

Topological materials have been recently regarded as ideal catalysts for heterogeneous reactions due to their surface metallic states and high carrier mobility. However, the underlying relationship between their catalytic performance and topological states is under debate. It has been discovered that the electride 12CaO·7Al

Two-dimensional (2D) half-metal and topological states have been the current research focus in condensed matter physics. Herein, we report a novel 2D material named EuOBr monolayer, which can simultaneously show 2D half-metal and topological fermions. This material shows a metallic state in the spin-up channel but a large insulating gap of 4.38 eV in the spin-down channel. In the conducting spin channel, the EuOBr monolayer shows the coexistence of Weyl points and nodal-lines near the Fermi level. These nodal-lines are classified by type-I, hybrid, closed, and open nodal-lines. The symmetry analysis suggests these nodal-lines are protected by the mirror symmetry, which cannot be broken even spin–orbit coupling is included because the ground magnetization direction in the material is out-of-plane [001]. The topological fermions in the EuOBr monolayer are fully spin-polarized, which can be meaningful for future applications in topological spintronic nano-devices.

Topological states of matter in two-dimensional (2D) materials have received increasing attention due to their potential applications in nanoscale spintronics. Here, we report the presence of unique topological electronic properties in a 2D planar octagon TiB4 compound. Particularly, without considering the spin–orbit coupling (SOC), we found that the material showed a coexistence of novel quadratic node (QN), and two different types of nodal rings (NRs), namely type-I and type-II. The protection mechanism of fermions has been fully clarified in this study. Furthermore, these fermions showed clear edge states. It is worth noting that QN had a topological charge of 2 since it is different from linear nodes and exhibit clear Fermi arc edge states. Under lattice strain, we found that the system could further exhibit rich topological phase transition. When SOC was included, we determined that these crossing points open very tiny energy gaps, which were smaller than previously reported 3D and 2D examples. These results show that monolayer TiB4 is an excellent nodal point and nodal ring semimetal, which also provides a feasible member for studying potential entanglements among multiple fermions.

The quantum anomalous Hall effect (QAHE) in intrinsic ferromagnets has attracted considerable attention recently. Previously, studies of the QAHE have mostly focused on the default assumption of out-of-plane magnetization. In fact, the QAHE can also be achieved via in-plane magnetization, but such candidate materials are very scarce. Here, we find that two-dimensional (2D) YN2 not only possesses the previously reported out-of-plane QAHE, but it also possesses a tunable in-plane QAHE. More importantly, unlike the previously reported in-plane QAHE in d/f-type ferromagnets, here we report the effect in a 2D d0 ferromagnet, namely YN2, for the first time. In the ground state, a YN2 monolayer has a half-metal band structure, and manifests six pairs of fully spin-polarized Weyl points at the Fermi level. When spin-orbit coupling is included, the YN2 monolayer can realize multiple topological phases, determined based on the magnetization direction. Under in-plane magnetization, the YN2 monolayer shows either the Weyl state or in-plane QAHE state. Remarkably, the Chern number (±1) and the propagating direction of QAHE edge channels can be continuously switched via shifting the direction of the in-plane magnetic field. When magnetization is applied out-of-plane, the YN2 monolayer realizes an out-of-plane QAHE phase with a high Chern number of 3. The nontrivial edge states for all the topological phases in the YN2 monolayer have been clearly identified. This work suggests that 2D YN2 is an excellent candidate for investigating in-plane QAHE phases in d0 ferromagnets.

Two-dimensional (2-D) materials, especially carbon allotropes, have larger storage capacity and faster diffusion rate due to their unique structures and are usually used in ion batteries. Recently, a new stable two-dimensional carbon allotrope, namely PAI-graphene, was reported by first-principles calculations. Due to its lightweight and multiple-ring structure, great stability and excellent properties, here, we theoretically reveal the excellent performance of PAI-graphene as an anode material for Li-/Na-ion batteries. Our results show that PAI-graphene has intrinsic metallicity before and after adsorption of Li/Na, which ensures that it has good conductivity when working as an electrode material. In addition, PAI-graphene exhibits quite low open circuit voltage (0.342–0.190 V for Li, 0.339–0.233 V for Na) and diffusion barrier (0.34 eV for Li, 0.17 eV for Na), which indicates its superiority as an anode material. Most noteworthily, the Na storage capacity of PAI-graphene is up to 1674 mA h g−1, which is much higher than that of most 2-D anode materials. Thus, we believe that PAI-graphene can be an outstanding anode material with outstanding performance.

Topological quantum catalysts (TQCs), where metallic surface states from nontrivial band topology serve as the mechanism to favor heterogeneous catalysis processes, have been well demonstrated in three dimensional (3D) examples but have been rarely discussed in 2D scale. Here, we develop a design scheme to realize 2D TQCs with showing traversing nodal line at the Brillouin zone boundary, large Fermi arc on the edge, and nearly zero Gibbs free energy ({\Delta}GH*) for hydrogen evolution reaction (HER). We demonstrate the 2D Cu2C2N4 sheet is a such example. The material manifests an open nodal line traversing the whole k-path S-Y. It shows a long Fermi arc that spans the entire edge boundary, which is robust against spin-orbit coupling and the H adsorption. As the result, the edge of Cu2C2N4 sheet is relatively active for HER catalysis with possessing a {\Delta}GH* as low as 0.10 eV, which is comparable with that of Pt and superior to other traditional catalysts and 3D TQCs as well. Our work offers an effective route to develop high performance HER catalysis without containing noble metals by utilizing 2D TQCs with traversing nodal line.

Electrides in a two-dimensional (2D) scale, especially those that capture inherent magnetism and have low work functions, have shown great application prospects in nanoscale spintronic devices and electronic emitters. However, searching for ideal 2D magnetic electrides is still a great challenge. Herein, based on first-principles calculations, we demonstrate that 2D CaCl is strippable from the heterostructure of experimental CaCl/graphene and reveal that the freestanding 2D CaCl has a novel electride phase. In this material, sufficient electrons are trapped in the lattice voids and act as anions within the positive crystalline framework, following the electride form of [CaCl]+·e−. Due to the unique electron behaviour of electrides, the 2D [CaCl]+·e− possesses a series of interesting physical phenomena: (1) the electride [CaCl]+·e− exhibits room-temperature ferromagnetism, where the magnetic moment originates from the excess electrons with an s-like orbital feature rather than the atomic orbital ones, which is drastically different from traditional 2D ferromagnets; (2) the electride [CaCl]+·e− shows magnetic metal characteristics, and by doping with halogen elements, its electronic structure can be effectively regulated; (3) most remarkably, the FM electride [CaCl]+·e− shows an extremely low work function (2.65 eV). This value is the lowest among the electrides in 2D materials reported so far. Besides, the dimension of excess electrons can be effectively regulated by controlling the temperature. This work provides an excellent candidate to investigate 2D magnetic electrides and their associated applications.

Recently, two-dimensional (2-D) materials with a Penta-atomic-configuration such as Penta-graphene have received considerable attention because of their potential applications in electronics, spintronics and ion batteries. Previously, Penta-graphene has been proposed as an excellent anode material for Li-/Na-ion batteries with a high theoretical capacity (1489 mA h g-1). Here, based on the first-principles calculations, we report that a new 2-D material namely Penta-B2C can become another excellent anode material with even higher theoretical capacity for Li-/Na-ion batteries than Penta-graphene. Our results demonstrate that Li/Na atoms can be stably adsorbed on Penta-B2C. Meanwhile, Penta-B2C shows metallic conductivity during the adsorption. Most strikingly, the theoretical capacities of Penta-B2C are as high as 1594 for Li and 2391 mA h g-1 for Na, which are superior to those of the most known 2-D anode materials. Especially, the Na theoretical capacity of Penta-B2C sets a new record among known 2-D anode materials. In addition, Penta-B2C possesses relatively low open-circuit voltage and a low diffusion barrier for ions, which are vital for anode materials. These results highly promise that Penta-B2C can be an excellent anode material with a fast charge/discharge rate and extremely high theoretical capacity for Li-/Na-ion batteries.

Our work reveals a class of three-dimensional materials whose main features are dominated by d-orbital states. Their unique properties are derived from the low-energy states t2g. Without spin-orbital coupling (SOC), we find a triple degenerate point with a quadratic dispersion, demonstrated by an effective Hamiltonian. When SOC is included, the sign of SOC could determine the topological phases of materials: a negative SOC contributes a Dirac semimetal phase with a quadratic energy dispersion, whereas a positive SOC leads to a strong topological insulator phase. There exist clear surface states for the corresponding topological phases. Very interestingly, by application of a triaxial strain, the sequence of bands can be exchanged, as do the topological phases. In particular, there exists a 6-fold degenerate point under a critical strain. Furthermore, we use a uniaxial compressive/tensile strain, changing the quadratic Dirac point into a linear Dirac/strong topological insulator phase.

Different types (type-I, hybrid, and type-II) of nodal lines exhibit diverse electron behaviors and show rich potential applications in electronic devices. To date, it is still a great challenge to...

Nonsymmorphic symmetry has been proved to protect band crossings in topological semimetals/metals. In this work, based on the symmetry analysis and first-principles calculations, we reveal rich topological phases in compounds Pd4X (X = S, Se), which are protected by nonsymmorphic symmetry. In the absence of spin–orbit coupling (SOC), it shows the coexistence of the type-I Weyl point and type-II Weyl point. Here, due to the screw rotation, the type-I Weyl point takes an hourglass form. However, this hourglass Weyl point can be gapped in the presence of SOC. Furthermore, a combination of nonsymmorphic twofold screw-rotational symmetry and time-reversal symmetry protects a nodal surface. Particularly, this nodal surface is robust against SOC. In addition, a combination of the glide mirror and time-reversal symmetry contributes a nodal line of double degeneracy. In the presence of SOC, there emerges hybridization of type-I and type-II Weyl points. Meanwhile, there also appears a Dirac nodal line—a fourfold degenerate nodal line under SOC, which is protected by nonsymmorphic symmetries. Our works suggest realistic materials to study Weyl nodes of type-I and type-II, and their hybridization, as well as symmetry-protected nodal surfaces and Dirac nodal lines.

Electrical conductivity, storage capacity and ion diffusion ability are three crucial parameters for battery electrode materials. However, rare existing two-dimensional (2-D) electrode materials can achieve high performances in all these parameters. Here, we report that a 2-D transition-metal phosphide, the Ti2P monolayer, is a promising superior electrode material which realizes high performances in all the parameters mentioned above. The Ti2P monolayer has a stable honeycomb crystal structure. It has a metallic electronic structure with Li/Na adsorption, which ensures good electrical conductivity during the battery operation. We find that Li/Na can chemically bond to the Ti2P substrate, with specific charge exchanges. Our results show the Li/Na capacity in the Ti2P monolayer is about 846 mA h g−1, which is much higher than that of the graphite anode. Remarkably, the Li/Na diffusion barrier on the Ti2P monolayer is only 12–16 meV, which is lower than that in all 2-D anode materials proposed till now. Our work highly promises that theTi2P monolayer can serve as a superior anode material for Li-ion/Na-ion batteries by providing good electrical conductivity, high storage capacity and ultrafast ion diffusion.

Novel spintronic materials combining both magnetism and nontrivial topological electronic structures have attracted increasing attention recently. Here, we systematically studied the doping effects, magnetism, half-metallicity, and topological properties in the family of Fe2−xVxPO5 (x = 0, 0.5, 1, 1.5, 2) compounds. Our results show that Fe2PO5 takes an antiferromagnetic (AFM) ordering with a zero total magnetic moment. Meanwhile, the material hosts a Dirac nodal line and a Weyl nodal line near the Fermi level. V2PO5 is a ferromagnetic (FM) nodal line half-metal with a 100% spin-polarized Weyl nodal line. After doping, we find that Fe1.5V0.5PO5, Fe1V1PO5 and Fe0.5V1.5PO5 all take ferrimagnetic (FiM) ordering, with the Fe and V atoms taking opposite spin directions. Both Fe1.5V0.5PO5 and Fe0.5V1.5PO5 are FiM half-metals. Meanwhile, they show several pairs of fully spin-polarized Weyl points near the Fermi level. Fe1V1PO5 is a FiM semiconductor with different sizes of band gaps in different spin channels. These Fe2−xVxPO5 materials not only provide a good research platform to study the novel properties combining magnetism and nontrivial band topology, but also have promising applications in spintronic applications.

Because of their promising applications in electronics, topological materials have been much investigated recently. Here, we propose that palladium oxide (PdO) is an excellent topological semimetal with 0-D and 1-D band crossings and definite nontrivial surface states. The 0-D band crossing produces a pair of triply degenerate nodal points, and the 1-D band crossings form two nodal loops in PdO. After spin-orbit coupling (SOC) is included, the triply degenerate nodal points transform into Dirac points, and the nodal loops open small gaps. The SOC gaps at the nodal loops are comparable or lower than those of typical nodal loop materials. These results suggest that PdO can naturally host multiple fermions. Remarkably, all the fermions in PdO manifest definite nontrivial surface states, whereas triply degenerate nodal points and Dirac fermions show Fermi arc surface states, and the nodal loop fermion shows drumhead surface states. The topological band structure for the fermions and their nontrivial surface states are quite promising to be detected in future experiments.

Topological aspects of electronic structures have received intensive research interest in recent years. Here, we systematically investigate the electronic structure, doping effect and topological signature in a family of realistic compounds Li3-xNaxM (x = 3, 2, 1, 0; M = N, P, As, Sb, Bi). Without considering SOC, their electronic band structures show a doubly degenerate nodal line (NL) near the Fermi level in the Γ-A path. In addition, some compounds including Li2NaN, LiNa2N, Na3N and Na3Bi also exhibit one (or two) pair(s) of triply-degenerate nodal points (TDNPs) in the Γ-A path, locating at both sides of the Γ point. When SOC is taken into account, the band degeneracy of the NLs splits, and the scale of band splitting follows a positive correlation with the atomic weight of the M elements. Due to the band splitting by SOC, most of the Li3-xNaxM compounds show a pair of Dirac points (DPs) near the Fermi level. Very interestingly, we find that these DPs possess different types of band dispersions, namely type-I, type-II and the critical-type. The Fermi arcs from the DPs are identified. Our results indicate that Li3-xNaxM compounds are good candidates to study the novel properties of NLs, TDNPs, and DPs with different slopes of band dispersions.

Type-I, type-II and hybrid nodal lines show distinct electronic characteristics and have potential applications in electronic devices. However, it is still a challenge to explore a topological electronic material that naturally holds all these types of nodal lines simultaneously. Herein, we report for the first time that the centrosymmetric compound TiS is a novel topological material, with coexisting type-I, type-II and hybrid nodal lines in the low-energy band structure without spin–orbit coupling (SOC). These nodal lines are situated in the kz = 0 plane, and share the same symmetry-protection mechanisms. All the nodal lines show clear drumhead surface states, which can be detected experimentally. Besides the nodal lines, without considering SOC, TiS also shows a pair of symmetry-protected type-II Dirac points near the Fermi level, characterized by nontrivial Fermi arcs on the surface. After SOC is included, the Dirac points split into two pairs of type-II Dirac points, and the nodal lines open small gaps. The SOC gaps of nodal lines are smaller than or comparable with those of previous nodal line materials. These results suggest that the TiS compound is an excellent material to study the novel properties of nodal lines with type-I, type-II, and hybrid band dispersions, as well as the type-II Dirac points.

Since the discovery of penta-graphene, two-dimensional (2-D) pentagonal-structured materials have been highly expected to have desirable performance because of their unique structures and accompanied physical properties. Hence, based on the first-principles calculations, we performed a systematical study on the structure, stability, mechanical and electronic properties, and potential applications on carbon-based pentagonal materials with binary compositions, namely, Penta-C

Magnetic topological semimetals have brought new insights into topological aspects because they nicely combine the band topology with intrinsic magnetic order. Comparing with ferromagnetic topological semimetals, antiferromagnetic (AFM) ones are even more special since they can break the time-reversal symmetry but show no net magnetic moment, and are highly expected for applications of topological AFM spintronics. Here, we report ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ compound is an ideal AFM Weyl nodal line semimetal. It shows time-reversal breaking Weyl nodal lines in both the spin-up and spin-down channels. Each nodal line arises from the band in one single spin channel, thus is spin-polarized. The nodal lines locate quite near the Fermi level and do not coexist with other extraneous bands. The drumhead surface state of the nodal line can be clearly identified. The nodal lines are protected by the glide mirror symmetry and are robust against spin-orbit coupling. We also show that ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can transform into an AFM Weyl semimetal under an in-plane external magnetic field. Our results suggest ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can serve as an excellent platform to investigate AFM topological semimetals with attractive features.

Unconventional fermions, such as threefold, fourfold, sixfold, and eightfold fermions have attracted intense attention in recent years. However, the concrete materials hosting unconventional fermions are still in urgent scarcity. In this work, based on first-principle calculations and symmetry analysis, we reveal rich unconventional fermions in existing compound ${R}_{2}{\mathrm{C}}_{3}$ ($R=\mathrm{Y}$, La, Ce, Pr, Nd, Sm, Tb, Dy, Ho, Er, Tm, Yb, Lu). We show that these compounds host quadratic dispersive threefold, linear dispersive fourfold, and sixfold points (SPs) near the Fermi level in their electronic band structures when spin-orbital coupling (SOC) is not included. We also find that a uniaxial strain can transform the unconventional fermions into other types of fermions, depending on the directions of strain. When SOC is considered, a SP transforms to an eightfold degenerate point and a fourfold degenerate point. Overall, our work provides a family of realistic materials to study the unconventional fermions.

A Cr3Al compound with a DO3 structure has previously been predicted to be nearly half metal and a promising spintronics material; however, its synthesis has not been reported. Here, a Cr3Al compound with a DO3 structure is successfully prepared in thin-film form by the magnetron sputtering method. It was found that the substrate temperature is crucial to the atomic ordering, thin-film density and lattice constant. The lattice constant varies with different substrate temperatures and is smaller than the theoretical equilibrium lattice constant. Theoretical investigations on the electronic structures and magnetic properties indicate that the Cr3Al compound with a DO3 structure is a rare material with zero-gap half-metallic characteristics under an experimental lattice constant of 5.83 Å. The experimental result is in agreement with the theoretical results in magnetization, and the Cr3Al compound synthesized in this work exhibits semi-metallic-like electrical transport characteristics and positive magnetoresistance of greater than 2% in the temperature range 2–250 K.

It has been, for the first time, reported that centrosymmetric Li2NaN is a realistic triply degenerate nodal point (TDNP) material with three superior characteristics. In the band structure of the centrosymmetric Li2NaN material, there is only a single pair of TDNPs at the Fermi level and not coexisting with other extraneous bands, which indicates that the unique physical properties of the topological semimetal can be clearly detected via experiments and the Li2NaN material is an ideal TDNP semimetal. More importantly, the TDNPs identified in the Li2NaN material show an unusual critical-type band crossing, which is different from previously reported ones. Under lattice strain, we show that the positions of the TDNPs can be tuned, and the TDNPs can even be annihilated. Upon increasing the spin–orbit coupling, the centrosymmetry in the material makes the TDNPs transform into a pair of critical-type Dirac points, which are different from those in noncentrosymmetric systems. So, the centrosymmetric Li2NaN material is considered to be a superior topological semimetal with an ideal band structure, clear topological signs of physical properties, the novel pair of Dirac points and TDNPs.

Topological metals/semimetals, as novel topological states of matter, have been well investigated in nonmagnetic and ferromagnetic materials. Here, by performing band structure calculations, we report the discovery of rich topological states in an antiferromagnetic metal β-Fe2PO5. When spin–orbit coupling (SOC) is not considered, it hosts a Weyl nodal line, Dirac point, and Dirac nodal line near the Fermi level. In particular, the Weyl nodal line in β-Fe2PO5 is formed by the crossing bands from a single spin channel. Such a fully spin-polarized Weyl nodal line has not been identified in realistic AFM materials before. The Dirac point and Dirac nodal line in β-Fe2PO5 occur in a specific high-symmetry path, and are formed by the crossing bands from both spin channels, showing different signatures with the Weyl nodal line. When SOC is taken into account, the Weyl nodal line is retained, and the Dirac nodal point and nodal line degenerate into their Weyl counterparts. The existence of rich fermionic states in antiferromagnetic β-Fe2PO5 not only provides an excellent platform to study the entanglement between magnetism and topological states, but also shows great potential in topological antiferromagnetic spintronics applications.

Superconductors with a nontrivial band structure are promising to realize a topological superconducting state. Herein, we report the presence of a topological phase in a well-known superconductor, NaAlSi. Our first-principles computations show that NaAlSi naturally possesses four nodal lines in the kz = 0 and kz = π planes and hosts clear drumhead surface states. Comparing with those identified in other superconductors, the nodal line band structure of NaAlSi can more favor experimental detection on considering that: (1) it possesses four nodal lines in total in the system; (2) all the nodal lines appear slightly below the Fermi level; (3) the nodal lines do not coexist with other fermions or extraneous bands. Our findings indicate that NaAlSi is an excellent material platform to investigate the entanglement of superconducting and topological nodal line states.

Recently, two-dimensional (2-D) materials with a Penta-atomic-configuration such as Penta-graphene have received considerable attention because of their potential applications in electronics, spintronics and ion batteries. Previously, Penta-graphene has been proposed as an excellent anode material for Li-/Na-ion batteries with a high theoretical capacity (1489 mA h g-1). Here, based on the first-principles calculations, we report that a new 2-D material namely Penta-B2C can become another excellent anode material with even higher theoretical capacity for Li-/Na-ion batteries than Penta-graphene. Our results demonstrate that Li/Na atoms can be stably adsorbed on Penta-B2C. Meanwhile, Penta-B2C shows metallic conductivity during the adsorption. Most strikingly, the theoretical capacities of Penta-B2C are as high as 1594 for Li and 2391 mA h g-1 for Na, which are superior to those of the most known 2-D anode materials. Especially, the Na theoretical capacity of Penta-B2C sets a new record among known 2-D anode materials. In addition, Penta-B2C possesses relatively low open-circuit voltage and a low diffusion barrier for ions, which are vital for anode materials. These results highly promise that Penta-B2C can be an excellent anode material with a fast charge/discharge rate and extremely high theoretical capacity for Li-/Na-ion batteries.

The quantum anomalous Hall effect (QAHE) in intrinsic ferromagnets has attracted considerable attention recently. Previously, studies of the QAHE have mostly focused on the default assumption of out-of-plane magnetization. In fact, the QAHE can also be achieved via in-plane magnetization, but such candidate materials are very scarce. Here, we find that two-dimensional (2D) YN

Recent investigation has connected topology with magnetization, which has been attracting great research interest. Here, based on symmetry analysis and first-principle calculations, we reveal rich band crossings in ferromagnetic quasi-one-dimensional compounds ${XYZ}_{3}$ ($X=\mathrm{Cs},\mathrm{Rb}$, $Y=\mathrm{Cr},\mathrm{Cu}$, $Z=\mathrm{Cl},\mathrm{I}$). We show that these materials host hourglass Weyl loops, nodal surfaces, and Dirac points in the absence of spin-orbital coupling. Notably, these topological phases only occur in a single spin channel, leading to fully spin-polarized phases. Based on symmetry analysis, we present that the hourglass-like Weyl loop is enforced by nonsymmorphic symmetries, which give rise to drumhead surface states. Particularly, the Weyl loop can persist when a magnetic direction is normal to the plane where it lies on. Additionally, we also find the nodal surfaces protected by the combination of screw rotation and time reversal symmetry. Besides, there exists a Dirac point enabled by nonsymmorphic symmetry and time reversal symmetry. Notably, this Dirac point shows a linear dispersion in one direction and quadratic dispersion in the normal plane, showing two Fermi arcs in its surface energy spectrum. By tuning the direction of magnetization, the Dirac point can be reduced to a pair of Weyl points. Our work suggests a concrete platform for exploring the fascinating physics associated with nonsymmorphic band crossings in quasi-one-dimensional ferromagnetic systems.

Here we systematically investigate the structure, phase stability, half-metallicity, and topological electronic structure for a topological spintronic material $\mathrm{Na}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$. The material has a tetragonal structure with excellent dynamical and thermal stabilities. It shows a half-metallic ground state, where only the spin-up bands are present near the Fermi level. These bands are demonstrated to form a nodal line with the double degeneracy on the ${k}_{z}=0$ plane. The nodal line is robust against spin-orbit coupling, under the protection of the mirror symmetry. The nodal line band structure is very clean, thus the drumhead surface states can be clearly identified. Remarkably, the nodal line and drumhead surface states have the $100%$ spin polarization, which are highly desirable for spintronics applications. In addition, by shifting the magnetic field in-plane, we find that the nodal line can transform into a single pair of Weyl nodes. The nodal-line and Weyl-node fermions in the bulk, as well as the drumhead fermions on the surface are all fully spin-polarized, which may generate interesting physical properties and promising applications.