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Stabilizing exotic quantum phases of matter, e.g. spin liquid, is an attractive topic in condensed matter. Here, by a Monte Carlo study of a two-orbital spin-fermion model on a honeycomb lattice, we show the cooperative effects of the orbital degeneracy of itinerant electrons and the exchange interaction of localized spins can significantly suppress both ferromagnetic and antiferromagnetic orders by generating topological defects and give rise to an intermediate spin liquid state via continuous phase transitions. This phase competition can also be achieved by tuning the electron filling. These results shed new light on realizing spin liquids on geometrically non-frustrated lattices., Comment: 7 pages, 4 figures

Altermagnetism, as a new branch of magnetism independent of traditional ferromagnetism and antiferromagnetism, has attracted extensive attention recently. At present, researchers have proved several kinds of three-dimensional altermagnets, but research on two-dimensional (2D) altermagnets remains elusive. Here, we propose a method for designing altermagnetism in 2D lattices: bilayer reversed stacking. This method could enable altermagnetism-type spin splitting to occur intrinsically and the spin-splitting can be controlled by crystal chirality. We also demonstrate it through a real material of bilayer PtBr$_3$ with AB' stacking order. Additionally, the combination of stacking order and slidetronics offers new opportunities for electrical writing and magnetic reading of electronic devices. In the case of AC' stacking, interlayer sliding results in reversible spontaneous polarization. This unique combination of antiferromagnetism and sliding ferroelectricity leads to polarization-controlled spin-splitting, thus enabling magnetoelectric coupling, which can be detected by magneto-optical Kerr effect even without net magnetization. Our research highlights that reversed stacking provides a platform to explore rich physical properties of magnetism, ferroelectricity, and spin-splitting., Comment: 5 figures

Collinear dipole orders such as ferroelectricity and antiferroelectricity have developed rapidly in last decades. While, the noncollinear dipole orders are rarely touched in solids. Noncollinear dipole orders can provide a route to realize ferrielectricity. Based on first-principles calculations, an inorganic molecular crystal MnO$_3$Cl has been demonstrated to own intrinsic noncollinear ferrielectricity, which originates from the stereo orientations of polar molecules. The large negative piezoelectricity effect ($d_{33}\sim-27$ pC/N) is also predicted. A strong light absorption and moderate optical anisotropy are found for this molecular crystal in the ultraviolet light window. Additionally, by electron doping via hydrogen intercalation, a ferromagnetic polar half-metals can be obtained. Our study here provide a material platform to explore the intriguing physics of noncollinear ferrielectricity and potential applications in devices., Comment: 7 pages, 4 figures

Owing to the strong spin-orbit coupling and the related fascinating physical properties, heavy 5d transition-metals exhibit desirable application prospects. However, up to now, the 5d magnetic materials are still very limited, especially very rare for tungsten. In this work, we theoretically predict a two-dimensional multiferroic W3Cl8 monolayer. Intrinsic 5d magnetism of tungsten is activated by the W ions' fractional valence in a breathing Kagome lattice of reduced effective dimension. A coplanar Y-type antiferromagnetism composed by ferromagnetic W3 trimers is confirmed as the magnetic ground state. The spontaneous ferroelectric polarization mainly originates from the ion displacement induced by the breathing distortion of Kagome lattice. An intrinsic magneto-optical Kerr effect with sizable Kerr angle can be observed to detect this trimeric Y-type antiferromagnetism, and it depends strongly on the detailed magnetic order. Thereby, we propose a general scheme for realizing more 5d magnetism in two-dimensional multiferroic systems.

The spin-fermion model was previously successful to describe the complex phase diagrams of colossal magnetoresistive manganites and iron-based superconductors. In recent years, two-dimensional magnets have rapidly raised up as a new attractive branch of quantum materials, which are theoretically described based on classical spin models in most studies. Alternatively, here the two-orbital spin-fermion model is established as a uniform scenario to describe the ferromagnetism in a two-dimensional honeycomb lattice. This model connects the magnetic interactions with the electronic structures. Then the continuous tuning of magnetism in these honeycomb lattices can be predicted, based on a general phase diagram. The electron/hole doping, from the empty $e_{g}$ to half-filled $e_{g}$ limit, is studied as a benchmark. Our Monte Carlo result finds that the ferromagnetic $T_{C}$ reaches the maximum at the quarter-filled case. In other regions, the linear relationship between $T_{C}$ and doping concentration provides a theoretical guideline for the experimental modulations of two-dimensional ferromagnetism tuned by ionic liquid or electrical gating.

Low-dimensional ferroelectricity and polar materials have attracted considerable attentions for their fascinating physics and potential applications. Based on first-principles calculations, here we investigate the stacking modes and polar properties of a typical series of quasi-one-dimensional ferroelectrics: double-chain oxyhalides NbO$X_3$ ($X$=Cl, Br, I). The geometry of their double-chains allows both the interchain/intrachain permutation. Thus, different stacking modes of double-chains lead to a variety of ferroelectric and antiferroelectric phases in both the tetragonal and monoclinic crystals. The proximate energies of these phases may lead to multiphase coexistence in real materials, as well as the hydrostatic pressure driving structural phase transition. Their spontaneous polarizations and piezoelectricity of the ferroelectric phases are prominent, comparable to commercially used ferroelectric BaTiO$_3$ and piezoelectric ZnO, respectively. Our work demonstrates that the van der Waals NbO$X_3$ are promising materials for exploring quasi-one-dimensional ferroelectricity and antiferroelectricity., Comment: 7 pages, 5 figures

Considerable research interest has been attracted to noncollinear magnetic structures for their intriguing physics and promising applications. In this work, based on relativistic density functional theory, we reveal the interesting magnetic order and relevant properties in monolayer RuF$_4$, which can be exfoliated from its bulk phase. Although the spins on Ru ions are almost antiferromagnetically aligned between nearest-neighbors, weak ferromagnetism is generated because of the antisymmetric Dzyaloshinskii-Moriya interaction as well as the single-ion anisotropy. A prominent magneto-optical Kerr effect can be observed for this antiferromagnet, similar to those of regular strong ferromagnets. In addition, a uniaxial strain can induce a ferroelastic switching together with the in-plane rotation of spin direction, giving rise to a strong intrinsic magnetoelasticity. Our work not only suggests an alternative direction for two-dimensional magnetic materials, but also provides hints to future devices based on antiferromagnetic magnetoelastic or magneto-optical materials., Comment: 7 pages, 5 figures

Two dimensional multiferroics inherit prominent physical properties from both low dimensional materials and magnetoelectric materials, and can go beyond their three dimensional counterparts for their unique structures. Here, based on density functional theory calculations, a MXene derivative, i.e., i-MXene (Ta$_{2/3}$Fe$_{1/3}$)$_2$CO$_2$, is predicted to be a type-I multiferroic material. Originated from the reliable $5d^0$ rule, its ferroelectricity is robust, with a moderate polarization up to $\sim12.33$ $\mu$C/cm$^2$ along the a-axis, which can be easily switched and may persist above room temperature. Its magnetic ground state is layered antiferromagnetism. Although it is a type-I multiferroic material, its N\'eel temperature can be significantly tuned by the paraelectric-ferroelectric transition, manifesting a kind of intrinsic magnetoelectric coupling. Such magnetoelectric effect is originated from the conventional magnetostriction, but unexpectedly magnified by the exchange frustration. Our work not only reveals a nontrivial magnetoelectric mechanism, but also provides a strategy to search for more multiferroics in the two dimensional limit., Comment: 15 pages, 5 figures

In semi-supervised fuzzy clustering, this paper extends the traditional pairwise constraint (i.e., must-link or cannot-link) to fuzzy pairwise constraint. The fuzzy pairwise constraint allows a supervisor to provide the grade of similarity or dissimilarity between the implicit fuzzy vectors of a pair of samples. This constraint can present more complicated relationship between the pair of samples and avoid eliminating the fuzzy characteristics. We propose a fuzzy discriminant clustering model (FDC) to fuse the fuzzy pairwise constraints. The nonconvex optimization problem in our FDC is solved by a modified expectation-maximization algorithm, involving to solve several indefinite quadratic programming problems (IQPPs). Further, a diagonal block coordinate decent (DBCD) algorithm is proposed for these IQPPs, whose stationary points are guaranteed, and the global solutions can be obtained under certain conditions. To suit for different applications, the FDC is extended into various metric spaces, e.g., the Reproducing Kernel Hilbert Space. Experimental results on several benchmark datasets and facial expression database demonstrate the outperformance of our FDC compared with some state-of-the-art clustering models., Comment: 15 pages,41 figures

In solids, charge polarity can one-to-one correspond to spin polarity phenomenologically, e.g. ferroelectricity/ferromagnetism, antiferroelectricity/antiferromagnetism, and even dipole-vortex/magnetic-vortex, but ferrielectricity/ferrimagnetism kept telling a disparate story in microscopic level. Since the definition of a charge dipole involves more than one ion, there may be multiple choices for a dipole unit, which makes most ferrielectric orders equivalent to ferroelectric ones, i.e. this ferrielectricity is not necessary to be a real independent branch of polarity. In this work, by using the spherical aberration-corrected scanning transmission electron microscope, we visualize a nontrivial ferrielectric structural evolution in BaFe2Se3, in which the development of two polar sub-lattices is out-of-sync, for which we term it as irreducible ferrielectricity. Such irreducible ferrielectricity leads to a non-monotonic behavior for the temperature-dependent polarization, and even a compensation point in the ordered state. Our finding unambiguously distinguishes ferrielectrics from ferroelectrics in solids., Comment: 15 figures

Layered materials with robust magnetic ordering have been attracting significant research interest. In recent experiments, a new layered material 1$T$-CrTe$_{2}$ has been synthesized and exhibits ferromagnetism above the room temperature. Here, based on first-principles calculations, we investigate the electronic, magnetic, and transport properties of 1$T$-CrTe$_{2}$, both in the bulk and in the two-dimensional (2D) limit. We show that 1$T$-CrTe$_{2}$ can be stable in the monolayer form, and has a low exfoliation energy. The monolayer structure is an intrinsic ferromagnetic metal, which maintains a high Curie temperature above the room temperature. Particularly, we reveal interesting features in the anomalous Hall transport. We show that in the ground state, both bulk and monolayer 1$T$-CrTe$_{2}$ possess vanishing anomalous Hall effect, because the magnetization preserves one vertical mirror symmetry. The anomalous Hall conductivity can be made sizable by tuning the magnetization direction or by uniaxial strains that break the mirror symmetry. The room-temperature 2D ferromagnetism and the tunable anomalous Hall effect make the material a promising platform for nanoscale device applications., Comment: 8 pages, 9 figures

Two-dimensional (2D) materials with nodal-loop band crossing have been attracting great research interest. However, it remains a challenge to find 2D nodal loops that are robust against spin-orbit coupling (SOC) and realized in magnetic states. Here, based on first-principles calculations and theoretical analysis, we predict that monolayer MnN is a 2D nodal-loop half metal with fully spin polarized nodal loops. We show that monolayer MnN has a ferromagnetic ground state with out-of-plane magnetization. Its band structure shows half metallicity with three low-energy bands belonging to the same spin channel. The crossing between these bands forms two concentric nodal loops centered around the $\Gamma$ point near the Fermi level. Remarkably, the nodal loops and their spin polarization are robust under SOC, due to the protection of a mirror symmetry. We construct an effective model to characterize the fully polarized emergent nodal-loop fermions. We also find that a uniaxial strain can induce a loop transformation from a localized single loop circling around $\Gamma$ to a pair of extended loops penetrating the Brillouin zone., Comment: 7 pages, 5 fgures

Most electronic properties of metals are determined solely by the low-energy states around the Fermi level, and for topological metals/semimetals, these low-energy states become distinct because of their unusual energy dispersion and emergent pseudospin degree of freedom. Here, we propose a class of materials which are termed as quadratic contact point (QCP) semimetals. In these materials, the conduction and valence bands contact at isolated points in the Brillouin zone, around which the band dispersions are quadratic along all three directions. We show that in the absence/presence of spin-orbit coupling, there may exist triply/quadruply-degenerate QCPs that are protected by the crystalline symmetry. We construct effective models to characterize the low-energy fermions near these QCPs. Under strong magnetic field, unlike the usual 3D electron gas, there appear unconventional features in the Landau spectrum. The QCP semimetal phase is adjacent to a variety of topological phases. For example, by breaking symmetries via Zeeman field or lattice strain, it can be transformed into a Weyl semimetal with Weyl and double Weyl points, a Z2 topological insulator/metal, or a Dirac semimetal. Via first-principles calculations, we identify realistic materials Cu2Se and RhAs3 as candidates for QCP semimetals., Comment: 10 pages and 9 figures

Novel two-dimensional (2D) emergent fermions and negative Poisson's ratio in 2D materials are fascinating subjects of research. Here, based on first-principles calculations and theoretical analysis, we predict that the hexacoordinated Mg$_{2}$C monolayer hosts both exotic properties. We analyze its phonon spectrum, reveal the Raman active modes, and show that it has small in-plane stiffness constants. Particularly, under the tensile strain in the zigzag direction, the Mg$_{2}$C monolayer shows an intrinsic negative Poisson's ratio $\sim -0.023$, stemming from its unique puckered hinge structure. The material is metallic at its equilibrium state. A moderate biaxial strain can induce a metal-semimetal-semiconductor phase transition, during which several novel types of 2D fermions emerge, including the anisotropic Dirac fermions around 12 tilted Dirac points in the metallic phase, the $2$D double Weyl fermions in the semimetal phase where the conduction and valence bands touch quadratically at a single Fermi point, and the 2D pseudospin-1 fermions at the critical point of the semimetal-semiconductor phase transition where three bands cross at a single point on the Fermi level. In addition, uniaxial strains along the high-symmetry directions break the three-fold rotational symmetry and reduce the number of Dirac points. Interestingly, it also generates 2D type-II Dirac points. We construct effective models to characterize the properties of these novel fermions. Our result reveals Mg$_{2}$C monolayer as an intriguing platform for the study of novel 2D fermions, and also suggests its great potential for nanoscale device applications., Comment: 9 pages, 8 figures