Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer

Controlling Noncollinear Ferromagnetism in van der Waals Metal-Organic Magnets

Van der Waals (vdW) magnets both allow exploration of fundamental 2D physics and offer a route toward exploiting magnetism in next generation information technology, but vdW magnets with complex, noncollinear spin textures are currently rare. We report here the syntheses, crystal structures, magnetic properties and magnetic ground states of four bulk vdW metal-organic magnets (MOMs): FeCl2(pym), FeCl2(btd), NiCl2(pym), and NiCl2(btd), pym = pyrimidine and btd = 2,1,3-benzothiadiazole. Using a combination of neutron diffraction and bulk magnetometry we show that these materials are noncollinear magnets. Although only NiCl2(btd) has a ferromagnetic ground state, we demonstrate that low-field hysteretic metamagnetic transitions produce states with net magnetization in zero-field and high coercivities for FeCl2(pym) and NiCl2(pym). By combining our bulk magnetic data with diffuse scattering analysis and broken-symmetry density-functional calculations, we probe the magnetic superexchange interactions, which when combined with symmetry analysis allow us to suggest design principles for future noncollinear vdW MOMs. These materials, if delaminated, would prove an interesting new family of 2D magnets.

Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials1-4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin-orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds.

Non-coplanar helimagnetism in the layered van-der-Waals metal DyTe3

Van-der-Waals magnetic materials can be exfoliated to realize ultrathin sheets or interfaces with highly controllable optical or spintronics responses. In majority, these are collinear ferro-, ferri-, or antiferromagnets, with a particular scarcity of lattice-incommensurate helimagnets of defined left- or right-handed rotation sense, or helicity. Here, we report polarized neutron scattering experiments on DyTe3, whose layered structure has highly metallic tellurium layers separated by double-slabs of dysprosium square nets. We reveal cycloidal (conical) magnetic textures, with coupled commensurate and incommensurate order parameters, and probe the evolution of this ground state in a magnetic field. The observations are well explained by a one-dimensional spin model, with an off-diagonal on-site term that is spatially modulated by DyTe3's unconventional charge density wave (CDW) order. The CDW-driven term couples to antiferromagnetism, or to the net magnetization in an applied magnetic field, and creates a complex magnetic phase diagram indicative of competing interactions in this easily cleavable van-der-Waals helimagnet.

2D Heterostructure of CoCl2 /Co3 O4 Built for Strong Enhanced Magnetism

As a remarkable structure, 2D magnetic heterojunctions have attracted researchers' attention owing to their controlled manipulation in the electronic device. However, successful fabrication as well as modulation of their structure and compound remain challenging. Herein, a novel method is designed to obtain a CoCl2 /Co3 O4 heterojunction on Si/SiO2 substrate with the assistance of supercritical CO2 (SC CO2 ), and the as-fabricated sample has significantly increased coercivity and saturation magnetization, which is 11 times higher than pure Co3 O4 . Further, it can be found that the CO2 pressure has the decisive effect on the saturation magnetization of the sample. Therefore, it suggests that the tunable electronic-magnetic device can be anticipated to be obtained in the future.

Nonvolatile Multistate Manipulation of Topological Magnetism in Monolayer CrI3 through Quadruple-Well Ferroelectric Materials

Nonvolatile multistate manipulation of two-dimensional (2D) magnetic materials holds promise for low dissipation, highly integrated, and versatile spintronic devices. Here, utilizing density functional theory calculations and Monte Carlo simulations, we report the realization of nonvolatile and multistate control of topological magnetism in monolayer CrI3 by constructing multiferroic heterojunctions with quadruple-well ferroelectric (FE) materials. The Pt2Sn2Te6/CrI3 heterojunction exhibits multiple magnetic phases upon modulating FE polarization states of FE layers and interlayer sliding. These magnetic phases include Bloch-type skyrmions and ferromagnetism, as well as a newly discovered topological magnetic structure. We reveal that the Dzyaloshinskii-Moriya interaction (DMI) induced by interfacial coupling plays a crucial role in magnetic skyrmion manipulation, which aligns with the Fert-Levy mechanism. Moreover, a regular magnetic skyrmion lattice survives when removing a magnetic field, demonstrating its robustness. The work sheds light on an effective approach to nonvolatile and multistate control of 2D magnetic materials.

Bloch-type magnetic skyrmions in two-dimensional lattices

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

Realistic Spin Model for Multiferroic NiI_{2}

A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i) the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii) the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional Monte Carlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.

Same effect of biquadratic exchange interaction and Heisenberg linear interaction in a spin spiral

Monolayer (ML) NiCl₂ exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms (B₁), as demonstrated by the spin spiral model in J. Ni et al., Phys. Rev. Lett., 2021, 127, 247204. This interaction is crucial for stabilizing the ferromagnetic collinear order within the ML NiCl₂. However, they neither point out the role of B₁ nor discuss the dispersion relation from spin orbit coupling (SOC) in the spin spiral. As we have done in this work, these parameters might theoretically potentially be derived directly by fitting the calculated spin spiral dispersion relation. Here, we draw attention to the fact that B₁ is equivalent to half of J₃ in Heisenberg linear interactions and that the positive B₁ partially counteracts the negative J₃'s impact on the spin spiral to make the ML NiCl₂ ferromagnetic. The comparatively small J₃ + 1/2B₁ from the spin spiral led us to believe that J₃ could be substituted by B₁, yet it still exists and plays a crucial function in magnetic semiconductors or insulators. The dispersion relation, which we also obtain from SOC, displays weak antiferromagnetic behavior in the spin spiral.

Deep-learning electronic-structure calculation of magnetic superstructures

Ab initio studies of magnetic superstructures are indispensable to research on emergent quantum materials, but are currently bottlenecked by the formidable computational cost. Here, to break this bottleneck, we have developed a deep equivariant neural network framework to represent the density functional theory Hamiltonian of magnetic materials for efficient electronic-structure calculation. A neural network architecture incorporating a priori knowledge of fundamental physical principles, especially the nearsightedness principle and the equivariance requirements of Euclidean and time-reversal symmetries ([Formula: see text]), is designed, which is critical to capture the subtle magnetic effects. Systematic experiments on spin-spiral, nanotube and moiré magnets were performed, making the challenging study of magnetic skyrmions feasible.

Theoretical Prediction of Antiferromagnetic Skyrmion Crystal in Janus Monolayer CrSi2N2As2

An antiferromagnetic skyrmion crystal (AF-SkX), a regular array of antiferromagnetic skyrmions, is a fundamental phenomenon in the field of condensed-matter physics. So far, very few proposals have been made to realize the AF-SkX, and most have been based on three-dimensional (3D) materials. Herein, using first-principles calculations and Monte Carlo simulations, we report the identification of AF-SkX in a two-dimensional lattice of the Janus monolayer CrSi2N2As2. Arising from the broken inversion symmetry and strong spin-orbit coupling, a large Dzyaloshinskii-Moriya interaction is obtained in the Janus monolayer CrSi2N2As2. This, combined with the geometric frustration of its triangular lattice, gives rise to the skyrmion physics and long-sought AF-SkX in the presence of an external magnetic field. More intriguingly, this system presents two different antiferromagnetic skyrmion phases, and such a phenomenon is distinct from those reported in 3D systems. Furthermore, by contacting with Sc2CO2, the creation and annihilation of AF-SkX in Janus monolayer CrSi2N2As2 can be achieved through ferroelectricity. These findings greatly enrich the research on antiferromagnetic skyrmions.

Nano-scale collinear multi-Q states driven by higher-order interactions

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

Multi-Q states are 2D typically non-collinear spin textures that can be stabilized at the nanoscale and at zero magnetic field by interactions between multiple spins. Gutzeit et al. uncover a variety of multi-Q states in Fe/Rh atomic bilayers on the Ir(111) surface, including unexpected 2D collinear states.

Two-dimensional antiferromagnetic semiconductor T'-MoTeI from first principles

Two-dimensional intrinsic antiferromagnetic semiconductors are expected to stand out in the spintronic field. The present work finds the monolayer T'-MoTeI is intrinsically an antiferromagnetic semiconductor by using first-principles calculation. Firstly, the dimerized distortion of the Mo atoms causes T'-MoTeI to have dynamic stability, which is different from the small imaginary frequency in the phonon spectrum of T-MoTeI. Secondly, T'-MoTeI is an indirect-bandgap semiconductor with 1.35 eV. Finally, in the systematic study of strain effects, there are significant changes in the electronic structure as well as the bandgap, but the antiferromagnetic ground state is not affected. Monte Carlo simulations predict that the Néel temperature of T'-MoTeI is 95 K. The results suggest that the monolayer T'-MoTeI can be a potential candidate for spintronics applications.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Qstate with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

Tunable, Ferroelectricity-Inducing, Spin-Spiral Magnetic Ordering in Monolayer FeOCl

Spin spirals (SS) are a special case of noncollinear magnetism, where the magnetic-moment direction rotates along an axis. They have generated interest for novel phenomena, spintronics applications, and their potential formation in monolayers, but the search for monolayers exhibiting SS has not been particularly fruitful. Here, we employ density functional theory calculations to demonstrate that SS form in a recently synthesized monolayer, FeOCl. The SS wavelength and stability can be tuned by doping and uniaxial strain. The SS-state band gap is larger by 0.6 eV compared to the gap of both the ferromagnetic and antiferromagnetic state, enabling bandgap tuning and possibly an unusual formation of quantum wells in a single material via magnetic-field manipulation. The SS-induced out-of-plane ferroelectricity enables switching of the SS chirality by an electric field. Finally, forming heterostructures, for example, with graphene or boron nitride, maintains SS ordering and provides another method of modulation and a potential for magnetoelectric devices.

Curved Magnetism in CrI_{3}

Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI_{3}, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models.

Limited Ferromagnetic Interactions in Monolayers of MPS3 (M = Mn and Ni)

We present a systematic study of the electronic and magnetic properties of two-dimensional ordered alloys, consisting of two representative hosts (MnPS₃ and NiPS₃) of transition metal phosphorus trichalcogenides doped with 3d elements. For both hosts, our DFT + U calculations are able to qualitatively reproduce the ratios and signs of all experimentally observed magnetic couplings. The relative strength of all antiferromagnetic exchange couplings, both in MnPS₃ and in NiPS₃, can successfully be explained using an effective direct exchange model: it reveals that the third-neighbor exchange dominates in NiPS₃ due to the filling of the t_2g subshell, whereas for MnPS₃, the first-neighbor exchange prevails, owing to the presence of the t_2g magnetism. On the other hand, the nearest neighbor ferromagnetic coupling in NiPS₃ can only be explained using a more complex superexchange model and is (also) largely triggered by the absence of the t_2g magnetism. For the doped systems, the DFT + U calculations revealed that magnetic impurities do not affect the magnetic ordering observed in the pure phases, and thus, in general in these systems, ferromagnetism may not be easily induced by such a kind of elemental doping. However, unlike for the hosts, the first and second (dopant-host) exchange couplings are of similar order of magnitude. This leads to frustration in the case of antiferromagnetic coupling and may be one of the reasons of the observed lower magnetic ordering temperature of the doped systems.

Toward Exotic Layered Materials: 2D Cuprous Iodide

Heterostructures composed of 2D materials are already opening many new possibilities in such fields of technology as electronics and magnonics, but far more could be achieved if the number and diversity of 2D materials were increased. So far, only a few dozen 2D crystals have been extracted from materials that exhibit a layered phase in ambient conditions, omitting entirely the large number of layered materials that may exist at other temperatures and pressures. This work demonstrates how such structures can be stabilized in 2D van der Waals (vdw) stacks under room temperature via growing them directly in graphene encapsulation by using graphene oxide as the template material. Specifically, an ambient stable 2D structure of copper and iodine, a material that normally only occurs in layered form at elevated temperatures between 645 and 675 K, is produced. The results establish a simple route to the production of more exotic phases of materials that would otherwise be difficult or impossible to stabilize for experiments in ambient.

Evidence for a single-layer van der Waals multiferroic

Multiferroic materials have attracted wide interest because of their exceptional static^1-3 and dynamical^4-6 magnetoelectric properties. In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii-Moriya effect^3,7. This intrinsic coupling between the magnetic and dipolar order parameters results in high-strength magnetoelectric effects^3,8. Two-dimensional materials possessing such intrinsic multiferroic properties have been long sought for to enable the harnessing of magnetoelectric coupling in nanoelectronic devices^1,9,10. Here we report the discovery of type-II multiferroic order in a single atomic layer of the transition-metal-based van der Waals material NiI₂. The multiferroic state of NiI₂ is characterized by a proper-screw spin helix with given handedness, which couples to the charge degrees of freedom to produce a chirality-controlled electrical polarization. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurements with theoretical modelling and simulations, we detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry, and supports polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly reveals an ordered magnetic polar state that persists down to the ultrathin limit of monolayer NiI₂. These observations establish NiI₂ and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the two-dimensional limit.

Giant Biquadratic Exchange in 2D Magnets and Its Role in Stabilizing Ferromagnetism of NiCl_{2} Monolayers

Two-dimensional (2D) van der Waals (vdW) magnets provide an ideal platform for exploring, on the fundamental side, new microscopic mechanisms and for developing, on the technological side, ultracompact spintronic applications. So far, bilinear spin Hamiltonians have been commonly adopted to investigate the magnetic properties of 2D magnets, neglecting higher order magnetic interactions. However, we here provide quantitative evidence of giant biquadratic exchange interactions in monolayer NiX_{2} (X=Cl, Br and I), by combining first-principles calculations and the newly developed machine learning method for constructing Hamiltonian. Interestingly, we show that the ferromagnetic ground state within NiCl_{2} single layers cannot be explained by means of the bilinear Heisenberg Hamiltonian; rather, the nearest-neighbor biquadratic interaction is found to be crucial. Furthermore, using a three-orbitals Hubbard model, we propose that the giant biquadratic exchange interaction originates from large hopping between unoccupied and occupied orbitals on neighboring magnetic ions. On a general framework, our work suggests biquadratic exchange interactions to be important in 2D magnets with edge-shared octahedra.

Noncollinear Magnetic Order in Two-Dimensional NiBr2 Films Grown on Au(111)

Metal halides are a class of layered materials with promising electronic and magnetic properties persisting down to the two-dimensional limit. While most recent studies focused on the trihalide components of this family, the rather unexplored metal dihalides are also van der Waals layered systems with distinctive magnetic properties. Here we show that the dihalide NiBr2 grows epitaxially on a Au(111) substrate and exhibits semiconducting and magnetic behavior starting from a single layer. Through a combination of a low-temperature scanning-tunneling microscopy, low-energy electron diffraction, X-ray photoelectron spectroscopy, and photoemission electron microscopy, we identify two competing layer structures of NiBr2 coexisting at the interface and a stoichiometrically pure layer-by-layer growth beyond. Interestingly, X-ray absorption spectroscopy measurements revealed a magnetically ordered state below 27 K with in-plane magnetic anisotropy and zero-remanence in the single layer of NiBr2/Au(111), which we attribute to a noncollinear magnetic structure. The combination of such two-dimensional magnetic order with the semiconducting behavior down to the 2D limit offers the attractive perspective of using these films as ultrathin crystalline barriers in tunneling junctions and low-dimensional devices.

Topological spin crystals by itinerant frustration

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Interplay between Single-Ion and Two-Ion Anisotropies in Frustrated 2D Semiconductors and Tuning of Magnetic Structures Topology

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.

Possible Persistence of Multiferroic Order down to Bilayer Limit of van der Waals Material NiI2

Realizing a state of matter in two dimensions has repeatedly proven a novel route of discovering new physical phenomena. Van der Waals (vdW) materials have been at the center of these now extensive research activities. They offer a natural way of producing a monolayer of matter simply by mechanical exfoliation. This work demonstrates that the possible multiferroic state with coexisting antiferromagnetic and ferroelectric orders persists down to the bilayer flake of NiI₂. By exploiting the optical second-harmonic generation technique, both magnitude and direction of the ferroelectric order, arising from the cycloidal spin order, are successfully traced. The possible multiferroic state's transition temperature decreases from 58 K for the bulk to about 20 K for the bilayer. Our observation will spur extensive efforts to demonstrate multifunctionality in vdW materials, which have been tried mostly by using heterostructures of singly ferroic ones until now.

Skyrmion crystals in centrosymmetric itinerant magnets without horizontal mirror plane

We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an effective spin model with an anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction for a multi-band periodic Anderson model. We find that the anisotropic RKKY interaction gives rise to two distinct SkXs with different skyrmion numbers of one and two depending on a magnetic field. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a field-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd[Formula: see text]PdSi[Formula: see text], but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets.

Antiferromagnetic skyrmion crystals in the Rashba Hund's insulator on triangular lattice

Motivated by the importance of antiferromagnetic skyrmions as building blocks of next-generation data storage and processing devices, we report theoretical and computational analysis of a model for a spin-orbit coupled correlated Hund’s insulator magnet on a triangular lattice. We find that two distinct antiferromagnetic skyrmion crystal (AF-SkX) states can be stabilized at low temperatures in the presence of external magnetic field. The results are obtained via Monte Carlo simulations on an effective magnetic model derived from the microscopic electronic Hamiltonian consisting of Rashba spin-orbit coupling, as well as strong Hund’s coupling of electrons to classical spins at half-filling. The two AF-SkX phases are understood to originate from a classical spin liquid state that exists at low but finite temperatures. These AF-SkX states can be easily distinguished from each other in experiments as they are characterized by peaks at distinct momenta in the spin structure factor which is directly measured in neutron scattering experiments. We also discuss examples of materials where the model as well as the two AF-SkX states can be realized.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

New atomic-scale insights into the I/Ni(100) system: phase transitions and growth of an atomically thin NiI2 film

We use a traditional surface science approach to create and study an atomically thin NiI2 film (a promising two-dimensional ferromagnetic material) formed on nickel substrate as a result of molecular iodine adsorption. The I/Ni(100) system was examined with scanning tunneling microscopy (STM), low energy electron diffraction (LEED) and density functional theory calculations. We found out that the iodine adsorption on Ni(100) at 300 K leads to the formation of non-equilibrium phases, whereas the adsorption at elevated temperature (≥390 K) gives rise to the thermodynamically stable phases. In both cases, a simple p(2 × 2) structure is formed at 0.25 ML. As more iodine is adsorbed at 300 K, the p(2 × 2) phase is replaced by the small coexisting domains of c(3 × 2) and c(6 × 2) phases both corresponding to the coverage of 0.33 ML, while adsorption at elevated temperature results in the formation of only one c(3 × 2) phase. At further iodine adsorption the c(3 × 2) phase transforms into the c(5 × 2) one, while the c(6 × 2) phase - into the one both corresponding to the coverage of 0.40 ML. In addition to simple chemisorbed phases, a new shifted-row reconstruction of Ni(100) induced by iodine adsorption was discovered. At coverages exceeding 0.40 ML, we observed complex LEED patterns and superstructures in STM and assigned them to specific surface reconstructions. We also found that prolonged iodine dosing leads to the nucleation of nickel iodide islands and the growth of a 2D atomically thin iodide film partially exfoliated from the substrate.