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

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.

Toward Fully Multiferroic van der Waals SpinFETs: Basic Design and Quantum Calculations

Manipulating spin transport enhances the functionality of electronic devices, allowing them to surpass physical constraints related to speed and power. For this reason, the use of van der Waals multiferroics at the interface of heterostructures offers promising prospects for developing high-performance devices, enabling the electrical control of spin information. Our work focuses primarily on a mechanism for multiferroicity in two-dimensional van der Waals materials that stems from an interplay between antiferromagnetism and the breaking of inversion symmetry in certain bilayers. We provide evidence for spin-electrical couplings that include manipulating van der Waals multiferroic edges via external voltages and the subsequent control of spin transport including for fully multiferroic spin field-effect transistors.

Giant Modulation of the Second Harmonic Generation by Magnetoelectricity in Two-Dimensional Multiferroic CuCrP2S6

Multiferroic materials have attracted considerable attention owing to their unique magnetoelectric or magnetooptical properties. The recent discovery of few-layer van der Waals multiferroic crystals provides a new research direction for controlling the multiferroic properties in the atomic layer limit. However, research on few-layer multiferroic crystals is limited and the effect of thickness-dependent symmetries on those properties is less explored. In this study, the symmetries and magnetoelectric responses of van der Waals multiferroic CuCrP2S6 are investigated by optical second harmonic generation (SHG). Structural and magnetic phase transitions are successfully probed by the temperature-dependent SHG signals, revealing significant changes by applying the magnetic field reflecting the magnetoelectric effect. Moreover, it is found that symmetries and resultant magnetoelectric responses can be modulated by the number of layers. These results offer a new principle of controlling the multiferroicity and indicate that 2D van der Waals multiferroic material is a promising building block for functional nanodevices.

Atomic-Scale Visualization of Multiferroicity in Monolayer NiI2

Progress in layered van der Waals materials has resulted in the discovery of ferromagnetic and ferroelectric materials down to the monolayer limit. Recently, evidence of the first purely 2D multiferroic material was reported in monolayer NiI2. However, probing multiferroicity with scattering-based and optical bulk techniques is challenging on 2D materials, and experiments on the atomic scale are needed to fully characterize the multiferroic order at the monolayer limit. Here, scanning tunneling microscopy (STM) supported by density functional theory (DFT) calculations is used to probe and characterize the multiferroic order in monolayer NiI2. It is demonstrated that the type-II multiferroic order displayed by NiI2, arising from the combination of a magnetic spin spiral order and a strong spin-orbit coupling, allows probing the multiferroic order in the STM experiments. Moreover, the magnetoelectric coupling of NiI2 is directly probed by external electric field manipulation of the multiferroic domains. The findings establish a novel point of view to analyze magnetoelectric effects at the microscopic level, paving the way toward engineering new multiferroic orders in van der Waals materials and their heterostructures.

Optical Second Harmonic Generation of Low-Dimensional Semiconductor Materials

In recent years, the phenomenon of optical second harmonic generation (SHG) has attracted significant attention as a pivotal nonlinear optical effect in research. Notably, in low-dimensional materials (LDMs), SHG detection has become an instrumental tool for elucidating nonlinear optical properties due to their pronounced second-order susceptibility and distinct electronic structure. This review offers an exhaustive overview of the generation process and experimental configurations for SHG in such materials. It underscores the latest advancements in harnessing SHG as a sensitive probe for investigating the nonlinear optical attributes of these materials, with a particular focus on its pivotal role in unveiling electronic structures, bandgap characteristics, and crystal symmetry. By analyzing SHG signals, researchers can glean invaluable insights into the microscopic properties of these materials. Furthermore, this paper delves into the applications of optical SHG in imaging and time-resolved experiments. Finally, future directions and challenges toward the improvement in the NLO in LDMs are discussed to provide an outlook in this rapidly developing field, offering crucial perspectives for the design and optimization of pertinent devices.

Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures

Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Exploitation of mixed-valency chemistry for designing a monolayer with double ferroelectricity and triferroic couplings

Mixed-valence compounds possess both intriguing chemical and physical properties such as the intervalence charge transfer band and thus have been excellent model systems for the investigation of fundamental electron- and charge-transfer phenomena. Herein, we show that valence stratification can be a source of symmetry breaking and generating ferroelectricity in two-dimensional (2D) materials. We present ab initio computation evidence of the monolayer Cu2Cl3 structure with Cu ions being stratified into two separated layers of Cu(I) and Cu(II). Chemically, this unique monolayer not only entails lower formation energy than the bulk CuCl + CuCl2, but also enables the swapping of two valences through vertical ferroelectric switching, leading to a hitherto unreported chemical valencing phenomenon. Notably, the Jahn-Teller distortion of the Cu(II) layer results in another source of symmetry breaking and thus in-plane ferroelectricity. Apart from the valence swapping and self-contained double ferroelectricity, the monolayer's ferroelasticity is also coupled with in-plane ferroelectricity, while the monolayer's ferromagnetism is coupled with vertical polarization owing to the distinct magnetization of each Cu(I) and Cu(II) layer, thereby evoking the long-sought 2D triferroicity as well as triferroic couplings.

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.

Multi-state data storage in a two-dimensional stripy antiferromagnet implemented by magnetoelectric effect

A promising approach to the next generation of low-power, functional, and energy-efficient electronics relies on novel materials with coupled magnetic and electric degrees of freedom. In particular, stripy antiferromagnets often exhibit broken crystal and magnetic symmetries, which may bring about the magnetoelectric (ME) effect and enable the manipulation of intriguing properties and functionalities by electrical means. The demand for expanding the boundaries of data storage and processing technologies has led to the development of spintronics toward two-dimensional (2D) platforms. This work reports the ME effect in the 2D stripy antiferromagnetic insulator CrOCl down to a single layer. By measuring the tunneling resistance of CrOCl on the parameter space of temperature, magnetic field, and applied voltage, we verified the ME coupling down to the 2D limit and probed its mechanism. Utilizing the multi-stable states and ME coupling at magnetic phase transitions, we realize multi-state data storage in the tunneling devices. Our work not only advances the fundamental understanding of spin-charge coupling, but also demonstrates the great potential of 2D antiferromagnetic materials to deliver devices and circuits beyond the traditional binary operations.

General Synthesis of 2D Magnetic Transition Metal Dihalides via Trihalide Reduction

Two-dimensional (2D) transition metal dihalides (TMDHs) have been receiving extensive attention due to their diversified magnetic properties and promising applications in spintronics. However, controlled growth of 2D TMDHs remains challenging owing to their extreme sensitivity to atmospheric moisture. Herein, using a home-built nitrogen-filled interconnected glovebox system, a universal chemical vapor deposition synthesis route of high-quality 2D TMDH flakes (1T-FeCl₂, FeBr₂, VCl₂, and VBr₂) by reduction of their trihalide counterparts is developed. Representatively, ultrathin (∼8.6 nm) FeCl₂ flakes are synthesized on SiO₂/Si, while on graphene/Cu foil the thickness can be down to monolayer (1L). Reflective magnetic circular dichroism spectroscopy shows an interlayer antiferromagnetic ordering of FeCl₂ with a Neel temperature at ∼17 K. Scanning tunneling microscopy and spectroscopy further identify the atomic-scale structures and band features of 1L and bilayer FeCl₂ on graphene/Cu foil.

Multiferroicity in a Two-Dimensional Non-van der Waals Crystal of AgCr2X4 (X = S or Se)

Two-dimensional (2D) intrinsic multiferroics have long been pursued not only for their potential technological applications but also as model systems for studying emergent quantum phenomena and coupling mechanisms between various order parameters in low-dimensional space. However, the realization of 2D multiferroics is still a challenge. In this paper, we reveal that 2D AgCr₂X₄ (X = S or Se) crystals, which have been synthesized from the non-van der Waals (non-vdW) AgCrX₂ bulk phase, are type I half-metallic/metallic multiferroics in which ferroelectricity and ferromagnetism coexist. The off-centering displacement of the Ag ion introduces out-of-plane polarization, and the magnetism originates from the interactions between Cr atoms. Remarkably, AgCr₂Se₄ shows topologically nontrivial spin textures, such as Meron pairs and Néel-type skyrmions, under suitable temperatures and magnetic fields. Our findings demonstrate that 2D multiferroics can be achieved from non-vdW materials and in turn open a new avenue for 2D multiferroics.

Observation of Giant Surface Second-Harmonic Generation Coupled to Nematic Orders in the van der Waals Antiferromagnet FePS3

Second-harmonic generation has been applied to study lattice, electronic, and magnetic proprieties in atomically thin materials. However, inversion symmetry breaking is usually required for the materials to generate a large signal. In this work, we report a giant second-harmonic generation that arises below the Néel temperature in few-layer centrosymmetric FePS₃. A layer-dependent study indicates the detected signal is from the second-order nonlinearity of the surface. The magnetism-induced surface second-harmonic response is 2 orders of magnitude larger than those reported in other magnetic systems, with the surface nonlinear susceptibility reaching 0.08-0.13 nm²/V in 2-5 L samples. By combing linear dichroism and second-harmonic generation experiments, we further confirm the giant second-harmonic generation is coupled to nematic orders formed by the three possible Zigzag antiferromagnetic domains. Our study shows that the surface second-harmonic generation is also a sensitive tool to study antiferromagnetic states in centrosymmetric atomically thin materials.

Multiferroic-Enabled Magnetic-Excitons in 2D Quantum-Entangled Van der Waals Antiferromagnet NiI2

Matter-light interaction is at the center of diverse research fields from quantum optics to condensed matter physics, opening new fields like laser physics. A magnetic exciton is one such rare example found in magnetic insulators. However, it is relatively rare to observe that external variables control matter-light interaction. Here, it is reported that the broken inversion symmetry of multiferroicity can act as an external knob enabling magnetic excitons in the van der Waals antiferromagnet NiI₂ . It is further discovered that this magnetic exciton arises from a transition between Zhang-Rice-triplet and Zhang-Rice-singlet fundamentally quantum-entangled states. This quantum entanglement produces an ultrasharp optical exciton peak at 1.384 eV with a 5 meV linewidth. The work demonstrates that NiI₂ is 2D magnetically ordered with an intrinsically quantum-entangled ground state.

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.

First observation on emergence of strong room-temperature ferroelectricity and multiferroicity in 2D-Ti3C2Tx free-standing MXene film

Two-dimensional (2D) multiferroics are key candidate materials towards advancement of smart technology. Here, we employed a simple synthesis approach to address the long-awaited dream of developing ferroelectric and multiferroic 2D materials, especially in the new class of materials called MXenes. The etched Ti₃C₂T_x MXene was first synthesized after HF-treatment followed by a delamination process for successful synthesis of free-standing Ti₃C₂T_x film. The free-standing film was then exposed to air at room-temperature and heated at different temperatures to form a TiO₂ layer derived from the Ti₃C₂T_x MXene itself. The ferroelectric measurement showed a clear polarization hysteresis loop at room-temperature. Also, due to the reported ferromagnetic behavior of Ti₃C₂T_x MXene, our composite could show multiferroic properties at room-temperature. The magnetoelectric coupling test was also performed that showed a clear, switchable spontaneous polarization under applied magnetic field. TiO₂ is reported to be an incipient ferroelectric that assumes a ferroelectric phase in composite form. The structural and morphological analysis confirmed successful synthesis of free-standing film and the Raman spectroscopy revealed the formation of different phases of TiO₂ and the observed ferroelectricity could be due to structural deformation as a result of the formation of this new phase. The measured value of remanent polarization is 0.5 μC cm⁻². This is the first report on the existence of a ferroelectric phase and multiferroic coupling in 2D free-standing MXene film at room-temperature which opens-up the possibility of 2D material-based electric and magnetic data storage applications at room-temperature.

Two-dimensional (2D) multiferroics are key candidate materials towards advancement of smart technology.

First-principles study on multiferroicity in the Cr2Ge2Te6/In2Se3 heterostructure influenced by finite strains

Multiferroic materials that have more than two ferroicities at the same time have long been regarded as one of the strongest candidates to achieve technological breakthroughs in many kinds of nanodevice applications. Various types of multiferroic materials have been discovered and devised to date; however, related studies have been conducted without identifying a complete winner because each has a decisive disadvantage. The recently discovered multiferroicity in the 2D Cr₂Ge₂Te₆/In₂Se₃ van der Waals heterostructure represents an important opportunity to create a new turning point in multiferroic research. Through first-principles density functional theory calculations, we studied the preferential characteristics of the spin magnetic moment of 2D Cr₂Ge₂Te₆ induced by the ferroelectric switching of the In₂Se₃ monolayer in the presence of the strains that inevitably exist in any kind of heterostructure. From the results, we found that the multiferroicity in the Cr₂Ge₂Te₆/In₂Se₃ heterostructure reacts quite sensitively to the strain level, revealing the possibility of manipulating multiferroic properties in the structure.

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.