Two-dimensional Multiferroics Research Articles

Evidence for multiferroicity in single-layer CuCrSe2

Multiferroic materials, which simultaneously exhibit ferroelectricity and magnetism, have attracted substantial attention due to their fascinating physical properties and potential technological applications. With the trends towards device miniaturization, there is an increasing demand for the persistence of multiferroicity in single-layer materials at elevated temperatures. Here, we report high-temperature multiferroicity in single-layer CuCrSe2, which hosts room-temperature ferroelectricity and 120 K ferromagnetism. Notably, the ferromagnetic coupling in single-layer CuCrSe2 is enhanced by the ferroelectricity-induced orbital shift of Cr atoms, which is distinct from both types I and II multiferroicity. These findings are supported by a combination of second-harmonic generation, piezo-response force microscopy, scanning transmission electron microscopy, magnetic, and Hall measurements. Our research provides not only an exemplary platform for delving into intrinsic magnetoelectric interactions at the single-layer limit but also sheds light on potential development of electronic and spintronic devices utilizing two-dimensional multiferroics.

Ferrielectricity controlled widely-tunable magnetoelectric coupling in van der Waals multiferroics

The discovery of various primary ferroic phases in atomically-thin van der Waals crystals have created a new two-dimensional wonderland for exploring and manipulating exotic quantum phases. It may also bring technical breakthroughs in device applications, as evident by prototypical functionalities of giant tunneling magnetoresistance, gate-tunable ferromagnetism and non-volatile ferroelectric memory etc. However, two-dimensional multiferroics with effective magnetoelectric coupling, which ultimately decides the future of multiferroic-based information technology, has not been realized yet. Here, we show that an unconventional magnetoelectric coupling mechanism interlocked with heterogeneous ferrielectric transitions emerges at the two-dimensional limit in van der Waals multiferroic CuCrP2S6 with inherent antiferromagnetism and antiferroelectricity. Distinct from the homogeneous antiferroelectric bulk, thin-layer CuCrP2S6 under external electric field makes layer-dependent heterogeneous ferrielectric transitions, minimizing the depolarization effect introduced by the rearrangements of Cu+ ions within the ferromagnetic van der Waals cages of CrS6 and P2S6 octahedrons. The resulting ferrielectric phases are characterized by substantially reduced interlayer magnetic coupling energy of nearly 50% with a moderate electric field of 0.3 V nm−1, producing widely-tunable magnetoelectric coupling which can be further engineered by asymmetrical electrode work functions.

Voltage-Controlled Dzyaloshinskii-Moriya Interaction Torque Switching of Perpendicular Magnetization.

Magnetization switching is the most important operation in spintronic devices. In modern nonvolatile magnetic random-access memory (MRAM), it is usually realized by spin-transfer torque (STT) or spin-orbit torque (SOT). However, both STT and SOT MRAM require current to drive magnetization switching, which will cause Joule heating. Here, we report an alternative mechanism, Dzyaloshinskii-Moriya interaction (DMI) torque, that can realize magnetization switching fully controlled by voltage pulses. We find that a consequential voltage-controlled reversal of DMI chirality in multiferroics can lead to continued expansion of a skyrmion thanks to the DMI torque. Enough DMI torque will eventually make the skyrmion burst into a quasiuniform ferromagnetic state with reversed magnetization, thus realizing the switching of a perpendicular magnet. The discovery is demonstrated in two-dimensional multiferroics, CuCrP_{2}Se_{6} and CrN, using first-principles calculations and micromagnetic simulations. As an example, we applied the DMI torque for simulating leaky-integrate-fire functionality of biological neurons. Our discovery of DMI torque switching of perpendicular magnetization provides tremendous potential toward magnetic-field-free and current-free spintronic devices, and neuromorphic computing as well.

Ferroelectrically tunable magnetic skyrmions in two-dimensional multiferroics.

Magnetic skyrmions are topologically protected entities that are promising for information storage and processing. Currently, an essential challenge for future advances of skyrmionic devices lies in achieving effective control of skyrmion properties. Here, through first-principles and Monte-Carlo simulations, we report the identification of nontrivial topological magnetism in two-dimensional multiferroics of Co2NF2. Because of ferroelectricity, monolayer Co2NF2 exhibits a large Dzyaloshinskii-Moriya interaction. This together with exchange interaction can stabilize magnetic skyrmions with the size of sub-10 nm under a moderate magnetic field. Importantly, arising from the magnetoelectric coupling effect, the chirality of magnetic skyrmions is ferroelectrically tunable, producing the four-fold degenerate skyrmions. When interfacing with monolayer MoSe2, the creation and annihilation of magnetic skyrmions, as well as phase transition between skyrmion and skyrmion lattice, can be realized in a ferroelectrically controllable fashion. A dimensionless parameter κ' is further proposed as the criterion for stabilizing magnetic skyrmions in such multiferroic lattices. Our work greatly enriches the two-dimensional skyrmionics and multiferroics research.

Two-Dimensional Multiferroics with Intrinsic Magnetoelectric Coupling in A-Site Ordered Perovskite Monolayers

The magnetoelectric coupling effect in multiferroics provides a route to realize the control of magnetism by electric field. Here, we demonstrate the coexistence and coupling of ferroelectricity and ferromagnetism in designed A-site ordered perovskite oxide monolayers by combining symmetry analysis and first-principles calculation. These monolayers all exhibit a layered ordering and tilt distortion, and some of them exhibit rotation or Jahn-Teller distortion simultaneously, leading to the emergence of in-plane ferroelectricity. The Mn-based monolayers exhibit robust ferromagnetism, while some monolayers tend to form E-type spin order due to the splitting of the nearest-neighbor exchange interactions. Whether polarization reversal can lead to magnetization reversal depends on the mode of ferroelectric switching, that is, only the ferroelectric switching that reversing the tilt distortion can lead to magnetization reversal. This work demonstrates the feasibility of controlling the direction of magnetization by electric field in the monolayer limit of perovskites.

Simultaneously improving Rashba-type and Zeeman effects in two-dimensional multiferroics

First-principles calculations are performed to investigate Rashba-type and Zeeman effects in two-dimensional three-atom-layer structures $X\mathrm{Te}$/MnTe/$X\mathrm{Te}$ ($XMX, X=\text{Sn}$, Ge). It is found that the Rashba-type and Zeeman effects that typically compete against each other rather cooperatively work together and are improved in $XMX$, as compared to $X\mathrm{Te}/X\mathrm{Te}/X\mathrm{Te}$ ($XXX$). This cooperation and improvement are highly required in Majorana qubits for topological quantum computing, Josephson junction of topological superconductivity, and other phenomena. The Rashba-type effect is improved because replacing $X\mathrm{Te}$ by MnTe leads to a reduction of the thickness of $XMX$ and increases the interaction between the surface state of the lowest conduction bands and its neighboring states. The improved Zeeman effect in the $XMX$ structure arises from s-d and p-d exchange interactions between Te and Mn ions. The present strategy of simultaneously largely improving Rashba-type and Zeeman effects therefore provides a route to realize stable Majorana fermions, topological superconductivity, and other phenomena that require both large Rashba-type and Zeeman effects.

Coexistence and Coupling of Spin-Induced Ferroelectricity and Ferromagnetism in Perovskites.

Spin-induced ferroelectricity usually does not occur in perovskites with simple collinear magnetic structures. Here, we demonstrate that in even-layer perovskite systems, some common distortion modes involving octahedral rotation and Jahn-Teller distortion can break the inversion symmetry, allowing the emergence of spin-dependent out-of-plane polarization in a simple magnetic structure. Such spin-induced ferroelectricity is very common in double-perovskite systems and can coexist with ferromagnetism or ferrimagnetism above room temperature. We explain its origin by modifying the spin-dependent p-d hybridization mechanism. Our Letter provides a universal design for two-dimensional multiferroics and enables the control of polarization by means of a magnetic field.

Multiferroic materials based on transition-metal dichalcogenides: Potential platform for reversible control of Dzyaloshinskii-Moriya interaction and skyrmion via electric field

Exploring novel two-dimensional multiferroic materials that can realize electric-field control of two-dimensional magnetism has become an emerging topic in spintronics. Using first-principles calculations, we demonstrate that non-metallic bilayer transition metal dichalcogenides (TMDs) can be an ideal platform for building multiferroics by intercalated magnetic atoms. Moreover, we unveil that with Co intercalated bilayer MoS2, Co(MoS2)2, two energetic degenerate states with opposite chirality of Dzyaloshinskii-Moriya interaction (DMI) are the ground states, indicating electric-field control of the chirality of topologic magnetism such as skyrmions can be realized in this type of materials by reversing the electric polarization. These findings pave the way for electric-field control of topological magnetism in two-dimensional multiferroics with intrinsic magnetoelectric coupling.

Intrinsic ferromagnetic triferroicity in bilayer T′-VTe2

Multiferroics, which combines two or more ferroic orders, is of significant fundamental and practical importance in condensed-matter physics and materials science. Although multiferroics has been broadly studied for decades, intrinsic triferroicity is rarely explored, especially with ferromagnetic ordering. Here, we propose a general mechanism for realizing intrinsic ferromagnetic triferroicity in two-dimensional van der Waals lattices through interlayer sliding and further demonstrate it in bilayer T′-VTe2. Using first-principles calculations, we reveal that bilayer T′-VTe2 exhibits spontaneous ferromagnetism, ferroelasticity, and ferroelectricity simultaneously, yielding the long-sought intrinsic triferroicity. We further predict that such a system could possess many distinctive physics, for example, the ferroelastic control of magnetization orientation and ferroelectric control of magnetic moment distribution. The explored mechanism and phenomena not only greatly enrich the research on two-dimensional multiferroics but also provide a promising avenue to realize novel quantum device applications.

Two-dimensional multiferroics in a breathing kagome lattice

Geometric frustrated kagome systems can show complex and exotic magnetic properties. We theoretically predict ways in which these can be manipulated in two-dimensional (2D) multiferroic materials from first-principles density functional theory calculations. We propose that ${\mathrm{Ti}}_{3}{X}_{8}$ ($X=\mathrm{Br}$ or I) compounds are shown to form 2D intrinsic semiconductors with breathing kagome lattices containing coexisting ferroelectric (FE) and ferromagnetic ordering. Inside the lattice, Ti atoms distort from high-symmetry locations to produce trimers with shorter interatomic distances that form the basis of local cluster magnets. Lattice breathing interchanges trimer patterns, switching the direction of out-of-plane FE polarization while simultaneously rearranging the interactions between the cluster magnets. FE switching of the monolayer ${\mathrm{Ti}}_{3}{X}_{8}$, which is concomitant with the direction reversal of the vector of the Dzyaloshinskii-Moriya interaction, is feasible to be manipulated by the application of out-of-plane electric fields. Through the interlayer interaction, the coupling of FE and magnetism is achieved in bilayer ${\mathrm{Ti}}_{3}{\mathrm{I}}_{8}$. The magnetic configurations are transformed between interlayer ferromagnetism and antiferromagnetism by switching the FE polarization directions of bilayer ${\mathrm{Ti}}_{3}{\mathrm{I}}_{8}$. Our findings expand the arena for realizing 2D multiferroics and magnetoelectric effect.

Intrinsic two-dimensional multiferroicity in CrNCl2 monolayer* *Project supported by the National Key R&D Program of China (Grant No. 2019YFB1704600), the International Cooperation Research Project of Shenzhen (Grant No. GJHZ20180413182004161), the Hubei Provincial Natural Science Foundation of China (Grant No. 2020CFA032), the National Natural Science Foundation of China (Grant No. 51805395), and the China Scholarship Council (Grant No. 201906270142).

Two-dimensional multiferroics, which simultaneously possess ferroelectricity and magnetism in a single phase, are well-known to possess great potential applications in nanoscale memories and spintronics. On the basis of first-principles calculations, a CrNCl2 monolayer is reported as an intrinsic multiferroic. The CrNCl2 has an antiferromagnetic ground state, with a Néel temperature of about 88 K, and it exhibits an in-plane spontaneous polarization of 200 pC/m. The magnetic moments of CrNCl2 mainly come from the d5 xy orbital of the Cr cation, but the plane of the d xy orbital is perpendicular to the direction of the ferroelectric polarization, which hardly suppresses the occurrence of ferroelectricity. Therefore, the multiferroic exits in the CrNCl2. In addition, like CrNCl2, the CrNBr2 is an intrinsic multiferroic with antiferromagnetic-ferroelectric ground state while CrNI2 is an intrinsic multiferroic with ferromagnetic-ferroelectric ground state. These findings enrich the multiferroics in the two-dimensional system and enable a wide range of applications in nanoscale devices.

Ferroelastic-ferroelectric multiferroics in a bilayer lattice

Two-dimensional multiferroics, combined with ferroelastic and ferroelectric orders, enable unprecedented exploration of applications, such as high-density multistate storage. However, current ferroelastic-ferroelectric-multiferroic research is based on the paradigm of unique symmetry in a single-layer lattice, which restricts ferroelastic ferroelectricity to being rarely explored. Here, going beyond the existing paradigm, we report a design principle for realizing ferroelastic ferroelectricity using the van der Waals interaction as perturbation in a bilayer lattice. Using first principles, we show that, through layer-stacking, bilayer ${\mathrm{ZrI}}_{2}$ not only possesses 120 \ifmmode^\circ\else\textdegree\fi{} ferroelasticity due to its crystal symmetry but also holds out-of-plane and in-plane polarizations caused by interlayer charge redistribution, thereby achieving ferroelastic-ferroelectric multiferroics in a bilayer lattice. The switch of out-of-plane polarization relates to interlayer sliding, while in-plane polarization reversal correlates with 120 \ifmmode^\circ\else\textdegree\fi{} ferroelastic switching. Based on this fact, we propose the six-logic-state multiferroicity. This paper illustrates a tantalizing scheme for achieving and developing two-dimensional ferroelastic ferroelectricity.

Terahertz optics-driven phase transition in two-dimensional multiferroics

Displacive martensitic phase transition is potentially promising in semiconductor-based data storage applications with fast switching speed. In addition to traditional phase transition materials, the recently discovered two-dimensional ferroic materials are receiving a lot of attention owing to their fast ferroic switching dynamics, which could tremendously boost data storage density and enhance read/write speed. In this study, we propose that a terahertz laser with an intermediate intensity and selected frequency can trigger ferroic order switching in two-dimensional multiferroics, which is a damage-free noncontacting approach. Through first-principles calculations, we theoretically and computationally investigate optically induced electronic, phononic, and mechanical responses of two experimentally fabricated multiferroic (with both ferroelastic and ferroelectric) materials, β-GeSe and α-SnTe monolayer. We show that the relative stability of different orientation variants can be effectively manipulated via the polarization direction of the terahertz laser, which is selectively and strongly coupled with the transverse optical phonon modes. The transition from one orientation variant to another can be barrierless, indicating ultrafast transition kinetics and the conventional nucleation-growth phase transition process can be avoidable.

Two-dimensional multiferroics.

Due to unprecedented application prospects such as high-density and low-power multistate storage, spintronics and nanoelectronics, two-dimensional (2D) multiferroics, coupled with at least two ferroic orders, have gotten a lot of interest in recent years. Multiple functions can be achieved in 2D multiferroics via coupling phenomena such as magnetoelectricity, piezoelectricity, and magnetoelasticity, which offers technical support for the creation of multifunctional devices. The research progress of 2D ferromagnetic-ferroelectric multiferroic materials, ferroelectric-ferroelastic multiferroic materials, and ferromagnetic-ferroelastic materials in recent years is reviewed in this paper. The categorization of 2D multiferroics is explored in terms of the multiple sources of ferroelectricity. The top-down approaches and the bottom-up methods used to fabricate 2D multiferroics materials are introduced. Finally, the authors outline potential research prospects and application scenarios for 2D multiferroic materials.

Electrical control of topological spin textures in two-dimensional multiferroics.

The electrical control of topological magnetism is an intensive topic in spintronic devices. Here, using first-principles calculations and micromagnetic simulations, we show the potential of two-dimensional (2D) magnetoelectric multiferroics in the area of topological magnetism. Intrinsic Dzyaloshinskii-Moriya interactions (DMIs) can promote the stabilization of sub-10 nm skyrmions or bimerons in 2D multiferroics. In addition, the electric polarization in 2D multiferroics provides an opportunity for the electrical control of interfacial DMI chirality and thereby the topological magnetism. These results provide a promising route for the modulation of topological magnetism in 2D spintronic devices.

Magnetoelectric Studies of Close-Packed and Hierarchically Ordered CoFe2O4/Pb(Zr0.52Ti0.48)O3/La0.6Sr0.4MnO3/LaNiO3 Multiferroic Thin Films

Enhanced magnetoelectric effects in two-dimensional multiferroics promise greater interests for fundamental understanding and for device applications. To ameliorate properties and multifunctionality of magnetoelectric materials, highly ordered multiferroic thin films ought to be optimally designed with a high surface area and with a minimum contact area between the substrate and the films. Fabrication of hierarchically ordered, hemispherical close-packed free-standing multiferroic thin film structures of CoFe2O4 (CFO)/Pb(Zr0.52Ti0.48)O3 (PZT)/La0.6Sr0.4MnO3 (LSMO)/LaNiO3 (LNO) on a Pt/Ti/SiO2/Si substrate using a RF magnetron sputtering technique is reported here. The hemispherical space inside the shell structures, inherited from the spherical polymer, are shown by the cross-sectional scanning transmission electron microscopy. Importantly, the observed enhancement of remanent polarization is elucidated based on the facts, like the generation of a high level of compressive stress, a large thermal expansion coefficient of LSMO, and a minimal lattice mismatch with the PZT thin film.

Ferroelectricity and ferromagnetism in a VOI2 monolayer: Role of the Dzyaloshinskii-Moriya interaction

Multiferroics with intrinsic ferromagnetism and ferroelectricity are highly desired but rather rare, while most ferroelectric magnets are antiferromagnetic. A recent theoretical work [Phys. Rev. B {\bf 99}, 195434 (2019)] predicted that oxyhalides VO$X_2$ ($X$: halogen) monolayers are two-dimensional multiferroics by violating the empirical $d^0$ rule. Most interestingly, the member VOI$_2$ are predicted to exhibit spontaneous ferromagnetism and ferroelectricity. In this work, we extend the previous study on the structure and magnetism of VOI$_2$ monolayer by using density functional theory and Monte Carlo simulation. The presence of the heavy element iodine with a strong spin-orbit coupling leads an effective Dzyaloshinskii-Moriya interaction in the polar structure, which favors a short-period spiral a magnetic structure.. Another interesting result is that the on-site Coulomb interaction can strongly suppress the polar distortion thus leading to a ferromagnetic metallic state. Therefore, the VOI2 monolayer is either a ferroelectric insulator with spiral magnetism or a ferromagnetic metal, instead of a ferromagnetic ferroelectric system. Our study highlights the key physical role of the Dzyaloshinskii-Moriya interaction.

Electric field control of molecular magnetic state by two-dimensional ferroelectric heterostructure engineering

Two-dimensional multiferroics have attracted tremendous attention due to their intriguing physics and promising applications. However, it has been a major challenge to discover and design two-dimensional multiferroic materials with large electric polarization and strong magnetoelectric coupling. In this work, we propose a strategy to design a two-dimensional van der Waals heterostructure with strong magnetoelectric coupling by stacking a transition metal phthalocyanine (TMPc) molecule with ferroelectric monolayer In2Se3. By first-principles electronic structure calculations, we predict that the magnetic states of the TMPc molecule can be controlled by electrically switching the polarization direction of In2Se3 using an external electric field. This strong magnetoelectric coupling effect originates from the interfacial charge transfer and orbital splitting, resulting in the different magnetic states of TMPc/In2Se3 heterostructures in two opposite ferroelectric phases. Based on the TMPc/In2Se3 heterostructure, a high-density magnetic memory device is proposed for pure electric writing and magnetic reading. Our predictions may open avenues for finding and designing multiferroic heterostructures by using two-dimensional ferroelectric materials and zero-dimensional magnetic molecules with a strong proximity effect.

Design of Two-Dimensional Multiferroics with Direct Polarization-Magnetization Coupling.

The recent discovery of two-dimensional (2D) ferromagnetism in van der Waals materials has opened the door to the control of 2D magnetism by means of electric field. Here we demonstrate the magnetization reversal through switching polarization in a designed 2D multiferroic oxide by combining group theory analysis and first-principles calculation. We show that ferroelectricity can be induced by a specific octahedral rotation in a perovskite bilayer. Ferromagnetism can be introduced simultaneously by extending the guideline to the B-site ordered double-perovskite bilayer. We have found two coupling mechanisms between polarization and magnetization that enable the reversal of the in-plane magnetization by ferroelectric switching. Our work provides guidelines for the design of 2D multiferroics with intrinsic magnetoelectric coupling and helps to control the 2D magnetism by electric field.

Strongly Correlated Molecular Magnet with Curie Temperature above 60 K

Summary Two-dimensional crystals with ferromagnetic ordering would lead to unprecedented possibilities for magnetic, magneto-optic, and magnetoelectric applications. However, long-range ferromagnetic ordering in two-dimensional van der Waals materials is strongly diminished by thermal fluctuation, while three-dimensional systems show the stiffness of magnetic ordering temperature to magnetic fields. Here, we report the discovery of intrinsic ferromagnetic ordering temperature of 60 K in an iron/tetracyanoquinodimethane layer via superconducting precursor. In such a molecular ferromagnet, an unprecedented control of ferromagnetic fluctuation temperature by ∼200% improvement is realized through magnetic fields. We demonstrate magnetodielectric coupling with a concomitant transition in magnetic ordering. A small magnetic field of 0.01 T enables an effective route to realize a sizable transition shift in magnetodielectric states. Stimulated by photoirradiation, it manifests a hidden metallic conducting state, declaring a metallic ferromagnet. The molecular ferromagnet and photoirradiation-induced hidden metallic phase present a “holy grail” in the field of molecular conducting magnets.