Recent advances in growth, characterization, and application of two-dimensional multiferroic materials

Abstract

Since the successful experimental fabrication of two-dimensional (2D) monolayer van der Waals (vdW) NiI₂ material, which belongs to type II multiferroics, there has been a surge of interest in the research on 2D multiferroics. Furthermore, 2D multiferroics exhibit multiple ferroic orders, expanding their applications to high-density data storage, low-power multistate memories, spintronics, nanoelectronics, and actuators, among others. The coupling of magnetoelectricity, magnetoelasticity, piezoelectricity, and magneto−valley effects in 2D multiferroics offers technological advancements for multifunctional devices. Therefore, this review focuses on recent progress in ferromagnetic−ferroelectric materials as well as ferromagnetic-ferroelastic materials, and explores their categorization, growth methods, and characterization techniques. Finally, potential research challenges, along with prospects and application scenarios for 2D multiferroic materials, are outlined.

Graphical abstract

Keywords

two-dimensional materials / multiferroic materials / magnetoelectric coupling

1 Introduction

Multiferroic materials, which exhibit more than one ferroic ordering – ferroelectricity (FE), ferromagnetism (FM), ferroelasticity (FA), ferrotoroidicity (FT), ferrovalley – in a single phase, are well known for their fundamental and technological applications, such as nonvolatile memories, sensors, efficient renewable energy harvesting, spintronics, synaptic devices, and actuators [1−7]. Over the past decades, numerous studies on different bulk multiferroics have been reported, and most of them were complex oxides [1, 8−11]. However, traditional bulk multiferroic materials are difficult to meet the demands of practical applications because of their size limitation, polarization origin, interface effect, and reversal mechanism. In comparison to the traditional systems, 2D materials exhibit obviously different and fancifully physical properties with stable layered structures depending on weak interlayer and strong intralayer forces [4, 12−16]. Recently, the first pure 2D monolayer NiI₂ multiferroic material was experimentally prepared [13]. Therefore, new strategies for designing artificial 2D multiferroic materials have been naturally raised [17−18]. These compounds consisting of the weak van der Waals (vdW) forces between the layers can easily reach the 2D limit to achieve the building blocks with different and novel properties [19−26]. 2D single layers can be easily exfoliated, stacked and twisted, resulting in a series of emergent phenomena including multiferroicity [27−30].

FE destructs the space-inversion symmetry, meanwhile FM breaks the time-reversal symmetry. However, FA does not break the space-inversion symmetry and the time-reversal symmetry. Moreover, FT destructs both the space-inversion and the time-reversal symmetry [4, 31], as shown in Fig.1. Generally, multiferroics can often be classified as type I and type II, which are based on the weak or strong coupling between the orders [2, 31−33], as depicted in Fig.2. Meanwhile, type I multiferroics can be also divided into three subgroups: (i) lone-pair multiferroics; (ii) charge ordered multiferroics; (iii) geometrically frustrated multiferroics. Charge-ordered multiferroics are often observed in transition metal compounds with ions that formally have a mixed valence. The advantages of type-I multiferroics are the large electric polarization (of nonmagnetic origin) and high magnetic transition temperatures, as magnetic frustration is not required. Bringing FE and magnetism together is a problem, since FE usually involves transition metal ions with empty d-shells that are non-magnetic [34]. An additional challenge on the way to the electric control of magnetism is the coupling between the electric polarization and magnetization in bulk and at domain walls.

Fig.1 Time-reversal and spatial-inversion symmetry in ferroics. (a) Ferromagnets. The local magnetic moment $\mathit{m}$ represented by a charge that dynamically traces an orbit by the arrowheads. A spatial inversion does not induce change, but time reversal changes the orbit and thus $\mathit{m}$. (b) Ferroelectrics. The local dipole moment $\mathit{p}$ denoted by a positive point charge, which depends asymmetrically on a crystallographic unit cell leading to disappearance of net charge. There is spatial inversion reverses $\mathit{p}$. (c) Multiferroics possess both ferromagnetic and ferroelectric order with neither symmetry. Reproduced from Ref. [1].

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Fig.2 Different ferroic orders with respect to the different time and space reversal symmetry and mutual cross-coupling, (a) the initial ferroic orders: ferromagnetism ($\mathit{M}$), ferroelectricity ($\mathit{P}$), and ferroelasticity ($\mathit{\epsilon }$); their conjugate magnetic ($\mathit{H}$), electric ($\mathit{E}$), and stress ($\mathit{\sigma }$) fields; and the cross-couplings between them (black and green arrows), (b) types of multiferroics, (c) mutual cross-coupling between ferroic orders. (d) Schematic illustration magnetic−elastic−electric couplings in multiferroic materials. $\mathit{M}$ denotes magnetization, $\mathit{S}$ represents mechanical strain, and $\mathit{P}$ describes dielectric polarization. (a) Reproduced from Ref. [35]; (b) Reproduced from Ref. [31]; (c) Reproduced from Ref. [36].

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Moreover, type II multiferroic is a FE as a derivative of magnetism in small polarizations and strong magnetoelectric coupling at low transition temperatures.

Type-II multiferroics exhibiting strong magnetoelectric couplings [1, 32] offer enormous technological applications, such as spintronics, memory and efficient energy management in computation [38−40]. Achieving multiferroicity and enhancing magnetoelectric coupling are accompanied by phase changes through magnetic phase transitions. Even plenty of theoretical studies on 2D multiferroic materials have been carried on, experimental explorations just have made a few breakthroughs in 2D multiferroic materials with single layers, such as NiI₂ [13] and Cr₂S₃ [40]. In addition, most materials, particularly multiferroic materials, face significant technological challenges in terms of downsizing and integration, which prompt scientists to seek out low-dimensional multiferroic materials with atomic thickness. Unlike bulk materials, 2D systems intriguingly tend to host multiple ferroic orders in one single phase, e.g., FE and FA, which was predicted in monolayer group IV monochalcogenides [41], and FM and FE in monolayer α-SnO [42]. 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 scanning tunnel microscopy (STM) experiments [43]. In this review, current research advances in 2D multiferroic materials have been discussed. A systematic review on fabrication methods, advances in characterization and experimental discoveries, as well as challenge and prospects for 2D multiferroic materials is introduced.

2 Growth methods of 2D multiferroic materials and advances in characterizations

Both top-down and bottom-up synthesis strategies of 2D materials are usually applied to research in the laboratory. Top-down schemes usually involve mechanical cleavage and chemical exfoliation by means of solvent or intercalated ion. The mechanical cleavage method depends on repeatedly exfoliating from bulk crystals with an adhesive tape, which was first used for the stripped graphene and then has been developed to boron nitride (BN), transition metal dichalcogenides (TMDs), etc. The acquired layered materials exhibit high crystalline nature and clean surface area, however, the thickness and lateral size of the obtained samples become uncontrollable. By contrast, chemical exfoliation represents a higher scalability, but there are increasing unavoidable yield comes for the flake size expense and extra solvent/ion contamination. Totally, the layered multiferroic materials can exfoliate from bulks despite mechanical, chemical, and electrical methods due to their weak interlayer forces. However, there exists challenges to remove from parent crystals attributing to the strong cross-binding for the non-vdW multiferroic materials such as Cr₂S₃ [40], BiFeO₃ [44], and Cr₅Te₈ [45]. However, there still lack of an operatable and scalable top-down method for obtaining acquired sizes and thicknesses of 2D multiferroics. Taking the bottom-up synthesis into considering, the techniques of chemical vapour deposition (CVD), physical vapor deposition (PVD) and molecular beam epitaxy (MBE) are comprehensively used to prepare atomic-thickness film via straightway depositing the premeditated compounds on a particular substrate. Then the obtained 2D materials reveal good crystallinity, high layer controllability, and large area uniformity, which provides a widespread prospect in fundamental research and device applications. Here, the synthesis and engineering of various types of ferroics (ferroelectrics, ferromagnetics and ferroelastics) based on the their characteristics are briefly described.

Generally, two current synthetic strategies, including top-down and bottom-up method, are used to prepare 2D materials [4]. The top-down method is that few-layer or single-layer 2D materials are exfoliated from bulk crystals by certain technical means, such as mechanical exfoliation and liquid phase exfoliation methods. The bottom-up method refers to nanoparticles (such as atoms, molecules, and clusters) through the interaction grow into 2D materials with vapour deposition method, typically including CVD, chemical vapor transport (CVT), PVD, MBE, etc.

The mechanical exfoliation method is firstly technically introduced to prepare 2D layered materials [46]. A process of the mechanical exfoliation method is shown in Fig.3. In this exfoliation process, the few-layer materials are exfoliated with the tape on the multilayer bulk materials’ surfaces and the normal force is to overcome the vdW attraction between adjacent flakes. Single-layer 2D materials can be achieved after repeating this process at numerous times. This mechanical exfoliation method exhibits fast and easily to obtain 2D layered materials. The qualities of preparing samples with this method are very high. It is a basically scientific research method to prepare 2D materials in the laboratory. And it is convenient to research their physical properties and electrical devices. However, this method faces many difficulties, such as poor repeatability, time-consuming, and low yield, to hinder extensive large-scale industrial applications.

Fig.3 Schematic illustration of the main liquid exfoliation mechanisms. (a) Ion intercalation. (b) Ion exchange. (c) Sonication-assisted exfoliation. Reproduced from Ref. [47].

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Liquid phase exfoliation method is classed as ultrasonic-assisted exfoliation, ion exchange and ion intercalation exfoliation method in Fig.3(b, c). Due to the draw backs of the mechanical exfoliation method leading to low yield, the layered compounds are put into the liquid to produce numerous dispersed nanosheets. A range of 2D materials can be exfoliated to satisfy the demand of existing industrial technologies. Graphene was firstly reported to obtained by dispersing graphite powder into specific organic solvents. After sonication and centrifugation, the low-cost and large-scale yield of graphene was achieved. This method has an advantage on easily producing graphene. But the graphene concentration is extremely low for practical applications. At present, the exfoliation method originates from liquid cavitation. In the sonication-assisted exfoliation method, ultrasonic waves generate cavitation bubbles, which collapse into high-energy jets, destroy layered crystallites and produce exfoliated nanosheets [47], as shown in Fig.3(c). This method for obtaining graphene is very successful, although several shortcomings of sonication exhibit basal and edges planes.

Ions prefer intercalation into the vdW gap of 2D layered materials, which is a promising synthesis strategy at low temperature. Among a large number of research approaches, vapour-phase deposition (VPD) method is a high promising strategy for synthesizing scaled-up 2D layered chalcogenides or chalogenides for industrial manufacture [48, 49]. Vapour-phase deposition includes CVD shown in Fig.4(a), CVT, PVD shown in Fig.4(b), MBE in Fig.4(c) and atomic-layer deposition (ALD) in Fig.4(d). Compared to the “bottom-up” liquid-phase synthesis methods with hydrothermal reaction or colloidal synthesis [50] and “top-down” exfoliation approaches [51], VPD methods provide better control over the crystal qualities, the layer numbers, and the large crystal sizes, which is suitable for the characterization of materials properties and the fabrication of devices. Despite the recent numerous advances in the 2D materials, the desired layers, and sizes of the 2D materials with facile and controllable strategies still face various challenges and difficulties.

Fig.4 Vapour-phase deposition approaches for 2D layered materials such as chalcogenides and chlogenides. (a) Chemical vapour deposition (CVD), categorized into (left) solid-source CVD and (right) gas-source CVD. (b) Physical vapour deposition (PVD). (c) Molecular beam epitaxy (MBE). (d) Atomic-layer deposition (ALD). (a, c) Reproduced from Ref. [54]; (b, d) Reproduced from Ref. [48].

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2.1 Chemical vapour deposition (CVD)

The CVD process involves the precursor species with vapour-phase reactions and the depositing materials. The metal and chalcogen or halogen precursors can be either solids that evaporate at elevated temperatures or volatile species introduced through a carrier gas [48, 49]. The distinct precursors lead to different growth setups and considerations. Accordingly, present CVD methods to synthesize 2D materials are often divided into two main categories, solid-source CVD and gas-source CVD as depicted in Fig.4(a).

In a typical solid-source CVD, the solid metal or metal compound precursors and the chalcogen or chalogen precursors are located at different temperature zones in a same tube furnace in Fig.4(a). After heating, the evaporated precursors either with the vapour phase or adsorbing on the substrate. To enhance the yield of the single-layer and increase the domain size of the monolayer, the growth promoters, such as alkali metal halides, are often used to increase the growth speed of precursor evaporation, lateral growth and 2D crystal nucleation [52]. In a gas-source CVD process for 2D layered chalcogenide or chalogenides growth, the volatile metal and chalcogen precursors are either directly introduced through a mass flow controller (MFC) or bubbled into the system using a carrier gas in Fig.4(a). Then the precursors produce reaction in the high-temperature zone and deposition of 2D layered chalcogenides or chalogenides. Apart from the hot-wall reactor, cold-wall reactors can also be used, in which only the substrate undergoes heating, leaving the chamber walls unheated [53].

Recently, numerous 2D atomic-scale multiferroic materials have been synthensized by CVD method, for example, wafer-scale one-unit-cell of chromium sulfide multiferroic 2D materials has been successfully synthensized by CVD method in Fig.5. Song et al. [40] have grown one-unit-cell non-layered Cr₂S₃ multiferroic material depending on an interface modulated strategy under the scheme of a facile CVD approach. 2D Cr₂S₃ contributes to tpye II multiferroicity, which exhibits room-temperature ferroelectricity, strong magnetoelectric coupling and long-range ferromagnetic order. The Curie temperature of ferromagneticity is 200 K, which is two times higher than bulk counterpart. Meanwhile, single crystal Cr₂S₃ is regarded as the largest and thinnest multiferroics, spontaneously making a great breakthrough toward the batch synthesis. These results can really provide a strategy for future industrial application of multiferroic materials in the fields of next-generation magnetoelectric devices.

Fig.5 Orientation-controlled synthesis of one-unit-cell Cr2S3 with 1-inch length on c-plane sapphire. (a) Schematic graph of unidirectionally aligned growth of Cr2S3. (b) Diagram of 1-inch length Cr2S3 synthesized on c-plane sapphire. (c) Optical microscopy (OM) image of Cr2S3 on c-plane sapphire, presenting the feature of unidirectionally aligned growth. Inset: AFM image shows the height profile of a single nanosheet, which reveals the one-unit-cell Cr2S3. (d) Statistical analysis of domain orientations of Cr2S3. (e) XPS spectra of grown samples, indicating the formation of Cr2S3 and Al−S bonds. Reproduced from Ref. [40].

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The CVT method is old yet powerful, which is recently adopted for synthesizing 2D layered materials, producing bulk crystals of layered materials or corresponding 2D films, such as single-layer NiI₂ as shown in Fig.6 [13, 43]. Notably, CVT reactions, which represent a common feature: a condensed phase, a typical solid, sub-limes in a gaseous reactant, and the usual crystal form, are different from CVD. Specifically, the main difference between CVT and CVD depends on the source materials to synthesize the products, where solid reactants are usually applied in CVT and gaseous precursors are typically used in CVD. The difference induces subsequently consequent distinctions in designing reactor, controlling operational, and holding desired product features. 2D multiferroic materials, such as NiI₂ and CuCrSe₂, have been synthesized via a CVT method [13, 55]. And it is discovered that 2D NiI₂ and CuCrSe₂ present type-II multiferroic order in a single atomic layer.

Fig.6 Single-layer and few-layer NiI2 have been synthesized by CVT method. (a) Optical photograph of one-layer (1L) and two-layer (2L) NiI2 materials grown on hBN, and the atomic step height profiles of grown samples measured by atomic force microscopy (AFM). (b) Polarized microscopy graphs at different temperatures on the same region of the samples mentioned above. Dashed curves indicate the one-layer and two-layer regions (scale bars: 5 μm). (c) Measurements of angular-dependent linear dichroism ∆R(θ) with single-layer NiI2 on the same three monodomain regions polarized microscopy as (b). Reproduced from Ref. [13].

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At the same time, single-layer CuCrSe₂ has been synthesized by a CVT method with polycrystalline powders [55], as denoted in Fig.7. Results show that single-layer CuCrSe₂ represents multiferroicity at high-temperature, hosting 120 K ferromagnetism and room-temperature FE. Notably, the FE-induced orbital shift of Cr atoms in single-layer CuCrSe₂ multiferroic material enhances the ferromagnetic coupling, which is different from both types-I and II multiferroicity, supported by a combination of scanning transmission electron microscopy (STEM), second-harmonic generation (SHG), piezo-response force microscopy (PFM), magnetic, and Hall measurements. These novel observations not only offer a unique avenue for studying intrinsic magnetoelectric couplings at the atomic thin limit but also have great breakthroughs in potential development of nanoelectronic and spintronic devices based on 2D multiferroics.

Fig.7 Crystal structure of single-layer CuCrSe2 with chemical exfoliation. (a) The crystal structure of CuCrSe2 in side view, where green, blue, and red balls denote Se, Cr, and Cu atoms, respectively. (b) Single-layer CuCrSe2 crystal structure for highlighting two different Cr atoms, marked as “Cr1” and “Cr2”, respectively. (c) Description of Cr orbital energy in single-layer CuCrSe2, clarifying the orbital energy shift to opposite directions induced by vertical polarization. (d) Typical optical microscopy (OM) image of CuCrSe2 flakes under chemical exfoliation, identified in the single-layer region. (e) AFM image of the single-layer CuCrSe2 region. Inset indicates the step height profile of the grown sample. Reproduced from Ref. [55].

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2.2 Physical vapour deposition (PVD)

PVD is a very simple and representative vapour-phase technique, where only the precursors are the bulk form of target materials [48]. Even though the direct coupling between ferroelectric and ferromagnetic order in a single material still remains challenging, 2D multiferroic material p-doped SnSe has been successfully synthesized on mica substrates by a physical vapor deposition approach [56]. To synthesize thin layers by PVD, offering a horizontal tube reactor is usually necessary. In a typical PVD process in Fig.4(b), the bulk precursor SnSe powders are evaporated at an elevation-temperature and then deposited on the target mica substrates that lie in a lower temperature zone. A low reactor pressure (~10¹–10² Pa, pressure-achievement depending on a mechanical pump) often favorably results in improving the effectively evaporated precursor and gas-phase diffusion of the precursor [57]. It is indicated that PVD-synthesized 2D metallic p-doped SnSe multiferroic material presents room-temperature ferrimagnetism of 337 K and ferroelectricity even under the depolarizing field in Fig.8. The locally segregated-phase SnSe microdomains are emerged. And the interfacial charge transfer in fabricated sample is also accompanied at the same time. Consequently, 2D SnSe multiferroic material exhibits degenerate semiconductor and metallic feature. The 2D p-doped SnSe exists both ferrimagnetism and ferroelectricity, which represents its multiferroic feature in Fig.8. Such results bear tremendous potential for delving into the magnetoelectric coupling to 2D limit, controllable synthesis of multiferroic material and constructing high-performance future industrial implement logic devices.

Fig.8 Controllable thickness-tunable SnSe nanosheets synthesized on mica substrate. (a) Schematic process-grown photograph and crystal structure of SnSe. (b) Raman spectrum of as-grown SnSe. (c) Raman intensity mapping diagram with mode in a tetragonal SnSe nanosheet, revealing its uniform thickness. (d–f) Optical microscopy (OM) images of as-grown SnSe, synthesized at distinct precursor-substrate distances of 12, 14, and 16 cm, respectively, showing various domain sizes and morphologies. (g) AFM images and comparative height profiles to analyze the tetragonal and circle SnSe nanosheets. Reproduced from Ref. [56].

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2.3 Molecular beam epitaxy (MBE)

MBE is a thin-film fabrication technique that has been extensively served as the epitaxial growth of topological insulators and single-crystalline semiconductors [48]. In the epitaxial process, ultra-high vacuum (UHV) and high-purity elemental sources are necessary in an effusion cell, as shown in Fig.4(c). The reactant sources are controllable with appropriate vapour pressures. The ane-beam evaporator promises extremely low vapour pressures for sources to produce molecular beams. During deposition, the generated molecular beams based on different elements arrive at the heated target substrate region, whose flux ratio should keep accurate balance and stability to form favourable materials. Usually, numerous characterization tools and strategies, such as reflection high-energy electron diffraction (RHEED) systems, flux monitors are offered for the MBE chamber in order to in situ monitor the epitaxial growth process.

At present, the 2D type-II NiI₂ multiferroic material has been very successfully grown by MBE on highly oriented pyrolytic graphite (HOPG) in the well-controllable ultra-high vacuum conditions (UHV, base pressure ≈ 1 × 10⁻¹³ bar) [43], as shown in Fig.9. The substrate temperature remains unchanged at ≈ 100 °C to obtain monolayer NiI₂. In the growth process, two kinds of sources, Ni (rod with 99.999% purity) and iodine (anhydrous powder, 99.95% purity) are offered. One is evaporated using an electron-beam evaporator, while another is deposited from a Knudsen cell. An iodine background pressure (≈ 9 × 10⁻¹¹ bar) and the growth duration (30 min) are used for the sample growth. After that, the sample is annealed for 5 min in an iodine background. The successful growth of NiI₂ cannot do without the exact controllable substrate temperature and a consistent stabilization ultra-low iodine pressure above ≈ 7 × 10⁻¹¹ bar. NiI₂ multiferroic order attributes to the combination of a strong spin−orbit coupling and a magnetic spin spiral order. Furthermore, manipulating the external local electric field in the multiferroic domains, the magnetoelectric coupling of NiI₂ can be straightly detected. These findings can present a significant advance for analyzing multiferroic materials at the microscopic level.

Fig.9 Structure of monolayer NiI2 and origin of multiferroicity. Unit cell of monolayer NiI2. The requirement of 9a × $\sqrt{3}$a supercell is used to depict the magnetic spin-spiral order with rotation vector $\mathit{e}$ along the z-direction and propagation vector $\mathit{q}$ along the x-direction. A net electric polarization $\mathit{P}$ is induced through spin-orbit coupling (SOC) in the y-direction. Reproduced from Ref. [43].

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2.4 Atomic layer deposition (ALD)

ALD is a variant of CVD. In the process, individually produced vapour-phase precursors can be alternately brought into the reaction chamber with pulsed form, and the growth process repeats with several periods. The growth of 2D materials by ALD usually involves four steps [Fig.4(d)]: a selective precursor is injected into the reacting chamber to be reacted with the surface functional groups such as −SH; both the unreacted metal precursor molecules and reaction by-products are purged out of the chamber; the chalcogen precursor is introduced into the chamber, the metal precursor ligands are replaced by chalcogen-containing groups; the unreacted chalcogen precursor molecules and reaction by-products are purified out of the chamber, so that a monolayer is subsequently grown [48].

Last year, 2D multiferroic materials have been fabricated by ALD method. Lebedev et al. [58] have fabricated multi-terminal electrical devices from exfoliation of NiI₂ with a dry flake transfer method combined by ALD method (Fig.10). This fabrication strategy generates ambient-stable electrical contacts with NiI₂, which is in favor of making charge transport measurements even at cryogenic temperatures. In this protocal, NiI₂ exhibits a gate-tunable semiconducting property down to the monolayer limit. A Hall mobility of multi-terminal devices is 15 cm²·V⁻¹·s⁻¹ at 1.7 K. These findings establish a novel avenue that NiI₂ is incorporated into heterostructures for other ambient-reactive 2D materials to expand the electrical interrogation in quantum, diverse magnetic, and spintronic phenomena down to the atomically thin limit.

Fig.10 (a, b) Schematic illumination of large and thick flakes removal. (c) Fabrication of electrical devices with few-layer NiI2. After being removed, thick NiI2 flakes promise the quality of the heterostructure according to the large height differences result in the poor flake-to-flake contact as well as incorporated gas bubble. (d−f) Schematic fabrication of the NiI2 (>10 layers) Hall bar, referring to flake pick-up and transfer, stacking hBN/graphene/NiI2/hBN, patterning, etching, and encapsulating by alumina ALD. Even though the appearance of overlapped graphene flakes in the assembling heterostructure happens, the required Hall bar geometry is subsequently determined by etching. Reproduced from Ref. [58].

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In conclusion, the fabrication methods of 2D multiferroic materials have been viewed, such as mechanical exfoliation, liquid exfoliation, and vapor-deposition. Among them, most popular methods are chemical vapour deposition and chemical vapour transport. PVD constitutes a powerful route to synthesize various 2D layered chalcogenides that hold promise for emerging technologies. Following the research aims discussed previously, future efforts are expected to continue enhancing the quality, scalability, and manufacturability of the resulting 2D layered chalcogenides to enable various target applications. Additionally, 2D multiferroic materials are actively and widely investigated owning to the cross-coupling effects. Thus, this kind of materials possesses multiple ferroic properties, simultaneously including ferromagnetism, ferroelectricity, ferroelasticity and ferrovalley. Multiferroic materials witness a surge of research in innovative, multifunctional devices, with ultra-scaled sizes and improved device performances in vdW cases. Recently, type-II multiferroic order NiI₂ with a single atomic layer has been discovered [13], which can break an inversion-symmetry magnetic order and directly introduce a ferroelectric polarization. Later on, 2D layered multiferroic CuCrP₂S₆ with strong polarization-magnetization coupling exhibits in-plane electrical and magnetic anisotropy, the coexistence of antiferroelectricity and antiferromagnetism [59]. Plenty of multiferroic materials have been sorted in Tab.1. The multiferroic magnetization is induced by electric fields, and vice versa. These functionalities have held great promise for the multiferroic development of fundamental research and practical applications in voltage-controlled magnetic anisotropy, and low-power switching devices.

Tab.1 Recent processes of 2D multiferroic materials with density functional theory (DFT) and experimental methods with different transition temperature (TT).

Name	Coupling	Year	Ref.	Type		Method		TT
NiX2	FE-FM	2019	[60]		Intrinsic
MnI2, CoI2	FE-FM				Intrinsic
CuCrSe2	FE-FM	2024	[61]	Type II	Intrinsic	Exp.	Exfoliation
Cr2S3	FE-FM	2024	[40]	Type II	Intrinsic	Exp.	CVD	200 K
CuCrP2S6	FE-FM	2023-2024	[12, 59]	Type II	Intrinsic	Exp.	CVT
NI2	FE-FM	2022-2024	[13, 43, 58, 62]	Type II	Intrinsic	Exp.	CVT	21 K
CrX3	FE-FM	2023	[63]	Type II		Theor.
AB2	FE-FM	2023	[64]	Type II		Theor.
Lu0.3In0.7FeO3	FE-FM	2022	[65]			Exp.	PLD
VNI	FM-FA	2022	[66]			Theor.
As-bilayer-In2Se3	FM-FE	2024	[3]			Theor.
Bi0.9La0.1FeO3	FM-FE	2022	[67]			Exp.	Exfoliation	300 K
AV2S4	FM-FA	2023	[68]			Theor.
SiN	FM-FE	2022	[69]	Type I		Theor.
InCrX3	FM-FE	2024	[70]	Type II	Intrinsic	Theor.
Co1−xNixI2	FM-FE	2024	[71]	Type II	Intrinsic	Exp.	PVT
FeGa	FM-FA	2023	[72]		Extrinsic	Exp.
H′-Co2CF2	FM-FE	2022	[73]	Type II		Theor.
Cu2OCl2	FM-FE	2022	[74]	Type II		Theor.
VSe2/In2Se3	FM-FE	2022	[75]	Type II		Theor.
SmFeO3	FM-FE	2022	[76]	Type II	Intrinsic	Theor.		300 K
VOXY	FM-FE	2023	[77]	Type II	Intrinsic	Theor.	DFT
InTlNO2	FM-FE	2024	[78]	Type II	Intrinsic	Theor.	DFT	300 K
AgCr2X4	FM-FE	2022	[79]	Type I	Intrinsic	Theor.	DFT	530 K
MnOF	FM-FE-FA	2022	[80]	Type II	Intrinsic	Theor.	DFT	420 K
TcIrGe2S6	FM-FE	2024	[81]	Type II	Intrinsic	Theor.	DFT	300 K
KYMnO4	FM-FE	2023	[82]	Type II	Intrinsic	Theor.	DFT
GdI2	FM-FE-FV	2024	[83]	Type II	Intrinsic	Theor.	DFT
Co2CF2	FM-FE	2023	[84]	Type II	Intrinsic	Theor.	DFT
Cr2NF2	FM-FA	2023	[85]	Type II	Intrinsic	Theor.	DFT
SnSe	FM-FE	2022	[56]	Type II	Intrinsic	Exp.	PVD	337 K
Te-doped WSe2	FM-FE	2023	[86]	Type II	Intrinsic	Exp.	CVT	300 K
MnSe2/In2Se3	FM-FE	2024	[87]	Type II	Intrinsic	Theor.	DFT	278 K
VSi2N4	FM-FE	2024	[88]	Type II	Intrinsic	Theor.	DFT
VX2	FM-FE	2024	[89]	Type II	Intrinsic	Theor.	DFT
Ti3C2Tx	FM-FE	2022	[90]	Type II	Intrinsic	Exp.	Exfoliation	300 K
XN	FM-FE	2024	[91]	Type II	Intrinsic	Theor.	DFT	205 K
Bi2NiMnO6	FM-FE	2024	[92]	Type II	Intrinsic	Exp.	PLD
BaFe2O4	FM-FE	2022	[93]	Type II	Intrinsic	Exp.	PED	300 K
CrI3/In2Se3	FM-FE	2024	[94]	Type II	Intrinsic	Exp.	Exfoliation
InTlNO2	FM-FE	2024	[78]	Type II	Intrinsic	Theor.	DFT	274 K

In general, the growth method of 2D multiferroic materials are viewed, such as mechanical exfoliation, liquid exfoliation, vapour deposition. Vapour deposition is generally classified into CVD, CVT, PVD and MBE. Bottom-up methods refer to build blocks through the chemical reaction of molecular to establish covalent-linked 2D networks. Among these methods, it is a typical technique of vapour phase deposition (VPD) to construct atomic-scale films or thin flakes through directly depositing suitable vapour-phase compounds on specific substrates, which can prepare well tunable, large-area uniform and high-quality 2D materials. Normally, two main kinds of vapour phase deposition methods are CVD and PVD. CVD or CVT method can prepare controllable-thickness, large-size, and high-quality 2D multiferroic materials for further positive application in the electronic industry. PVD is an efficient method to prepare thin-film materials in industry and commerce, which is the reason that the PVD method can immediately construct 2D multiferroic materials on the appropriate substrate without another additional chemical reactions. Moreover, MBE growth method and magnetron sputtering (MS) method in the PVD method are always applied to prepare 2D multilayer multiferroic materials. Above all, the CVD and CVT methods are usually used to prepare 2D multiferroic materials due to their strict requirement on large size, high quality, and controllable thickness.

2.5 Advances in characterization and modelling tools of 2D multiferroics

Advances in characterization of ferroic orders, including ferromagnetic, ferroelectric, and ferroelastic via the observation of magnetic moments, electric polarization, and structural deformations combined by progressive techniques, are well established. Over the last years, new developments and advanced techniques have witnessed a surge of research in multiferroic materials characterization, such as scanning probe microscopy (SPM), Raman spectroscopy, X-ray diffraction (XRD), neutron scattering, optical second-harmonic generation (SHG), transmission electron microscopy (TEM). All these techniques are demonstrably suitable to study the properties of multiferroics to fetch critical information on numerous length scales down to nanoscales. Unambiguously structural features and strictly ambient conditions for fabricating multiferroics are extremely important to promise the accurate modelling and understanding. The external conditions are dependent on the pressure, temperature, humidity, electric field, magnetic field, light field, and so on. Well-defined and reliable structural data depend on both computational and experimental efforts.

Magnetic characterization usually relies on the commercial superconducting quantum interference device (SQUID) magnetometer or vibrating sample magnetometer for the polycrystalline powder samples or the single crystals. DC magnetization in a very wide range of temperatures (2–400 K) and fields (up to 70 kOe) is permitted to acquire nature of magnetic order, the magnetic phase transitions, as well as the magnetic interactions between the spins.

The electric polarization is extracted from integrating the temperature-dependent pyroelectric current over the time. Spontaneously electric polarization generated current, resulting in accumulating charge on the crystal surface. The measurement of surface charge can be made via exact femtoampermeters or electrometers. Even the measurement method is mature, dependent-sample measurements also become challenging [95]. Alternatively, the electric hysteresis loops in different conditions [96] shed light on the another understanding of the electrical properties.

The development of advanced microscopy technologies, such as STM and TEM, enables the fundamental understanding of ferroic ordering structures, atomic distortion, and phase transitions and their dynamics of 2D ferroics. Achieving accurate atomic-scale observation and even the in situ manipulation of 2D ferroic materials will be an essential task for this field. In addition, many other characterization techniques enable the quantification of physical properties associated with ferroic orders. For example, Raman scattering can reveal the structure, symmetry, and phase transition of materials. PFM and polarized-light microscopy can be used to study the ferroic domain patterns. Spin-polarized STM (SP-STM) and X-ray magnetic circular dichroism can be used to study the physical properties of magnets, including the local electron configuration of valence states and the spin and orbital moments of elements. These techniques rapidly advance the insights into the ferroicity of 2D materials. The current experimental investigation and understanding of 2D ferroics is just a tip of the iceberg, and more phases, properties, and indepth characterization techniques should be explored.

2.5.1 Scanning tunneling microscopy (STM) and scanning probe microscopy (SPM)

Scanning tunneling microscopy (STM), as a powerful tool to detect the microscopic domain structures in 2D multiferroic monolayers, can provide detailed information on the atomic-structure surface, originating from the electron tunneling mechanism. Scanning probe microscopy (SPM) allows the spatial imaging, measurement, and manipulation of nano and atomic scale surfaces in real space. The tunneling current relies on the vacuum-barrier thickness between two metallic or semiconducting electrodes. For practical STM facilities, the one electrode is used as a metallic tip that consists of gold, silver, tungsten, or platinum-iridium, etc; the other electrode is an investigative sample. The feedback system in STM can adjust the height of the tip over the sample surface with a continuously variable gap so that any change in the tunneling current is compensated by the feedback loop during scanning. The STM image of the sample is thus obtained by continuously digitizing the feedback signal, which can derive the surface morphology of the sample. The constant current mode is very useful for the analysis of rough surfaces. The scan rate of another constant height mode can be very fast, which provides the opportunity of recording the real-time video of the rather flat sample. STM is used to probe and characterize the multiferroic order in monolayer NiI₂ [43].

2.5.2 Second harmonic generation (SHG)

Second harmonic generation (SHG) is a powerful tool to determine the ferroelectric and magnetic order in multiferroics, as an essential second-order nonlinear optical effect consisting of the synchronous transformation of two photons interplaying with other materials into a single photon. SHG effects often appear in the noncentro-symmetric mediums (materials lacking inversion symmetry), where the radiation frequency is twice of the incident with an extreme light field such as a pulsed laser [93, 94]. Among the various optical characterizing methods, optical SHG has generated most tremendous impact on characterization of multiferroic materials due to its sensitivity, simplicity, and versatility at the atomic scale. The SHG technique is sufficiently sensitive to study 2D multiferroic materials for both spatial-inversion symmetry and time-reversal symmetry. A variety of 2D multiferroics have exhibited excellent SHG response, such as NiI₂ [43, 58, 99, 100], CuCrSe₂ [61], Cr₂S₃ [40], CuCrP₂S₆ [12, 59], p-doped SnSe [56], Te-doped WSe₂ [86], Ti₃C₂T_x [90], Bi₂NiMnO₆ [92], BaFe₂O₄ [93], and CrI₃/In₂Se₃ [94], have exhibited strong SHG response due to their intrinsic noncentrosymmetric structures.

2.5.3 Raman measurement

Raman spectroscopy, as a powerful tool, is of prime importance to determine the ferroelectric and magnetic order in multiferroics, particularly at surfaces and buried interfaces of samples, which has more congenital access and advantages than other measurement techniques in Fig.11. However, multiferroics regularly demonstrate complex domain structures and many techniques are so circumscribed to probe multiferroicity with the desired spatial resolution for nanoscale regions, especially for thin films. Recently, circular dichroic Raman measurements are successfully used to directly probe the magneto-chiral ground state of few-layer NiI₂ multiferroic [13]. As the complex ground state synchronously breaks rotational, mirror and inversion symmetries, complementary optical techniques are adopted to extract the various features of the polar and magneto-chiral orders, which are dependent on temperature and layer numbers. Consequently, Raman spectroscopy based on circularly polarized light is used to demonstrate the magneto-chiral order configuration for the helimagnetic phase of NiI₂, which arises a spin-lattice electromagnon excitation coupling with high-strength optical activity in spin chirality.

Fig.11 Diagram of angular resolved polarized Raman spectroscopy (ARPRS) in cross-polarized (XY) construction. (a, b) The polar plots of the 31 cm−1 and 37 cm−1 modes in ARPRS represented in the multiferroics, which are different from both a pure phonon and magnon mode, in agreement with electromagnons. (c, d) The 80 cm−1 peak consists of two phonons below TN,2 (one is at 79.9 cm−1 and another is at 80.2 cm−1). These closely-spaced phonon modes demonstrate out-of-phase modulation referring to the incident linear polarization. Both of them represent an Eg symmetry appearing in the high-temperature $R\overline{3}m$ phase. (e, f) The 120.8 cm−1 and 168.8 cm−1 belong to magnon modes. Red lines: In ARPRS, the Raman tensors are fitted for various mode symmetries. Reproduced from Ref. [13].

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2.5.4 Birefringence measurements

Birefringence measurement is a powerful tool to emerge from the magnetoelectric coupling for multiferroic materials characterization. The gyrotropic birefringence (GB) represents light-propagation-direction-dependent nonreciprocal response, which originates from a multiferroic manganite of the dynamical magnetoelectric coupling effect with spin-cycloid order as far as time-domain terahertz polarimetry is concerned [101]. The GB exposes the existing electromagnon resonance for the enhanced nonreciprocal optical rotation. The GB magnitude scale is proportional to the bilinear coupling ferroic order parameters P· M (P: electric polarization, M: magnetization) via the magnetic-field induced spin-flop transition. The enhancing GB originates from the dynamical magnetoelectric intermode coupling of electromagnon and antiferromagnetic resonance in a multiferroic helimagnet [102].

Optical birefringence arises from the low lattice symmetry at both the T_N,1 and T_N,2 transitions, and breaking the c-axis three-fold rotational symmetry (C_3z) in the parent point group and reducting a single in-plane two-fold symmetry operation (C₂) [13]. The optical anisotropy of NiI₂ directly extracted from cross-polarized microscopy on birefringent domains in the one- and two-layer regions at T = 5, 15, 25 K [see Fig.6(b)]. Significantly, the reduction of rotational symmetry in single-layer NiI₂ from three- to two-fold is verified by angular-dependent linear dichroism measurements [see Fig.6(c)].

2.5.5 Transmission electron microscopy (TEM)

STEM technologies have significant advancements in investigating material chemistry and structure from the micro to the atomic scale due to ultra-high energy resolution monochromators, aberration-correction technology and state-of-the-art detectors/cameras [103]. This technique is powerful to comprehend and characterize the origins of multiferroic material and engineering materials, such as ferroelectricity, ferromagnetism, ferroelasticity, and piezoelectricity. STEM is directly able to observe the structural characteristics to establish a link with macroscopic properties. In addition, the methods available for exploring structures of multiferroic materials on the nanoscale and atomic scale require high-resolution electron microscopy (HREM) [31, 104]. These methods can directly visualize the lattice distortion across a multiferroic domain wall via measuring the continuous deviation of planes in the case of the undistorted lattice. Nowadays, most advanced techniques allow atomic scale resolution to 0.5 Å by means of aberration-corrected imaging. As the exit-wave reconstruction approach is used to eliminate the objective-lens spherical aberrations, images can be immediately analyzed in accordance with the projection of the atomic columns. Weak beam transmission electron microscopy (WBTEM) has been applied to quantitatively analyze the thickness fringes on the images of inclined domain walls. HRTEM can also be able to image the local polarization dipoles at atomic scale resolution, thus quantitatively exploring the local polarization and interpreting the domain structure [105].

2.5.6 Electron energy loss spectroscopy (EELS)

EELS has also been applied to the study of multiferroic materials such as domain walls [106]. Electron probes can now reveal chemical information, through electron energy-loss spectroscopy (EELS), and structural information, using aberration-corrected microscopes, at sub-nanometre spatial resolution. Light elements such as oxygen, and in turn the oxygen octahedral rotations and tilts in perovskites, can be identified [107]. These are of particular importance since they determine bandwidths and magnetic exchanges, to which the magnetic and ferroelectric properties are sensitive [2].

2.5.7 Terahertz reflection spectroscopy

Terahertz reflection spectroscopy is used to investigate the multiferroic vdW insulator NiI₂. The results indicate that multiferroicity occurs below TN₂ (59.5 K) and antiferromagnetism occurs below TN₁ (78 K) [62]. The presence of the helimagnetic-multiferroic phase with two electromagnon modes at 34 and 37 cm⁻¹ below T_N,2 is extracted. The NiI₂ crystal sample of a thickness of 171 μm is used for the transmission measurement in Fig.12(a). Another NiI₂ crystal sample of a thickness of 515 μm is used for the reflection measurement in Fig.12(b). Terahertz time-domain signals of transmission measurements at T = 1.5 K and H_ext = 0 are shown in Fig.12(c, d). A divided reflection measurement demonstrates that the electric dipole active nature leads to the two electromagnon modes [62].

Fig.12 Schematic diagrams of terahertz reflection measurements conducted on NiI2: (a) transmission and (b) reflection. Hcool is the in-plane magnetic field during the cooling process. P is the electric polarization (below TN,2 59.5 K). P is in-plane and perpendicular to Hcool. For the transmission, an external magnetic field Hext is out of plane. Terahertz time-domain pulsed signals for the transmission measurements in (c) $E//P$ and (d) $E\mathrm{\perp }P$ polarizations at 1.5 K and Hext = 0. Red lines denote the signals of NiI2 and blue lines represent reference signals. Reproduced from Ref. [62].

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2.5.8 X-ray diffraction (XRD)

X-ray diffraction (XRD) has been broadly adopted to characterize the crystal structure of the multiferroic materials and detect the structural phase transitions. In XRD, the intensity for elastically scattered X-ray radiation is employed to interpret the underlying structure information as shown in Fig.13. In the case of strong diffraction and tremendous perfect crystals, the dynamical diffraction theory is adopted to solve Maxwell’s equations with translational symmetry [108]. In most commonly encountered conditions, the dynamical theory can be replaced by the simple kinematical theory, which hypothesizes the diffracted intensity is so sufficiently weak to consider multiple scattering processes [109]. Here we will briefly recapitulate some of the most important results and explain their relevance for determining ferroelectric order both in and out of equilibrium. Actually, temperature-dependent XRD measurement confirms the presence of the concurrent transition of magnetic and ferroelectric ordering near room temperature [110]. Remarkably, the ferroelectric state undergoes a first-order transition to another ferroelectric state simultaneously with the magnetic transition temperature, which provides a unique example of a concurrent magnetic and ferroelectric transition at the same temperature among proper ferroelectrics, taking a step toward room temperature magnetoelectric applications. XRD of chemical vapour transport grown crystals NiI₂ is performed in Bragg geometry using Cu Kα radiation (PANalytical), and the refined unit cell at room temperature is a = 3.91 Å, c = 19.93 Å [13] (see Fig.13).

Fig.13 X-ray and electron diffraction of NiI2 crystals. (a) X-ray diffraction of a NiI2 single crystal grown by CVT along the c-axis. (b) X-ray powder diffraction of NiI2 grown by CVT. (c) An optical image of NiI2 flake thickness of 7 nm grown by PVD then transferred onto a SiNx membrane. (d) The electron diffraction pattern of the NiI2 flake grown by PVD as exhibited in (c) with a transmission electron microscope (TEM). Reproduced from Ref. [13].

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2.5.9 Neutron scattering

Neutron scattering has been used to investigate properties of multiferroics. Neutron scattering has a central role in determining the crystal and magnetic structures of a vast variety of materials. Neutron diffraction studies often provide information that cannot be obtained by other experimental techniques. In the investigation of the spin dynamics of systems, neutrons play a truly unique role. Neutron scattering is the only technique that can directly determine the complete magnetic excitation spectrum, whether it is in the form of the dispersion relations for spin wave excitations, wave vector and energy dependence of critical fluctuations, crystal field excitations, moment fluctuations and so on, which can be readily compared with theory [111]. In summary, neutron-based techniques offer many interesting insights into multiferroic materials.

2.5.10 Atomic force microscope (AFM)

The AFM is a multifunctional tool to image the topography of multiferroic systems at nanometre resolution [112]. An atomic force microscope crucially composes of a sharp tip apex less than nanometre, which attaches to the soft-cantilever end. The operating principle is mainly required to monitor the forces interacting between the tip and the surface of the preparation sample, which cause the cantilever deflected to record via a laser beam focusing on the cantilever end and reflecting onto a position-sensitive photodiode. A piezoelectric scanner that moves either the cantilever or the sample allows the tip to scan the sample surface in x and y directions whereas a feedback loop between the deflection of the cantilever and the z-piezo allows control of the precise position of the tip and the applied force. In dynamic mode AFM, the tip is oscillated near the sample surface, either in non-contact or intermittent contact, and the oscillation amplitude or frequency is kept constant through the feedback loop. Large forces acting between the tip and the sample during imaging may also dramatically reduce the image resolution and cause molecular damage or displacement. In theory, the spatial resolution achieved on flat and smooth surfaces can be ≤1 nm in the horizontal plane and as low as 0.1 nm in the vertical plane [113]. Numerous multifunctional AFM-based techniques have been developed to characterize the local mechanical properties, electrical properties, optical characteristics, and thermal properties of the sample. AFM is a useful tool to extract the detail insight of the microstructure of 2D multiferroic material, for example, few-layer NiI₂ as shown in Fig.14.

Fig.14 Atomic force microscopy measurements on few-layer NiI2 crystals. (a−c) Wide-field optical photographs of one- to four-layer NiI2 samples in the optical measurements. (d−h) Corresponding AFM images of the region described in the optical images. Reproduced in Ref. [13].

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In short, advances in characterization of multiferroic orders via the observation of magnetic moments, electric polarization, and structural deformations combined by progressive techniques, are well established. New developments and advanced techniques have witnessed a surge of research in multiferroic materials characterization, such as SPM, Raman spectroscopy, XRD, neutron scattering, optical SHG, TEM, AFM, terahertz reflection spectroscopic, and birefringence measurement.

3 Exploration of devices and applications for 2D multiferroics

Multiferroic materials offer comprehensive applications in memory devices, sensors, radio frequency (RF) and microwave tunable devices, phase shifters, energy harvesting and conversion devices [2, 4, 7, 37, 114, 115] as shown in Fig.15.

Fig.15 Outline diagrams of 2D multiferroics. Internal alignments of magnetization M, electric polarization P, or strain ε are presented in the core circle, meanwhile external ramification of magnetic field H, electric field E, or stress σ and corresponding 2D ferromagnetic (FM), ferroelectric (FE), and ferroelastic (FA) materials are denoted in blue, gray, and pink regions, respectively. Magnetoelectric, piezoelectric, and magnetoelastic coupling effects and corresponding applications are depicted in the outermost circle. Reproduced from Refs. [4, 116−119].

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3.1 Nonvolatile memory

The burgeoning nonvolatile memory technologies based on multiferroic materials show great promise in various applications of low-power, high-speed and high-density memory for integrated circuits, which arises from the observation of long-range ferroic orders in 2D materials [5]. Unlike traditional storage devices, 2D multiferroic memories use electricity to calculate and store data simultaneously with low energy [76, 120]. In multiferroics (MF), high-speed energy efficient memory devices based on electric-field control magnetism manipulate magnetic states by recommending weak electric field instead of magnetic field. Magnetoelectric random access memory device (MERAM) consists of a single-phase thin-layer multiferroic material, whose specific magnetization direction is produced by exchange bias between a free FM layer and the MF layer. In MF layers, magnetoelectric (ME) coupling between ferroelectric and magnetic orders permit multistate memory where two polarization (P↑, P↓) directions control two magnetization (M↑, M↓) directions.

Multiferroics hold the future for the ultimate memory device. The demonstration of a four-state resistive memory element in a tunnel junction with multiferroic barriers represents a major step in this direction [121]. In multiferroics, the coexistence of several order parameters and the magnetoelectric coupling can both be exploited in novel types of memory elements. As ferroelectric polarization and magnetization are used to encode binary information in ferroelectric random access memories (FERAMs) and magnetic random access memories (MRAMs), respectively [122]. Beyond the combination of ferroic properties in a single device, the electrical control of magnetization via the magnetoelectric coupling offers the opportunity of combining the respective advantages of FERAMs and MRAMs in the form of non-volatile magnetic storage bits that are switched by an electrical field. Indeed, although the characteristics of MRAMs equal or surpass those of alternative non-volatile memory technologies in terms of access time and endurance, they have a large handicap in their high writing energy. A possible solution for reducing the writing energy uses a spin-polarized current to reverse the magnetization of the storage layer by spin-transfer [123] rather than magnetic fields. Spin-transfer MRAMs are currently being developed by several companies and a 2 Mb memory was recently demonstrated [124]. Rare-earth orthoferrite SmFeO₃ (SFO) is a promising single-phase multiferroic material because of simultaneous coexistence of magnetic and ferroelectric orders at room temperature. This kind of material will produce wide application prospect in future electric-write magnetic-read high-density memories [76]. Multiferroic and magnetoelectric composites, which are at the breakthrough toward technological applications [125]. On the one hand there is an ever-growing multitude of efficient classic materials combinations. On the other hand, specific solutions still exist beyond this main-stream evolution.

3.2 Spintronics

The magnetoelectric coupling in multiferroic materials opens up an avenue for energy efficient spintronic devices, which are prospectively relying on nanomaterials with a smaller size than the spin relaxation length and tunable interface characteristics [126]. In comparison to the charge degree of freedom, electrons also have a spin degree of freedom. When spin-up and spin-down electrons are intrinsically or extrinsically separated, the spin polarization can be generated for spin-based devices [127]. The high efficiency of spin injection (detection) and the easy-control spin polarization states are always desired [128]. In recent years, compared to magnetically controlled spin-based devices, the electrically controlled spin-based devices have become more attractive owing to the lower power consumption. However, the disordered system obtained by the traditional method usually has low magnetic properties and is not suitable for the application. Therefore, exploring 2D materials with inherent magnetic properties is the goal of spintronics. For next-generation technology, magnetic systems attract broad attention due to the natural ability to store information and propagate information for logic functions through spin transport. Currents manipulating the magnetization state is turned out to be energy inefficient. Multiferroic thin-film heterostructures, combining ferromagnetic and ferroelectric orders, witness a surge of research in energy efficient electronics. The electric-field controlling magnetic order reduce energy dissipation by 2−3 orders of magnitude with respect to the state-of-the-art current control. The interfacial coupling determine magnetoelectric coupling between magnetic and electrical orders in multiferroic thin-film heterostructures though mechanical strain or magnetic exchange and the correlation domains in the neighbourhood of functional ferroic layers [129].

The recent research focuses on the functional multiferroics for spintronics applications. Several types of integration architectures for antiferromagnetic and ferroelectric BiFeO₃ are concerned to serve the ferroelectric and ferromagnetic (La,Bi)MnO₃ as an active tunnel barrier under the magnetic tunnel junctions with (La,Sr)MnO₃ and Au electrodes [130]. The antiferromagnetic and magnetoelectric features also have induced an exchange coupling with a ferromagnet, which paves the way for electrically controlling magnetization and possibly manipulating the logic state of spintronic devices. There have been four resistance states existing in device, where two states originate from a spin filtering effect because of the ferromagnetic character of the barrier and another two states arise from the ferroelectric behavior in the ultrathin (La,Bi)MnO₃ film. The ferroelectric polarization provides additional degree of freedom to novel functional spintronics, either handling gate-controlled magnetic memories or extracting extra order parameter for multiple-state memory elements. The generation and manipulation of spin-polarized current are critical for spintronic devices [39, 131]. The mechanism to generate and switch spin-polarized current by an electric field in multiferroic tunnel junctions (MFTJs), with symmetric interface terminations in an antiparallel magnetic state are proposed. In such devices, different spin tunneling barriers are realized by the magnetoelectric coupling effect, resulting in a spin-polarized current. By reversing the electric polarization of the ferroelectric layer, the spin polarization current is efficiently switched for the exchange of spin tunneling barriers.

Manipulating spin transport can enhance the functional electronic devices to surpass physical constraints in the speed and power. The multiferroics at the interface of heterostructures offer promising prospects for developing high-performance devices to control the electrical spin information. 2D multiferroic materials primarily focus on the stems from an interaction between antiferromagnetism and the breaking inversion symmetry in certain bilayers. An evidence of spin-electrical couplings, manipulating multiferroic edges via external voltages and subsequently controlling spin transport for fully multiferroic spin field-effect transistors, is exhibited [132].

2D multiferroic materials garner widespread interest in field of facilitating the integration and miniaturization of nanodevices. However, one 2D material simultaneously possesses the magnetic, ferroelectric, and ferrovalleyic properties is rare to appear. Interlayer sliding manipulating magnetism, ferroelectric, and valley polarization in a 2D GdI₂ bilayer material is amazed to discover at a ferromagnetic semiconductor with a valley polarization up to 155.5 meV [83]. More interestingly, the magnetism and valley polarization of bilayer GdI₂ can be tunable and reversible. In addition, the magnetic phase transition by a spin Hamiltonian and electron hopping between layers is finally uncovered. These investigations of 2D multiferroics provide a novel direction with implications for next-generation valleytronic, electronic and spintronic devices.

3.3 Sensors & actuators

The multifunctional properties of multiferroics enable researchers to construct novel electronic devices for various sensors, transduction applications [37]. Multiferroic magnetoelectric (ME) composites are attractive for various electrically and magnetically cross-coupled devices. Focusing on fundamental understanding, fabrication processes, and applications of ME composite material systems has been always concerned in the last four decades, which stimulates the technology into realization for practical devices, for example, 2D multiferroic with piezoelectric effect as ideal material for actuators and sensors with wearable and low power consumption [133].

Magnetic-field ME material-based sensors are promisingly alternative for conventional Hall sensors and giant magnetoresistive (GMR) devices. Because of their passive nature and self-powered operation at room temperature, ME sensors enable the replacement of bulky and expensive superconducting quantum interference devices (SQUIDs). ME sensors generate tremendous impact on performing biomagnetic measurements parallel to all the performance of MEG and fMRI. The magnetic field sensors are put into practical applications including two key factors: (i) sensitivity of ~pT to fT per Hz at low frequencies (10² to 10³ Hz) and (ii) ambient temperature and wide bandwidth (0.1 to 100 Hz) operation.

Traditional current sensors, in which the induced electric current by magnetic fields are under detection, typically represent the Hall and reluctance devices [134]. The power of Hall devices needs highly stable constant current, and signal conditioners depend on the inherently weak Hall voltages (5−40 μV/Oe). The interface requirement of reluctance devices is highly precise for integrators, and real-time measurements at low frequencies (100 Hz) are generally inhibited. In contrast, current ME sensors are not subjected to these problems because of the extrinsic ME effect represented by the composites. According to Ampère’s Law, a straight wire bringing an AC or a DC current generally stimulates an AC or DC vortex magnetic field around the wire. The strength of the magnetic field relies on the current I from the wire and the distance r in the wire [H = I/(2πr)]. Therefore, ring-type ME laminates catch the essential configure.

3.4 Energy harvesters

The function for magnetoelectric energy harvester directly depends on magnetoelectric coupling where a magnetoelectric sensor extracts energy from external magnetic field [135]. First prototype magnetoelectric energy harvester consists of composite plates of PZT/Terfenol-D on an ultrasonic horn substrate [136]. Subsequently, many other similar different configuration devices are performed to improve the output power up to 2.11 mW [136, 137]. A dual-band ME energy harvester is of the particular attention for FeCoSiB/PVDF performing wireless energy harvesting and sensing at a limit detection in ultra-small magnetic field of 300–500 pT at 200 Hz, which provides suitable applications for biomedical fields [138]. Nowadays, energy harvesters are still subjected to narrow operational frequency bandwidth. A wideband energy harvester is turned out to compose of series of composite individual fibers for different lengths, which have their own resonance frequencies and the overlapping frequencies to broaden the operating band [139]. Recently, an effective wide band spiral shaped cantilever arrangement multimodal harvester can acquire energy from five frequency bands in the frequency range of 15−70 Hz [140]. What’s more, nonlinear energy harvesters are extracted by interaction between movable magnets and fixed magnets in wide band energy [141].

3.5 Microwave and radio frequency (RF) devices

Magnetoelectric (ME) coupling in multiferroics also opens up an avenue for constructing electrically controllable high frequency deices via switching ferromagnetic resonance frequency (FMR) to modulate ferroelectric polarization of multiferroic [142]. Giant voltage controlled FMR in strain-mediated magnetic/piezoelectric heterostructures provides a strategy for applications in microwave devices, voltage tunable RF, phase shifters, and mini antennas [143]. Electrically tunable strain states in a piezoelectric allow the strain-induced change in magnetic permeability of FM via ME coupling and electrically switchable FMR at very low voltage, which is easy to integrate on a chip for miniaturization and works at very low power consumption. The main drawback exists high noise due dielectric loss at the interface in magnetostrictive alloys. Highquality interface and low noise materials produce low magnetostriction and strain-mediated coupling, so the challenge remains to find low loss magnetic ferrites that can be grown epitaxially with high strain-mediated coupling with piezoelectric material. Among ferrite materials, yttrium iron garnet (YIG) possesses advantage of low absorption, narrow FMR line width and high Q factor at microwave frequencies. YIG/piezoelectric heterostructures have been frequency utilized for synthesizing microwave phase shifter, filter and antenna [114, 144]. ME coupling-induced large FMR shift is of particular attention at ambient temperature in YIG/BTO heterostructures as well as an efficient FMR tuning at low loss and small level voltage in YIG: BTO self-assembled heterostructure and YIG/PMN-Pt layered thin films [144, 145]. The multiferroic heterojunction with both ferroelectric and ferromagnetic properties can achieve voltage-controlled magnetic properties through the strain-induced magnetoelectric coupling effect. The microwave and RF device prepared by this mechanism can meet the requirements of miniaturization, ultra-fast response, and low power consumption, and can generate new functionality. The development of such devices provides broad prospects for the realization of next generation tunable magnetic microwave components and ultra-low power electronic devices.

3.6 Phase shifters

Multiferroic materials can be applied for phase shifters arising from the magnetoelectric coupling. Microwave phase shifters are important elements for telecommunications, oscillators, radar applications and phased array antenna systems. A various phase shifters based on ferrites, semiconductors, and ferroelectrics have been developed [114, 146, 147]. The ferrite phase shifters are based upon the Faraday rotation of electromagnetic radiation with magnetized ferrite rods under waveguides. Magnetic bias fields promise large enough to tune phase, involving high power dissipation; consequently, they have deminiaturized size and compatible integrated circuit technologies. Ferroelectric materials conduct a second category of microwave phase shifters. The big different features are low power consumption and fast electric tunability. A ferrite-ferroelectric layered structure, consisting of a ME composite, provides a route for the application of dual-tunable microwave devices, which offers lower noise, higher efficiency, lightweight and compact size respect to conventional microwave deceives.

In summary, multiferroic materials based on magnetoelectric coupling provide routes to applications in memory devices, spintronics, sensors, actuators, ratio frequency and microwave tunable devices, phase shifters, energy harvesters, and so on. The interface-induced magnetoelectric coupling in multiferroic magnetoelectric nanostructures is exploited for so many various exciting device technologies. In comparison to bulk multiferroic heterostructures, these magnetoelectric nanostructures are much easier to integrate on a chip, and their interfaces become controllable to improve magnetoelectric coupling or designable to realize new functionalities. Despite the appearance of the bright future and amazing progress, numerous challenges and difficulties need to be conquered before these multiferroic nanostructures are put into practical use in the mentioned devices. Facing with the high complexity but strong effectivity of HAMR techniques, the large electric-field-induced coercive magnetic field and perpendicular magnetic anisotropy are desired to reduce for EAMR. The converse magnetoelectric coupling requires further enhancement across the magnetic-ferroelectric interface in the layered thin film, which has huge challenges due to the limitation of the electric-field-induced strain on clamping substrate. One prospective strategy is to excavate the charge-mediated converse magnetoelectric coupling of the interface. Via exchange coupling or magnon excitation, the converse magnetoelectric coupling turns out to be a long spatial scalable effectiveness up to tens of nanometers near the interface. The other more promising solution is to take advantage of the high-density arrays of the layered magnetic-ferroelectric nanoislands. As for the applications of electrically adjustable RF/microwave devices, multiferroic materials need to be energetically developed because low microwave loss and large magnetostriction with high strainmodulated electrical tunability simultaneously exhibit. Selecting and designing great flexible 2D materials is a promising approach to exploit magnetoelectric coupling. Replacement of the expensive and bulky SQUID is necessary, and sensors with low-cost and compactsized magnetoelectric-nanostructure for biomedical imaging and diagnosis become more popular and catch up with faster development. One of the most important requirements is to further improve the sensitivity at low frequency magnetic field. The enhancement approach of the direct magnetoelectric coupling is to optimize the microstructure and interfaces of such multiferroic nanostructures, operate the device in shear mode and reduce the noise level.

4 Conclusion and prospects

2D multiferroic materials have widespread application prospects in facilitating the integration and miniaturization of nanodevices, such as spintronics, nonvanatile memory, sensors, actuators, phase shifters, ratio frequency, energy harvesters. However, the magnetic, ferroelectric, and ferrovalley properties in one 2D material are rarely coupled. In this paper, the fundamental mechanism, category, growth method, advanced characterization method, application, prospects and challenges are overviewed. Multiferroic materials are usually divided into two categories, type I and type II multiferroics. Particularly, type-II multiferroics are rare, representing an inversion-symmetry-breaking magnetic order that immediately introduces ferroelectric polarization via a variety of originated mechanisms, such as the inverse Dzyaloshinskii−Moriya effects or the spin-current. 2D materials equipped with such intrinsic magnetoelectric coupling provide various routes to be long sought for applications in nanoelectronic devices. Bracingly, the discovery of type-II multiferroic order NiI₂ with a single atomic layer, which couples to the charge degree freedoms to induce a chirality-controlled electrical polarization [13] promotes great development for experimentally synthesizing 2D multiferroic materials down to single layer limit.

First, the growth methods of 2D multiferroic materials are viewed, such as mechanical exfoliation, liquid exfoliation, and vapour deposition. Vapour deposition is generally classified into chemical vapour deposition, chemical vapour transport, physical vapour deposition and molecular beam epitaxy. Among these methods, it is a typical technique of VPD to construct atomic-scale films or thin flakes through directly depositing suitable vapour-phase compounds on specific substrates, which can prepare well tunable, large-area uniform and high-quality 2D multiferroic materials. Normally, two main kinds of vapour phase deposition methods are CVD and PVD. CVD is a kind of technique that involves plasma excitation, heating and chemically reacting reactants under certain temperature and gaseous conditions, then the resulting substances are deposited on the substrate surface at an applicable position to fabricate a solid thin film. CVD method can prepare controllable-thickness, large-size, and high-quality 2D materials for further positive application in the electronic industry. PVD is a thin film preparation technique, where materials are deposited on substrates via evaporating, emitting and ion-beam evaporating in a high vacuum environment. It is an efficient method to prepare thin-film materials in industry and commerce, which is the reason that the PVD method can immediately construct 2D materials on the appropriate substrate without another additional chemical reactions. Moreover, MBE growth method and MS method in the PVD method are always applied to prepare 2D multilayer materials. Above all, the CVD and CVT methods are usually sued to prepare 2D multiferroic materials due to their strict requirements on large size, high quality, controllable thickness.

Second, the characterization tools of 2D multiferroic materials have been outlined, such as Raman spectrum, optical second harmonic generator (SHG), XRD, TEM, STM, reflection birefringence (RB), and scanning probe microscope (SPM). Circular dichroic Raman measurements are used to directly probe the magneto-chiral ground state and its electromagnon modes originate from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurements to detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry supports the results of 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 2D limit.

Third, the magnetoelectric counpling for 2D multiferroic materials provide extreme platforms for the application in nonvanatile low power memory, spintronics, sensors, actuators, phase shifters, microwave, ratio frequency, energy harvesters. Even the development of multifunctional 2D materials has been a long-standing research objective, it is still very challenging to observe stable multiferroicity at room temperature in the existing 2D materials.

Fourth, challenges and prospects of 2D multiferroic materials have been performed. Multiferroic materials provide a promising route to operate digital information through making use of the cross-coupling between ferromagnetic and ferroelectric orders. Even though the ferroelectricity has been appeared via interlayer-sliding or ion displacement, one-unit-cell design, and wafer-scale synthesis of multiferroic materials have yet to be achieved. Thus, the interface modulated approach to prepare one-unit-cell of one-inch non-layered multiferroic material Cr₂S₃ with single orientation on the substrate of industry-compatible c-plane sapphire is employed [40]. The interfacial interaction between Cr₂S₃ and substrate introduces the intralayer-sliding of self-intercalated Cr atoms and thus destroys the space reversal symmetry. Consequently, one-unit-cell Cr₂S₃ exhibits robust room-temperature ferroelectricity with ultrahigh remanent polarization. Besides, one-unit-cell Cr₂S₃ represents long-range ferromagnetic order with the Curie temperature of 200 K, which is nearly two times higher than bulk counterpart. Simultaneously, Cr₂S₃ has the magnetoelectric coupling to be certified for the largest and thinnest multiferroics [40].

In general, the researches on 2D multiferroics, including ferroelectric−ferromagnetic, ferromagnetic−ferroelastic, and ferroelectric−ferroelastic, triferroics are still in the infancy, and most of the reported studies are only based on theoretical simulations. In last few years, triferroics synchronously exhibiting ferromagnetic, ferroelectric, and ferrovalley features have been sequentially discovered, which opens greatly novel avenue to capturing the interaction of spin, electronic charge, and valley degrees of freedom. The curious appearance of new physical phenomena and multi-signal response provides great potential application in next-generation multi-information storage devices. The proposed valley polarization spontaneously existed in monolayer orthorhombic group-IV monochalcogenides, modulating valley states by means of electric field and the usual ferromagnetism [148]. Under non-degenerate light excitation, single-layer GeSe experiences an electrically switching polarization of selective x- or y-polarized light under electric field. Particularly, a rare 2D dual-metal trihalide WRuCl₆ monolayer triferroic, ferromagnetism and ferroelasticity are strongly coupled to the ferroelectricity of 120° rotation symmetry from the perspectives of first-principle calculations [149], which enable the flexible and reversible switching of ferroic orders via electric field. In addition, WRuCl₆ monolayer is an intrinsic bipolar magnetic semiconductor; thus, the switchable spin-polarized carrier can be obtained by applying an electric gate voltage to further improve the storage density. Later on, exfoliation from the layered bulk, single-layer FeO₂H identified to harbor in-plane piezoelectric effect exists an intrinsically triferroic semiconductor, simultaneously presenting antiferromagnetism, ferroelasticity, and ferroelectricity, in which the directional-control ferroelectric polarization by 90° reversible ferroelastic switching [150].

Recently, the simultaneous ferroelectricity−ferromagnetism-ferrovalley coexistence in a Nb₃X₈ (X = Cl, Br, I) monolayer is discovered with the breathing kagome lattices [151]. The out-of-plane ferroelectricity polarization as well as the intralayer ferromagnetism is ascribed to the breathing process of Nb-trimer. Besides, ferrovalley polarization can also be switched by the robust ferroelectricity-valley coupling or spin−valley coupling. The breathing process of kagome lattice trimer patterns corresponds to the out-of-plane ferroelectric polarization directions. The magnetism of the Nb-trimer clusters can be generated and annihilated simultaneously at neighboring magnetic sites by reversing the direction of ferroelectric polarization due to magnetoelectric coupling. In addition, a single-phase triferroic in the hole doped GdCl₂ monolayer where three ferroic orders-ferromagnetism, ferroelectricity, and ferroelasticity coexist, simultaneously represents a ferromagnetic semiconductor achieved by substituting 1/3rd of the Gd²⁺ ions with Eu²⁺ in the hexagonal structure of the GdCl₂ monolayer [152]. The metallic state undergoes a bond-centered charge ordering driving a distortion in the hexagonal structure, making it semiconducting again and ferroelastic. Furthermore, the lattice distortion accompanied by breaking the lattice centrosymmetry renders a noncentrosymmetric charge distribution, which makes the monolayer ferroelectric, at the same time. The two ferroic orders, ferroelectricity and ferroelasticity, present in the Eu-substituted GdCl₂ monolayer are found to be strongly coupled, making it a promising candidate for device applications. The Eu-substituted monolayer remains a ferromagnetic semiconductor with a large 4 magnetic moment just like the parent monolayer and possesses an even higher (out-of-plane) magnetic anisotropy energy than its pristine counterpart as desired for two-dimensional magnets to have high transition temperature.

Moreover, a general mechanism for realizing intrinsic ferromagnetic triferroicity in two-dimensional van der Waals lattices through interlayer sliding in bilayer T′-VTe₂, spontaneously exhibiting ferromagnetism, ferroelasticity, and ferroelectricity, shedding the long-sought light for intrinsic triferroicity [153]. Such a system could possess many distinctive physics, for example, the ferroelastic control of magnetization orientation and ferroelectric control of magnetic moment distribution. Additionally, ferroelectric−ferromagnetic-valley coupling has been achieved in monolayer 2H-VSe₂/BiFeO₃(111) heterostructure, where BiFeO₃ is a multiferroic material with ferroelectric polarization and G-type antiferromagnetic orders [154].

Although multiferroics are not new to us, there are still numerous issues that must be addressed. Till now, only a small amount of 2D multiferroic materials, such as NiI₂, Cr₂S₃, CuCrP₂S₆, and CuCrSe₂, have been successfully prepared in experiment with vapour phase deposition method. There plenty of efforts need make for preparing stable, high-quality, large-scale, uniform 2D multiferroic materials to provide various routes in the applications of nonvanatile memory, sensors, actuators, ratio frequency, energy harvesters, spintronics. A novel approach to fabricate 2D non-layered multiferroic materials need be promoted using vdW epitaxy through CVD. New room-temperature multiferroics with strong magnetoelectric coupling need to be discovered. The voltage required for ferroelectric/magnetoelectric switching should be less than 100 mV which can make good impact on those materials. A multiferroic device controlled by an electric field, especially at low voltages, at room temperature, and with rapid switching, remains a primary target. New more efficient mechanisms need to be developed, as the world is progressing at a faster rate. There has been no link to quantum physics as far as multiferroics are concerned, so if this link is established, it would be of great help to the entire community. Dynamical phenomena are still underappreciated issues in multiferroic studies.

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 1264004), the Natural Science Foundation Joint Fund of Hubei Province, China (No. 2024AFD069), the Catching-up Science and Technology Research Funds of Enshi (No. XYJ2023000170), and the Key Laboratory of Green Manufacturing of Super-light Elastomer Materials of State Ethnic Affairs Commission (No. PT092208).

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