Single-phase multiferroics: new materials, phenomena, and physics

Impact of Gd doping on structural and magnetic characteristics of SrFeO3perovskite nanomaterial

The SrFeO3nanoparticles doped with 5% and 10% Gd were synthesized using the solution combustion method. The phase formation of the synthesized nanoparticles was confirmed by powder x-ray diffraction analysis. Field emission scanning electron microscope and HRTEM were employed to examine the morphology of the samples, revealing well-ordered, agglomerated nanoparticles. Energy dispersive x-ray spectroscopy analysis was conducted on all samples, confirming the presence of the desired elements. X-ray photoelectron spectroscopy confirmed the presence of mixed oxidation states of Fe3+and Fe4+. Magnetization studies, performed using a SQUID magnetometer, showed ferromagnetic behaviour in all samples, with a significant increase in magnetic moment observed with higher Gd doping. The enhanced magnetic moments and reduced coercivity in Gd-doped SrFeO3suggest that these materials could be suitable for spintronic applications.

A Multiferroic Spin-Crossover Molecular Crystal

Spin-crossover (SCO) ferroelectrics with dual-function switches have attracted great attention for significant magnetoelectric application prospects. However, the multiferroic crystals with SCO features have rarely been reported. Herein, a molecular multiferroic Fe(II) crystalline complex [FeII(C8-F-pbh)2] (1-F, C8-F-pbh = (1Z,N'E)-3-F-4-(octyloxy)-N'-(pyridin-2-ylmethylene)-benzo-hydrazonate) showing the coexistence of ferroelectricity, ferroelasticity, and SCO behavior is presented for the first time. By H/F substitution, the low phase transition temperature (270 K) of the non-fluorinated parent compound is significantly increased to 318 K in 1-F, which exhibits a spatial symmetry breaking 222F2 type ferroelectric phase transition with clear room-temperature ferroelectricity. Besides, 1-F also displays a spin transition between high- and low-spin states, accompanied by the d-orbital breaking within the t2g 4eg 2 and t2g 6eg° configuration change of octahedrally coordinated FeII center. Moreover, the 222F2 type ferroelectric phase transition is also a ferroelastic one, verified by the ferroelectric domains reversal and the evolution of ferroelastic domains. To the knowledge, 1-F is the first multiferroic SCO molecular crystal. This unprecedented finding sheds light on the exploration of molecular multistability materials for future smart devices.

Single Molecular Semi-Sliding Ferroelectricity/Multiferroicity

In recent years, the unique mechanism of sliding ferroelectricity with ultralow switching barriers has been experimentally verified in a series of 2-dimensional (2D) materials. However, its practical applications are hindered by the low polarizations, the challenges in synthesis of ferroelectric phases limited in specific stacking configurations, and the low density for data storage since the switching process involves large-area simultaneous sliding of a whole layer. Herein, through first-principles calculations, we propose a type of semi-sliding ferroelectricity in the single metal porphyrin molecule intercalated in 2D bilayers. An enhanced vertical polarization can be formed independent on stacking configurations and switched via sliding of the molecule accompanied by the vertical displacements of its metal ion anchored from the upper layer to the lower layer. Such semi-sliding ferroelectricity enables each molecule to store 1 bit data independently, and the density for data storage can be greatly enhanced. When the bilayer exhibits intralayer ferromagnetism and interlayer antiferromagnetic coupling, a considerable difference in Curie temperature between 2 layers and a switchable net magnetization can be formed due to the vertical polarization. At a certain range of temperature, the exchange of paramagnetic-ferromagnetic phases between 2 layers is accompanied by ferroelectric switching, leading to a hitherto unreported type of multiferroic coupling that is long-sought for efficient "magnetic reading + electric writing".

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.

A Route to Two-Dimensional Room-Temperature Organometallic Multiferroics: The Marriage of d-p Spin Coupling and Structural Inversion Symmetry Breaking

Two-dimensional (2D) room-temperature multiferroic materials are highly desirable but still very limited. Herein, we propose a potential strategy to obtain such materials in 2D metal-organic frameworks (MOFs) by utilizing the d-p direct spin coupling in conjunction with center-symmetry-breaking six-membered heterocyclic rings. Based on this strategy, a screening of 128 2D MOFs results in the identification of three multiferroics, that is, Cr(1,2-oxazine)2, Cr(1,2,4-triazine)2, and Cr(1,2,3,4-trazine)2, simultaneously exhibiting room-temperature ferrimagnetism and ferroelectricity/antiferroelectricity. The room-temperature ferrimagnetic order (306-495 K) in these MOFs originates from the strong d-p direct magnetic exchange interaction between Cr cations and ligand anions. Specifically, Cr(1,2-oxazine)2 exhibits ferroelectric behavior with an out-of-plane polarization of 4.24 pC/m, whereas the other two manifest antiferroelectric characteristics. Notably, all three materials present suitable polarization switching barriers (0.18-0.31 eV). Furthermore, these MOFs are all bipolar magnetic semiconductors with moderate band gaps, in which the spin direction of carriers can be manipulated by electrical gating.

Coexistence of Ferroelectricity and Ferromagnetism in Atomically Thin Two-Dimensional Cr2S3/WS2 Vertical Heterostructures

Two-dimensional (2D) heterostructures with ferromagnetism and ferroelectricity provide a promising avenue to miniaturize the device size, increase computational power, and reduce energy consumption. However, the direct synthesis of such eye-catching heterostructures has yet to be realized up to now. Here, we design a two-step chemical vapor deposition strategy to growth of Cr2S3/WS2 vertical heterostructures with atomically sharp and clean interfaces on sapphire. The interlayer charge transfer and periodic moiré superlattice result in the emergence of room-temperature ferroelectricity in atomically thin Cr2S3/WS2 vertical heterostructures. In parallel, long-range ferromagnetic order is discovered in 2D Cr2S3 via the magneto-optical Kerr effect technique with the Curie temperature approaching 170 K. The charge distribution variation induced by the moiré superlattice changes the ferromagnetic coupling strength and enhances the Curie temperature. The coexistence of ferroelectricity and ferromagnetism in 2D Cr2S3/WS2 vertical heterostructures provides a cornerstone for the further design of logic-in-memory devices to build new computing architectures.

Robust multiferroic in interfacial modulation synthesized wafer-scale one-unit-cell of chromium sulfide

Multiferroic materials offer a promising avenue for manipulating digital information by leveraging the cross-coupling between ferroelectric and ferromagnetic orders. Despite the ferroelectricity has been uncovered by ion displacement or interlayer-sliding, one-unit-cell of multiferroic materials design and wafer-scale synthesis have yet to be realized. Here we develope an interface modulated strategy to grow 1-inch one-unit-cell of non-layered chromium sulfide with unidirectional orientation on industry-compatible c-plane sapphire. The interfacial interaction between chromium sulfide and substrate induces the intralayer-sliding of self-intercalated chromium atoms and breaks the space reversal symmetry. As a result, robust room-temperature ferroelectricity (retaining more than one month) emerges in one-unit-cell of chromium sulfide with ultrahigh remanent polarization. Besides, long-range ferromagnetic order is discovered with the Curie temperature approaching 200 K, almost two times higher than that of bulk counterpart. In parallel, the magnetoelectric coupling is certified and which makes 1-inch one-unit-cell of chromium sulfide the largest and thinnest multiferroics.

Model for Nonrelativistic Topological Multiferroic Matter

We provide a model capable of accounting for the multiferroicity in certain materials. The model's base is on free electrons and spin moments coupled within nonrelativistic quantum mechanics. The synergistic interplay between the magnetic and electric degrees of freedom that turns into the multiferroic phenomena occurs at a profound quantum mechanical level, conjured by Berry's phases and the quantum theory of polarization. Our results highlight the geometrical nature of the multiferroic order parameter that naturally leads to magnetoelectric domain walls, with promising technological potential.

Colossal Linear Magnetoelectricity in Polar Magnet Fe_{2}Mo_{3}O_{8}

The linear magnetoelectric effect is an attractive phenomenon in condensed matters and provides indispensable technological functionalities. Here a colossal linear magnetoelectric effect with diagonal component α_{33} reaching up to ∼480  ps/m is reported in a polar magnet Fe_{2}Mo_{3}O_{8}. This effect can persist in a broad range of magnetic field (∼20  T) and is orders of magnitude larger than reported values in literature. Such an exceptional experimental observation can be well reproduced by a theoretical model affirmatively unveiling the vital contributions from the exchange striction, while the sign difference of magnetocrystalline anisotropy can also be reasonably figured out.

Ferroic Phases in Two-Dimensional Materials

Two-dimensional (2D) ferroics, namely ferroelectric, ferromagnetic, and ferroelastic materials, are attracting rising interest due to their fascinating physical properties and promising functional applications. A variety of 2D ferroic phases, as well as 2D multiferroics and the novel 2D ferrovalleytronics/ferrotoroidics, have been recently predicted by theory, even down to the single atomic layers. Meanwhile, some of them have already been experimentally verified. In addition to the intrinsic 2D ferroics, appropriate stacking, doping, and defects can also artificially regulate the ferroic phases of 2D materials. Correspondingly, ferroic ordering in 2D materials exhibits enormous potential for future high density memory devices, energy conversion devices, and sensing devices, among other applications. In this paper, the recent research progresses on 2D ferroic phases are comprehensively reviewed, with emphasis on chemistry and structural origin of the ferroic properties. In addition, the promising applications of the 2D ferroics for information storage, optoelectronics, and sensing are also briefly discussed. Finally, we envisioned a few possible pathways for the future 2D ferroics research and development. This comprehensive overview on the 2D ferroic phases can provide an atlas for this field and facilitate further exploration of the intriguing new materials and physical phenomena, which will generate tremendous impact on future functional materials and devices.

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

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

Antiferromagnetic to Ferrimagnetic Phase Transition and Possible Phase Coexistence in Polar Magnets (Fe1-xMnx)2Mo3O8 (0 ≤ x ≤ 1)

In the present work, the magnetic properties of a single crystal (Fe_1-xMn_x)₂Mo₃O₈ (0 ≤ x ≤ 1) have been studied by performing extensive measurements. A detailed magnetic phase diagram is built up, in which the antiferromagnetic state dominates for x ≤ 0.25 and the ferrimagnetic phase arises for x ≥ 0.3. Meanwhile, a sizeable electric polarization of spin origin is commonly observed in all samples, no matter what the magnetic state is. For the samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops are revealed, while the remnant magnetization and coercive field can be tuned drastically by simply varying the Mn content or temperature. A possible coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be responsible for the remarkable modulation of magnetic properties in the samples.

Quintuple Function Integration in Two-Dimensional Cr(II) Five-Membered Heterocyclic Metal Organic Frameworks via Tuning Ligand Spin and Lattice Symmetry

Two-dimensional (2D) semiconductors (SCs) integrated with two or more functions are the cornerstone for constructing multifunctional nanodevices but remain largely limited. Here, by tuning the spin state of organic linkers and the symmetry/topology of crystal lattices, we predict a class of unprecedented multifunctional SCs in 2D Cr(II) five-membered heterocyclic metal organic frameworks that simultaneously possess auxetic effect, room-temperature ferrimagnetism, chiral ferroelectricity (FE), electrically reversible spin polarization, and topological nodal lines/points. Taking 2D Cr(TDZ)₂ (TDZ = 1.2.5-thiadiazole) as an exemplification, the auxetic effect is produced by the antitetra-chiral lattice structure. The high temperature ferrimagnetism originates from the strong d-p direct magnetic exchange interaction between Cr cations and TDZ doublet radical anions. Meanwhile, the clockwise-counterclockwise alignment of TDZ's dipoles results in unique 2D chiral FE with atomic-scale vortex-antivortex states. 2D Cr(TDZ)₂ is an intrinsic bipolar magnetic SC where half-metallic conduction with switchable spin-polarization direction can be induced by applying a gate voltage. In addition, the symmetry of the little group C₄ of the lattice structure endows 2D Cr(TDZ)₂ with topological nodal lines and a quadratic nodal point in the Brillouin zone near the Fermi level.

Nanomedicine and nanobiotechnology applications of magnetoelectric nanoparticles

Unlike any other nanoparticles known to date, magnetoelectric nanoparticles (MENPs) can generate relatively strong electric fields locally via the application of magnetic fields and, vice versa, have their magnetization change in response to an electric field from the microenvironment. Hence, MENPs can serve as a wireless two-way interface between man-made devices and physiological systems at the molecular level. With the recent development of room-temperature biocompatible MENPs, a number of novel potential medical applications have emerged. These applications include wireless brain stimulation and mapping/recording of neural activity in real-time, targeted delivery across the blood-brain barrier (BBB), tissue regeneration, high-specificity cancer cures, molecular-level rapid diagnostics, and others. Several independent in vivo studies, using mice and nonhuman primates models, demonstrated the capability to deliver MENPs in the brain across the BBB via intravenous injection or, alternatively, bypassing the BBB via intranasal inhalation of the nanoparticles. Wireless deep brain stimulation with MENPs was demonstrated both in vitro and in vivo in different rodents models by several independent groups. High-specificity cancer treatment methods as well as tissue regeneration approaches with MENPs were proposed and demonstrated in in vitro models. A number of in vitro and in vivo studies were dedicated to understand the underlying mechanisms of MENPs-based high-specificity targeted drug delivery via application of d.c. and a.c. magnetic fields. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Therapeutic Approaches and Drug Discovery > Nanomedicine for Neurological Disease Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease Therapeutic Approaches and Drug Discovery > Emerging Technologies.

Designing a ferrimagnetic-ferroelastic multiferroic semiconductor in FeMoClO4 nanosheets via element substitution

Exploring two-dimensional multiferroic semiconductors, combined with ferro-/ferrimagnetism and ferroelasticity as well as large spin polarization around the valence band maximum (VBM) and conduction band minimum (CBM), is highly desirable but remains a challenging task. Here, via first-principles calculations, we predict such a material based on the square phase FeMoClO₄ nanosheet, which is experimentally accessible by exfoliating its layered bulk. Pristine FeMoClO₄ nanosheets are a weak antiferromagnet with zero spin polarization. After substituting nonmagnetic Mo with magnetic Mn, the resulting FeMnClO₄ nanosheet becomes ferrimagnetic with magnetic ordering temperature significantly enhanced from 14 to 127 K. Besides, the FeMnClO₄ nanosheet is a half semiconductor with its VBM and CBM 100% spin-polarized in the same spin direction. Interestingly, the initial square lattice is distorted into a rectangular one, inducing an in-plane ferroelasticity in the FeMnClO₄ nanosheet with a switching barrier of 27 meV per atom. Moreover, under ferroelastic transition, the orientation of the magnetic easy axis can be reversibly rotated by 90°, indicating a strong magnetoelastic coupling.

Two-dimensional multiferroic material of metallic p-doped SnSe

Two-dimensional multiferroic materials have garnered broad interests attributed to their magnetoelectric properties and multifunctional applications. Multiferroic heterostructures have been realized, nevertheless, the direct coupling between ferroelectric and ferromagnetic order in a single material still remains challenging, especially for two-dimensional materials. Here, we develop a physical vapor deposition approach to synthesize two-dimensional p-doped SnSe. The local phase segregation of SnSe₂ microdomains and accompanying interfacial charge transfer results in the emergence of degenerate semiconductor and metallic feature in SnSe. Intriguingly, the room-temperature ferrimagnetism has been demonstrated in two-dimensional p-doped SnSe with the Curie temperature approaching to ~337 K. Meanwhile, the ferroelectricity is maintained even under the depolarizing field introduced by SnSe₂. The coexistence of ferrimagnetism and ferroelectricity in two-dimensional p-doped SnSe verifies its multiferroic feature. This work presents a significant advance for exploring the magnetoelectric coupling in two-dimensional limit and constructing high-performance logic devices to extend Moore’s law.

2D multiferroic materials have garnered broad interests due to their magnetoelectric properties and multifunctional applications. Here, the authors discover a multiferroic feature in physical vapor deposition synthesized 2D metallic p-doped SnSe.

Magnetic field reversal of electric polarization and pressure-temperature-magnetic field magnetoelectric phase diagram of the hexaferrite Ba0.4Sr1.6Mg2Fe12O22

Pressure, as an independent thermodynamic parameter, is an effective tool to obtain novel material system and exotic physical phenomena not accessible at ambient conditions, because it profoundly modifies the charge, orbital and spin state by reducing the interatomic distance in crystal structure. However, the studies of magnetoelectricity and multiferroicity are rarely extended to high pressure dimension due to properties measured inside the high pressure vessel being a challenge. Here we reported the temperature-magnetic field-pressure magnetoelectric (ME) phase diagram of Y type hexaferrite Ba_0.4Sr_1.6Mg₂Fe₁₂O₂₂derived from static pyroelectric current measurement and dynamic magnetodielectric in diamond anvil cell and piston cylinder cell. We found that a new spin-driven ferroelectric phase emerged atP= 0.7 GPa and sequentially ME effect disappeared aroundP= 4.3 GPa. The external pressure may enhance easy plane anisotropy to destabilize the longitudinal conical magnetic structure with the suppression of ME coefficient. These results offer essential clues for the correlation between ME effect and magnetic structure evolution under high pressure.

Two-Dimensional Organic-Inorganic Room-Temperature Multiferroics

Organic-inorganic multiferroics are promising for the next generation of electronic devices. To date, dozens of organic-inorganic multiferroics have been reported; however, most of them show a magnetic Curie temperature much lower than room temperature, which drastically hampers their application. Here, by performing first-principles calculations and building effective model Hamiltonians, we reveal a molecular orbital-mediated magnetic coupling mechanism in two-dimensional Cr(pyz)₂ (pyz = pyrazine) and the role that the valence state of the molecule plays in determining the magnetic coupling type between metal ions. Based on these, we demonstrate that a two-dimensional organic-inorganic room-temperature multiferroic, Cr(h-fpyz)₂ (h-fpyz = half-fluoropyrazine), can be rationally designed by introducing ferroelectricity in Cr(pyz)₂ while keeping the valence state of the molecule unchanged. Our work not only reveals the origin of magnetic coupling in 2D organic-inorganic systems but also provides a way to design room-temperature multiferroic materials rationally.

2D Multiferroicity with Ferroelectric Switching Induced Spin-Constrained Photoelectricity

Multiferroic materials with tunable magnetoelectric orders enable the integration of sensing, data storage, and processing into one single device. The scarcity of single-phase multiferroics spurs extensive research in pursuit of composite systems combining different types of ferroic materials. In this work, spin-constrained photoelectric memory is proposed in two-dimensional (2D) layered magnetic/ferroelectric heterostructures, holding the possibility of low-power electrical write operation and nondestructive optical read operation. The ground state of ferromagnetic (FM) and antiferromagnetic (AFM) orderings in the magnetic layer is altered by polarization direction of the ferroelectric layer. Specifically, the FM heterostructure exhibits a type-II band alignment. Due to the light-induced charge transfer, spin-polarized/unpolarized current arises from the FM/AFM state, which can be recorded as the "1"/"0" state and served for logic processing and memory applications. Our first-principles calculations demonstrate that the NiI₂/In₂Se₃ heterobilayer is an ideal candidate to realize such a spin-dependent photoelectric memory. The reversible FM state (easy-axis magnetic anisotropy) and AFM state (easy-plane magnetic orientation) in the NiI₂ layer originate from interfacial charge transfer and effective electric field due to the proximity effect. This work offers considerable potential in the integration of memory processing capability into one single device with 2D layered multiferroic heterostructures.

Pressure Control of the Structure and Multiferroicity in a Hydrogen-Bonded Metal-Organic Framework

Multiferroic materials with the cross-coupling of magnetic and ferroelectric orders provide a new platform for physics study and designing novel electronic devices. However, the weak coupling strength of ferroelectricity and magnetism is the main obstacle for potential applications. The recent research focuses on enhancing the coupling effect via synthesizing novel materials in a chemical route or tuning the multiferroicity in the physical way. Among them, pressure is an effective method to modify multiferroic materials, especially when the chemical doping has reached its tuning limit. In this work, we systemically studied the multiferroic properties in a hydrogen-bonded metal-organic framework (MOF) [(CH₃)₂NH₂]Ni(HCOO)₃ under high pressure. X-ray diffraction and Raman scattering reveal that a structural phase transition occurs in a pressure region of 6-9 GPa, and the crystal structure is greatly modified by pressure. With the ac magnetic susceptibility, pyroelectric current, and dielectric constant measurements, we obtain the multiferroic property evolution under high pressure and create a temperature-pressure phase diagram. Our study demonstrates that the pressure can modify the magnetic superexchange interaction and hydrogen bonding simultaneously in these perovskite-like MOFs. The multiferroic phase region has been expanded to higher temperature due to the pressure-enhanced spin-phonon coupling effect.

On-demand quantum spin Hall insulators controlled by two-dimensional ferroelectricity

We propose a new class of quantum materials, type-II two-dimensional ferroelectric topological insulators (2DFETIs), which allow non-volatility and an on-off switch of quantum spin Hall states. A general strategy is developed to realize type-II 2DFETIs using only topologically trivial 2D ferroelectrics. The built-in electric field arising from the out-of-plane polarization across the bilayer heterostrucuture of 2D ferroelectrics enables robust control of the band gap size and band inversion strength, which can be utilized to manipulate the topological phase transitions on-demand. Using first-principles calculations with hybrid density functionals, we demonstrate that a series of bilayer heterostructures are type-II 2DFETIs characterized with a direct coupling between the band topology and polarization state. We propose a few 2DFETI-based quantum electronics, including domain-wall quantum circuits and topological memristors.

Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) reside on the topological Roman surface-a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.

Carrier doping-induced strong magnetoelastic coupling in 2D lattice

The realization of intertwined ferroelasticity and ferromagnetism in two-dimensional (2D) lattices is of great interest for broad nanoscale applications but still remains a remarkable challenge. Here, we propose an alternative approach to realize the strongly coupled ferromagnetism and ferroelasticity by carrier doping. We demonstrate that prototypical 2D β-PbO is dynamically, thermally and mechanically stable. Under hole doping, 2D β-PbO possesses ferromagnetism and ferroelasticity simultaneously. Moreover, the robustness of ferromagnetic and ferroelastic orders is doping tunable. In particular, 2D β-PbO features an in-plane easy magnetization axis that is coupled with the lattice direction, enabling the ferroelastic manipulation of the spin direction. Furthermore, the efficient ferroelastic control of the anisotropic optical property and spin splitting in 2D β-PbO are also clarified. Our study highlights a new direction for 2D magnetoelastic research and enables the possibility for multifunctional devices.

Material research from the viewpoint of functional motifs

As early as 2001, the need for the ‘functional motif theory’ was pointed out to assist the rational design of functional materials. The properties of materials are determined by their functional motifs and by how they are arranged in the materials. Uncovering the functional motifs and their arrangements is crucial in understanding the properties of materials and rationally designing new materials of desired properties. The functional motifs of materials are the critical microstructural units (e.g. constituent components and building blocks) that play a decisive role in generating certain material functions, and could not be replaced with other structural units without losing or significantly suppressing the relevant functions. The role of functional motifs and their arrangements in materials with representative examples was presented. These examples could be classified into six types of material microscopic structures on a length scale smaller than ∼10 nm with maximum subatomic resolution, i.e. the crystal, magnetic, aperiodic, defect, local, and electronic structures. The method of functional motif analysis could be employed in the function-oriented design of materials, as elucidated by taking infrared nonlinear optical materials as an example. Machine learning is more efficient in predicting material properties and screening materials with high efficiency than high-throughput experimentation and high-throughput calculations. In extracting the functional motifs and finding their quantitative relationships, developing sufficiently reliable databases for material structures and properties is imperative.

Crystal Structure and Concentration-Driven Phase Transitions in Lu(1-x)ScxFeO3 (0 ≤ x ≤ 1) Prepared by the Sol-Gel Method

The structural state and crystal structure of Lu_(1−x)Sc_xFeO₃ (0 ≤ x ≤ 1) compounds prepared by a chemical route based on a modified sol–gel method were investigated using X-ray diffraction, Raman spectroscopy, as well as scanning electron microscopy. It was observed that chemical doping with Sc ions led to a structural phase transition from the orthorhombic structure to the hexagonal structure via a wide two-phase concentration region of 0.1 < x < 0.45. An increase in scandium content above 80 mole% led to the stabilization of the non-perovskite bixbyite phase specific for the compound ScFeO₃. The concentration stability of the different structural phases, as well as grain morphology, were studied depending on the chemical composition and synthesis conditions. Based on the data obtained for the analyzed samples, a composition-dependent phase diagram was constructed.

Prediction of two-dimensional monolayer C2O2Fe with chiral magnetic and ferroelectric orders

Low-dimensional multiferroics are highly desired for applications and contain exotic physics properties. Here we predict a two-dimensional material, C2O2Fe monolayer, through Fe intercalation in the graphene oxide monolayer. The crystal...

Direct Evidence for an Intermediate Multiferroic Phase in LiCuFe2(VO4)3

Magnetic susceptibility, specific heat, dielectric, and electric polarization of LiCuFe₂(VO₄)₃ have been investigated. Two sequential antiferromagnetic transitions at T_N1 ∼ 9.95 K and T_N2 ∼ 8.17 K are observed under zero magnetic field. Although a dielectric peak at T_N1 is clearly identified, the measured pyroelectric current also exhibits a sharp peak at T_N1, implying the magnetically relevant ferroelectricity. Interestingly, another pyroelectric peak around T_N2 with an opposite signal is observed, resulting in the disappearance of electric polarization below T_N2. Besides, the electric polarization is significantly suppressed in response to external magnetic field, evidencing a remarkable magnetoelectric effect. These results suggest the essential relevance of the magnetic structure with the ferroelectricity in LiCuFe₂(VO₄)₃, deserving further investigation of the underlying mechanism.

Magnetoelectric Effect in Garnet Mn3Al2Ge3O12

Searching for novel magnetoelectric (ME) materials has been one of the major issues of multiferroics. In this work, we present a systematic research study on garnet Mn₃Al₂Ge₃O₁₂, including structural, magnetic, heat capacity, and ME characterizations. Below the Néel temperature T_N ∼ 6.8 K, Mn²⁺ spins form a long-range antiferromagnetic order, and a magnetic field H-driven electric polarization P is identified simultaneously. The relationship between P and H is nonlinear under low H and becomes linear under high H. Such transition is believed to originate from the H-induced variation of the magnetic structure. In addition, the P reaches 0.6 μC/m² under μ₀H = 9 T, corresponding to an ME coupling coefficient of α_ME ∼ 0.08 ps/m under high H. The small α_ME is attributed to the weak spin-orbit coupling and weak magnetic interactions in Mn₃Al₂Ge₃O₁₂. Furthermore, we realize the stable control of P by periodically varying H, which is crucial for potential application. We provide a rare case that a garnet material shows a first-order ME effect.

Sliding ferroelectricity in 2D van der Waals materials: Related physics and future opportunities

Near the 100th anniversary of the discovery of ferroelectricity, so-called sliding ferroelectricity has been proposed and confirmed recently in a series of experiments that have stimulated remarkable interest. Such ferroelectricity exists widely and exists only in two-dimensional (2D) van der Waals stacked layers, where the vertical electric polarization is switched by in-plane interlayer sliding. Reciprocally, interlayer sliding and the "ripplocation" domain wall can be driven by an external vertical electric field. The unique combination of intralayer stiffness and interlayer slipperiness of 2D van der Waals layers greatly facilitates such switching while still maintaining environmental and mechanical robustness at ambient conditions. In this perspective, we discuss the progress and future opportunities in this behavior. The origin of such ferroelectricity as well as a general rule for judging its existence are summarized, where the vertical stacking sequence is crucial for its formation. This discovery broadens 2D ferroelectrics from very few material candidates to most of the known 2D materials. Their low switching barriers enable high-speed data writing with low energy cost. Related physics like Moiré ferroelectricity, the ferroelectric nonlinear anomalous Hall effect, and multiferroic coupling are discussed. For 2D valleytronics, nontrivial band topology and superconductivity, their possible couplings with sliding ferroelectricity via certain stacking or Moiré ferroelectricity also deserve interest. We provide critical reviews on the current challenges in this emerging area.

A two-dimensional multiferroic metal with voltage-tunable magnetization and metallicity

We design a multiferroic metal that combines seemingly incompatible ferromagnetism, ferroelectricity, and metallicity by hole doping a two-dimensional (2D) ferroelectric with high density of states near the Fermi level. The strong magnetoelectric effect is demonstrated in hole-doped and arsenic-doped monolayer α-In₂Se₃ using first-principles calculations. Taking advantage of the oppositely charged surfaces created by an out-of-plane polarization, the 2D magnetization and metallicity can be electrically switched on and off in an asymmetrically doped monolayer. The substitutional arsenic defect pair exhibits an intriguing electric field-tunable charge disproportionation process accompanied by an on-off switch of local magnetic moments. The charge ordering process can be controlled by tuning the relative strength of on-site Coulomb repulsion and defect dipole-polarization coupling via strain engineering. Our design principle relying on no transition metal broadens the materials design space for 2D multiferroic metals.

Two-Dimensional van der Waals Ferroelectrics: Scientific and Technological Opportunities

Recent breakthroughs in two-dimensional (2D) van der Waals ferroelectrics have been impressive, with a series of 2D ferroelectrics having been realized experimentally. The discovery of ferroelectric order in atom-thick layers not only is important for exploring the interplay between dimensionality and ferroelectric order but may also enable ultra-high-density memory, which has attracted significant interest. However, understanding of 2D ferroelectrics goes beyond simply their atomic-scale thickness. In this Perspective, I suggest possible innovations that may resolve a number of conventional issues and greatly transform the roles of ferroelectrics in nanoelectronics. The major obstacles in the commercialization of nanoelectronic devices based on current ferroelectrics involve their insulating and interfacial issues, which hinder their combination with semiconductors in nanocircuits and reduce their efficiency in data reading/writing. In comparison, the excellent semiconductor performance of many 2D ferroelectrics may enable computing-in-memory architectures or efficient ferroelectric photovoltaics. In addition, their clean van der Waals interfaces can greatly facilitate their integration into silicon chips, as well as the popularization of nondestructive data reading and indefatigable data writing. Two-dimensional ferroelectrics also give rise to new physics such as interlayer sliding ferroelectricity, Moiré ferroelectricity, switchable metallic ferroelectricity, and unconventional robust multiferroic couplings, which may provide high-speed energy-saving data writing and efficient data-reading strategies. The emerging 2D ferroelectric candidates for optimization will help resolve some current issues (e.g., weak vertical polarizations), and further exploitation of the aforementioned advantages may open a new era of nanoferroelectricity.

A multiaxial lead-free two-dimensional organic-inorganic perovskite ferroelectric

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) have recently gained tremendous interest because of their unique features in contrast to three-dimensional counterparts and traditional 2D materials. However, although some 2D HOIP ferroelectrics have been achieved, the issue of toxic Pb and uniaxial nature impede their further application. Herein, for the first time, we report a lead-free 2D HOIP multiaxial ferroelectric, [3,3-difluorocyclobutylammonium]2CuCl4 (1), which shows four ferroelectric axes and eight equivalent polarization directions, more than those of the other 2D HOIP ferroelectrics and even the inorganic perovskite ferroelectric BaTiO3 (three ferroelectric axes and six equivalent polarization directions). 1 also features a high Curie temperature of 380 K and exhibits remarkable thermochromism of color change from green-yellow to dark brown. To our knowledge, 1 is the first multiaxial lead-free 2D HOIP ferroelectric. This work sheds light on the exploration of better lead-free 2D HOIP ferroelectrics.

Nanoscale Magnetization Reversal by Magnetoelectric Coupling Effect in Ga0.6Fe1.4O3 Multiferroic Thin Films

The control of magnetism by electric means in single-phase multiferroic materials is highly desirable for the realization of next-generation magnetoelectric (ME) multifunctional devices. Nevertheless, most of these materials reveal either low working temperature or antiferromagnetic nature, which severely limits the practical applications. Herein, we selected room-temperature multiferroic Ga_0.6Fe_1.4O₃ (GFO) with ferrimagnetism to study electric-field-induced nanoscale magnetic domain reversal. The GFO thin film fabricated on the (111)-orientated Nb-doped SrTiO₃ single-crystal substrate was obtained through the pulsed laser deposition method. The test results indicate that the thin film not only exhibits ferroelectricity but also ferrimagnetism at room temperature. More importantly, reversible and nonvolatile nanoscale magnetic domains reversal under pure electrical fields is further demonstrated by taking advantage of its ME coupling effect with dependent origins based on iron ions. When providing an appropriate applied voltage, clear magnetic domain structures with large size can be easily manipulated. Meanwhile, the change ratio of the electrically induced magnetizations in the defined areas can reach up to 72%. These considerable merits of the GFO thin film may provide a huge potential in the ME multifunctional devices, such as the multi-value, low-energy-consuming, and nonvolatile memory and beyond.

Manipulation of Magnetic Domain Walls by Ferroelectric Switching: Dynamic Magnetoelectricity at the Nanoscale

Controlling magnetism using voltage is highly desired for applications, but remains challenging due to a fundamental contradiction between polarity and magnetism. Here, we propose a mechanism to manipulate magnetic domain walls in ferrimagnetic or ferromagnetic multiferroics using the electric field. Different from those studies based on static domain-level couplings, here the magnetoelectric coupling relies on the collaborative spin dynamics around domain walls. Accompanying the reversal of spin chirality driven by polarization switching, a "rolling-downhill"-like motion of the domain wall is achieved in nanoscale, which tunes the magnetization locally. Our mechanism opens an alternative route to the pursuit of practical and fast converse magnetoelectric functions via spin dynamics.

The observed topological vortex domains and the rotating magnetocaloric effect in the hexagonal RMnO3 (R = Ho, Er, and Yb) crystals

Hexagonal RMnO₃ (R = Er, Ho and Yb) single crystals were grown and their unique vortex domain structures, magnetic properties and magnetocaloric effect (MCE) were comprehensively investigated. The topological vortex domains/structures were clearly illustrated by polarized optical microscope and piezo response force microscopy, confirming a high quality of the crystals. The magnetic transitions related to R ³⁺-Mn³⁺ interactions and anisotropic properties were observed in the RMnO₃ crystals. The broad peaks of magnetic entropy change -ΔS _M appeared around [Formula: see text] revealed that the order of R ³⁺ moments is crucial to the large MCE. A giant rotating MCE (RMCE: ∼10.57 J kg^-1 K^-1) was obtained with magnetic field changing from 0 to 50 kOe in ErMnO₃, accompanied with a large refrigerant capacity (RC: ∼159 J kg^-1). These significant RMCE and RC behaviors are found to be closely related to the R ³⁺-R ³⁺, and R ³⁺-Mn³⁺ interactions in these RMnO₃. These results may open up a possibility for designing low-temperature magnetic cooling devices by tailoring the R-4f and Mn-3d orbit interactions.

Magnetoelectrics: Three Centuries of Research Heading towards the 4.0 Industrial Revolution

Magnetoelectric (ME) materials composed of magnetostrictive and piezoelectric phases have been the subject of decades of research due to their versatility and unique capability to couple the magnetic and electric properties of the matter. While these materials are often studied from a fundamental point of view, the 4.0 revolution (automation of traditional manufacturing and industrial practices, using modern smart technology) and the Internet of Things (IoT) context allows the perfect conditions for this type of materials being effectively/finally implemented in a variety of advanced applications. This review starts in the era of Rontgen and Curie and ends up in the present day, highlighting challenges/directions for the time to come. The main materials, configurations, ME coefficients, and processing techniques are reported.

Multiferroic decorated Fe2O3 monolayer predicted from first principles

Two-dimensional (2D) multiferroics exhibit cross-control capacity between magnetic and electric responses in a reduced spatial domain, making them well suited for next-generation nanoscale devices; however, progress has been slow in developing materials with required characteristic properties. Here we identify by first-principles calculations robust 2D multiferroic behaviors in decorated Fe2O3 monolayers, showcasing Li@Fe2O3 as a prototypical case, where ferroelectricity and ferromagnetism stem from the same origin, namely Fe d-orbital splitting induced by the Jahn-Teller distortion and associated crystal field changes. These findings establish strong material phenomena and elucidate the underlying physics mechanism in a family of truly 2D multiferroics that are highly promising for advanced device applications.

Two-Dimensional Multifunctional Metal-Organic Frameworks with Simultaneous Ferro-/Ferrimagnetism and Vertical Ferroelectricity

Exploring 2D multifunctional materials with intrinsic ferro-/ferrimagnetism and vertical ferroelectricity is a highly desirable but challenging task. Here, motivated by the recently synthesized organometallic frameworks K₃Fe₂[PcFeO₈], we propose to realize such materials in a series of 2D K₃M₂[PcMO₈] (M = Cr-Co) nanosheets. First-principles calculations suggest 2D K₃Cr₂[PcCrO₈] as a ferromagnetic half metal with a Curie temperature of 140 K, whereas others (M = Mn, Fe, and Co) are all ferrimagnetic semiconductors with the Curie temperatures between 66 and 150 K. Moreover, the structural distortion due to the out-of-plane K⁺ counterions leads to a significant vertical electric polarization. The estimated intensity of polarization for K₃Fe₂[PcFeO₈] is 143 pC/m, with the ferroelectric phase-transition barrier being 0.38 eV per formula. This work highlights the potential of 2D organometallic frameworks such as K₃M₂[PcMO₈] as a versatile platform for designing multifunctional materials with simultaneous ferro-/ferrimagnetism and vertical ferroelectricity.

Room-temperature multiferroicity and diversified magnetoelectric couplings in 2D materials

Multiferroics are rare in nature due to the mutual exclusive origins of magnetism and ferroelectricity. The simultaneous coexistence of robust magnetism/ferroelectricity and strong magnetoelectric coupling in single multiferroics is hitherto unreported, which may also be attributed to their potential conflictions. In this paper, we show the first-principles evidence of such desired coexistence in ultrathin-layer CuCrS2 and CuCrSe2. The vertical ferroelectricity is neither induced by an empty d shell nor spin-driven, giving rise to an alternative possibility of resolving those intrinsic exclusions and contradictions. Compared with their bulk phases, the ferromagnetism in the thin-layer structures (two-six layers) can be greatly stabilized due to the enhanced carrier density and orbital shifting by vertical polarization, and the Curie temperatures of both ferromagnetism and ferroelectricity can be above room temperature. Moreover, a considerable net magnetization can be reversed upon ferroelectric switching, where the change in spin-resolved band structure also renders efficient 'magnetic reading + electrical writing'. The thickness-different layers may even exhibit diversified types of magnetoelectric coupling, which both enriches the physics of multiferroics and facilitates their practical applications.