Magnetoelectricity in multiferroics: a theoretical perspective

Defect effects on the electronic, valley, and magnetic properties of the two-dimensional ferrovalley material VSi2N4

Due to their novel spin and valley properties, two-dimensional (2D) ferrovalley materials are expected to be promising candidates for next-generation spintronic and valleytronic devices. However, they are subject to various defects in practical applications. Therefore, the electronic, valley, and magnetic properties may be modified in the presence of the defects. In this work, utilizing first-principles calculations, we systematically studied the effects of defects on the electronic, valley, and magnetic properties of the 2D ferrovalley material VSi2N4. It has been found that C doping, O doping, and N vacancies result in the half-metallic feature, Si vacancies result in the metallic feature, and V vacancies result in a bipolar gapless semiconductor. These defect-induced electronic properties can be effectively tuned by changing defect concentration and layer thickness. Since the impurity bands do not affect the K and K' valleys, valley polarization is well maintained in O-doped and N-defective systems. Importantly, these defects play a crucial role in modifying the magnetic properties of the pristine VSi2N4, especially the magnitude of local magnetic moments and the magnetic anisotropy energy. Detailed analysis of the density of states demonstrates that the variations of the total magnetic moment and magnetic anisotropy energy with biaxial strain are determined by the electronic states near the Fermi level rather than the type of defect, which provides a new understanding of the effects of defects on the magnetic properties of 2D materials. Moreover, the layer thickness can affect the magnetic coupling between defects and surrounding V atoms. Our results offer insight into the electronic, valley, and magnetic properties of VSi2N4 in the presence of various point defects.

Molecular ferroelectric with low-magnetic-field magnetoelectricity at room temperature

Magnetoelectric materials, which encompass coupled magnetic and electric polarizabilities within a single phase, hold great promises for magnetic controlled electronic components or electric-field controlled spintronics. However, the realization of ideal magnetoelectric materials remains tough due to the inborn competion between ferroelectricity and magnetism in both levels of symmetry and electronic structure. Herein, we introduce a methodology for constructing single phase paramagnetic ferroelectric molecule [TMCM][FeCl4], which shows low-magnetic-field magnetoelectricity at room temperature. By applying a low magnetic field (≤1 kOe), the halogen Cl‧‧‧Cl distance and the volume of [FeCl4]- anions could be manipulated. This structural change causes a characteristic magnetostriction hysteresis, resulting in a substantial deformation of ~10-4 along the a-axis under an in-plane magnetic field of 2 kOe. The magnetostrictive effect is further qualitatively simulated by density functional theory calculations. Furthermore, this mechanical deformation significantly dampens the ferroelectric polarization by directly influencing the overall dipole configuration. As a result, it induces a remarkable α31 component (~89 mV Oe-1 cm-1) of the magnetoelectric tensor. And the magnetoelectric coupling, characterized by the change of polarization, reaches ~12% under 40 kOe magnetic field. Our results exemplify a design methodology that enables the creation of room-temperature magnetoelectrics by leveraging the potent effects of magnetostriction.

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.

Spin-Reorientation-Driven Linear Magnetoelectric Effect in Topological Antiferromagnet Cu_{3}TeO_{6}

The search for new materials for energy-efficient electronic devices has gained unprecedented importance. Among the various classes of magnetic materials driving this search are antiferromagnets, magnetoelectrics, and systems with topological spin excitations. Cu_{3}TeO_{6} is a material that belongs to all three of these classes. Combining static electric polarization and magnetic torque measurements with phenomenological simulations we demonstrate that magnetic-field-induced spin reorientation needs to be taken into account to understand the linear magnetoelectric effect in Cu_{3}TeO_{6}. Our calculations reveal that the magnetic field pushes the system from the nonpolar ground state to the polar magnetic structures. However, nonpolar structures only weakly differing from the obtained polar ones exist due to the weak effect that the field-induced breaking of some symmetries has on the calculated structures. Among those symmetries is the PT (1[over ¯]^{'}) symmetry, preserved for Dirac points found in Cu_{3}TeO_{6}. Our findings establish Cu_{3}TeO_{6} as a promising playground to study the interplay of spintronics-related phenomena.

Spin-Chirality-Driven Multiferroicity in van der Waals Monolayers

Driven by the expected contribution of two-dimensional multiferroic systems with strong magnetoelectric coupling to the development of multifunctional nanodevices, here we propose, by means of first-principles calculations, vanadium-halide monolayers as a new class of spin-chirality-driven van der Waals multiferroics. The frustrated 120-deg magnetic structure in the triangular lattice induces a ferroelectric polarization perpendicular to the spin-spiral plane, whose sign is switched by a spin-chirality change. It follows that, in the presence of an applied electric field perpendicular to the monolayers, one magnetic chirality can be stabilized over the other, thereby allowing the long-sought electrical control of spin textures. Moreover, we demonstrate the remarkable role of spin-lattice coupling on magnetoelectricity, which adds to the expected contribution of spin-orbit interaction determined by an anion. Indeed, such compounds exhibit sizeable spin-driven structural distortions, thereby promoting the investigation of multifunctional spin-electric-lattice couplings.

Two-Dimensional Asymmetric Multiferroics: Unique Way toward Strong Magnetoelectric Coupling and Multistate Memory

Two-dimensional (2D) materials have provided a fascinating platform for exploring novel multiferroics and emergent magnetoelectric coupling mechanisms. Here, a novel 2D asymmetric multiferroic based on Janus 2D multiferroic MXene-analogous oxynitrides (InTlNO2) is presented by using first-principles calculations. We find three inequivalent phases for InTlNO2, including two metallic phases (p1 and p2) and one semiconducting phase (p3) with a band gap of 0.88 eV. All phases are room-temperature multiferroics with different Curie temperatures, leading to tunability by phase transitions. We show that there is a 90° rotation of the magnetic anisotropy easy axis between p1 and p2, where p1 favors the in-plane and p2 the out-of-plane easy axis. Therefore, the magnetic anisotropy can be tuned by reversing the out-of-plane polarization. Our strategy provides a unique way toward strong magnetoelectric coupling and multistate memory.

Electrical 180° switching of Néel vector in spin-splitting antiferromagnet

Antiferromagnetic spintronics have attracted wide attention due to its great potential in constructing ultradense and ultrafast antiferromagnetic memory that suits modern high-performance information technology. The electrical 180° switching of Néel vector is a long-term goal for developing electrical-controllable antiferromagnetic memory with opposite Néel vectors as binary "0" and "1." However, the state-of-art antiferromagnetic switching mechanisms have long been limited for 90° or 120° switching of Néel vector, which unavoidably require multiple writing channels that contradict ultradense integration. Here, we propose a deterministic switching mechanism based on spin-orbit torque with asymmetric energy barrier and experimentally achieve electrical 180° switching of spin-splitting antiferromagnet Mn5Si3. Such a 180° switching is read out by the Néel vector-induced anomalous Hall effect. On the basis of our writing and readout methods, we fabricate an antiferromagnet device with electrical-controllable high- and low-resistance states that accomplishes robust write and read cycles. Besides fundamental advance, our work promotes practical spin-splitting antiferromagnetic devices based on spin-splitting antiferromagnet.

Oxidation tuning of ferroic transitions in Gd2C monolayer

Tuning of ferroic phases provides great opportunities for material functionalities, especially in two-dimensional materials. Here, a 4f rare-earth carbide Gd2C monolayer is predicted to be a ferromagnetic metal with large magnetization, inherited from its bulk property. Based on first-principles calculations, we propose a strategy that the surface passivation can effectively tune its ferroicity, namely, switching among ferromagnetic, antiferromagnetic, and ferroelectric phases. Metal-insulator transition also occurs accompanying these ferroic transitions. Our calculation also suggests that the magneto-optic Kerr effect and second harmonic generation are effective methods in monitoring these phase transitions.

Alterferroicity with seesaw-type magnetoelectricity

Primary ferroicities like ferroelectricity and ferromagnetism are essential physical properties of matter. Multiferroics, with coexisting multiple ferroic orders in a single phase, provide a convenient route to magnetoelectricity. Even so, the general trade-off between magnetism and polarity remains inevitable, which prevents practicable magnetoelectric cross-control in the multiferroic framework. Here, an alternative strategy, i.e., the so-called alterferroicity, is proposed to circumvent the magnetoelectric exclusiveness, which exhibits multiple but noncoexisting ferroic orders. The natural exclusion between magnetism and polarity, as an insurmountable weakness of multiferroicity, becomes a distinct advantage in alterferroicity, making it an inborn rich ore for intrinsic strong magnetoelectricity. The general design rules for alterferroic materials rely on the competition between the instabilities of phononic and electronic structures in covalent systems. Based on primary density functional theory calculations, Ti-based trichalcogenides are predicted to be alterferroic candidates, which exhibit unique seesaw-type magnetoelectricity. This alterferroicity, as an emerging branch of the ferroic family, reshapes the framework of magnetoelectricity, going beyond the established scenario based on multiferroicity.

Large off-diagonal magnetoelectricity in a triangular Co2+-based collinear antiferromagnet

Magnetic toroidicity is an uncommon type of magnetic structure in solid-state materials. Here, we experimentally demonstrate that collinear spins in a material with R-3 lattice symmetry can host a significant magnetic toroidicity, even parallel to the ordered spins. Taking advantage of a single crystal sample of CoTe6O13 with an R-3 space group and a Co2+ triangular sublattice, temperature-dependent magnetic, thermodynamic, and neutron diffraction results reveal A-type antiferromagnetic order below 19.5 K, with magnetic point group -3' and k = (0,0,0). Our symmetry analysis suggests that the missing mirror symmetry in the lattice could lead to the local spin canting for a toroidal moment along the c axis. Experimentally, we observe a large off-diagonal magnetoelectric coefficient of 41.2 ps/m that evidences the magnetic toroidicity. In addition, the paramagnetic state exhibits a large effective moment per Co2+, indicating that the magnetic moment in CoTe6O13 has a significant orbital contribution. CoTe6O13 embodies an excellent opportunity for the study of next-generation functional magnetoelectric materials.

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.

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.

Optical and Photocatalytic Properties of Cobalt-Doped LuFeO3 Powders Prepared by Oxalic Acid Assistance

B-site cobalt (Co)-doped rare-earth orthoferrites ReFeO3 have shown considerable enhancement in physical properties compared to their parent counterparts, and Co-doped LuFeO3 has rarely been reported. In this work, LuFe1-xCoxO3 (x = 0, 0.05, 0.1, 0.15) powders have been successfully prepared by a mechanochemical activation-assisted solid-state reaction (MAS) method at 1100 °C for 2 h. X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy studies demonstrated that a shrinkage in lattice parameters emerges when B-site Fe ions are substituted by Co ions. The morphology and elemental distribution were investigated by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). The UV-visible absorbance spectra show that LuFe0.85Co0.15O3 powders have a narrower bandgap (1.75 eV) and higher absorbance than those of LuFeO3 (2.06 eV), obviously improving the light utilization efficiency. Additionally, LuFe0.85Co0.15O3 powders represent a higher photocatalytic capacity than LuFeO3 powders and can almost completely degrade MO in 5.5 h with the assistance of oxalic acid under visible irradiation. We believe that the present study will promote the application of orthorhombic LuFeO3 in photocatalysis.

Magnetoelectric effect generated through electron transfer from organic radical to metal ion

Magnetoelectric (ME) materials induced by electron transfer are extremely rare. Electron transfer in these materials invariably occurs between the metal ions. In contrast, ME properties induced by electron transfer from an organic radical to a metal ion have never been observed. Here, we report the ME coupling effect in a mononuclear molecule-based compound [(CH₃)₃NCH₂CH₂Br][Fe(Cl₂An)₂(H₂O)₂] (1) [Cl₂An = chloranilate, (CH₃)₃NCH₂CH₂Br⁺ = (2-bromoethyl)trimethylammonium]. Investigation of the mechanism revealed that the ME coupling effect is realized through electron transfer from the Cl₂An to the Fe ion. Measurement of the magnetodielectric (MD) coefficient of 1 indicated a positive MD of up to ∼12% at 10^3.0 Hz and 370 K, which is very different from that of ME materials with conventional electron transfer for which the MD is generally negative. Thus, the current work not only presents a novel ME coupling mechanism, but also opens a new route to the synthesis of ME coupling materials.

Doping-induced magnetism and magnetoelectric coupling in one-dimensional NbOCl3 and NbOBr3

Low-dimensional multiferroic systems with magnetoelectric coupling have attracted considerable attention due to their important applications in high-density low-power storage. Based on the first-principles calculations, we demonstrated that the recently proposed one-dimensional (1D) ferroelectric materials NbOCl₃ and NbOBr₃ have good stabilities, and found that they can be easily separated from the bulk phase. Due to the flat band near the Fermi level, the itinerant ferromagnetism can be induced over a wide range of electron-doping concentrations, and it leads to the coexistence of ferroelectricity and ferromagnetism in 1D NbOX₃ (X = Cl, Br) and finite-length nanochains. More interestingly, there is strong magnetoelectric coupling on finite-length nanochains, which is caused by the spontaneous electrical polarization and redistribution of magnetic carriers. In addition, magnetism also can be introduced by oxygen vacancies. We also analyzed the effects of doping concentration, strain, and length on ferroelectric polarization and magnetism. Our findings provide a way to design and search low-dimensional multiferroics.

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.

Researching progress on bio-reactive electrogenic materials with electrophysiological activity for enhanced bone regeneration

Bone tissues are dynamically reconstructed during the entire life cycle phase, which is an exquisitely regulated process controlled by intracellular and intercellular signals transmitted through physicochemical and biochemical stimulation. Recently, the role of electrical activity in promoting bone regeneration has attracted great attention, making the design, fabrication, and selection of bioelectric bio-reactive materials a focus. Under specific conditions, piezoelectric, photoelectric, magnetoelectric, acoustoelectric, and thermoelectric materials can generate bioelectric signals similar to those of natural tissues and stimulate osteogenesis-related signaling pathways to enhance the regeneration of bone defects, which can be used for designing novel smart biological materials for engineering tissue regeneration. However, literature summarizing studies relevant to bioelectric materials for bone regeneration is rare to our knowledge. Consequently, this review is mainly focused on the biological mechanism of electrical stimulation in the regeneration of bone defects, the current state and future prospects of piezoelectric materials, and other bioelectric active materials suitable for bone tissue engineering in recent studies, aiming to provide a theoretical basis for novel clinical treatment strategies for bone defects.

Toward Room-Temperature Electrical Control of Magnetic Order in Multiferroic van der Waals Materials

Electrical control of magnetic order in van der Waals (vdW) two-dimensional (2D) systems is appealing for high-efficiency and low-dissipation nanospintronic devices. For realistic applications, a vdW 2D material with ferromagnetic (FM) and ferroelectric (FE) orders coexisting and strongly coupling at room temperature is urgently needed. Here we present a potential candidate for nonvolatile electric-field control of magnetic orders at room temperature. Using first-principles calculations, we predict the coexistence of room-temperature FM and FE orders in a 2D transition metal carbide, where the spatial distribution of magnetic moments strongly couples with the orientation of out-of-plane electric polarization. Furthermore, an electric-field switching between interfacial FM and ferrimagnetic orders is realizable through constructing a multiferroic vdW heterostructure based on this material. These findings make a significant step toward realizing room-temperature multiferroicity and strong magnetoelectric coupling in 2D materials.

Magnetoelectric coupling effects on the band alignments of multiferroic In2Se3-CrI3 trilayer heterostructures

Due to unique magnetoelectric coupling effects, two-dimensional (2D) multiferroic van der Waals heterostructures (vdWHs) are promising for next-generation information processing and storage devices. Here, we design theoretically multiferroic In₂Se₃/CrI₃ trilayer vdWHs with different stacking patterns. For the CrI₃/In₂Se₃/CrI₃ trilayer vdWHs, whether ferroelectric upward or downward polarization, type-I and type-II band alignments are formed for spin-up and spin-down channels. However, for the CrI₃/In₂Se₃/In₂Se₃ trilayer vdWHs, downward polarization induces the type-III band alignment, which is typical for spin-tunnel transistors. Moreover, nonvolatile ferroelectric polarization and stacking patterns can induce the conversion between a unipolar semiconductor and a bipolar (unipolar) half-metal. These results provide a possible route to realize nanoscale multifunctional spintronic devices based on 2D multiferroic systems.

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.

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

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

Effect of Co and Mg doping at Cu site on structural, magnetic and dielectric properties of α-Cu2V2O7

We have studied the effect of doping of both magnetic (Co) and nonmagnetic (Mg) ions at the Cu site on phase transition in polycrystalline α-Cu₂V₂O₇through structural, magnetic, and electrical measurements. X-ray diffraction reveals that Mg doping triggers an onset ofα- toβ-phase structural transition in Cu_2-xMg_xV₂O₇above a critical Mg concentrationx_c= 0.15, and both the phases coexist up tox= 0.25. Cu₂V₂O₇possesses a non-centrosymmetric crystal structure and antiferromagnetic ordering along with a non-collinear spin structure in theαphase, originated from the microscopic Dzyaloshinskii-Moriya interaction between the neighboring Cu spins. Accordingly, a weak ferromagnetic (FM) behavior has been observed up tox= 0.25. However, beyond this concentration, Cu_2-xMg_xV₂O₇exhibits complex magnetic properties. A clear dielectric anomaly is observed in α-Cu_2-xMg_xV₂O₇around the magnetic transition temperature, which loses its prominence with the increase in Mg doping. The analysis of experimental data shows that the magnetoelectric coupling is nonlinear, which is in agreement with the Landau theory of continuous phase transitions. Co doping, on the other hand, initiates a sharpαtoβphase transition around the same critical concentrationx_c= 0.15 in Cu_2-xCo_xV₂O₇but the FM behavior is very weak and can be detected only up tox= 0.10. We have drawn the magnetic phase diagram which indicates that the rate of suppression in transition temperature is the same for both types of doping, magnetic (Co) and nonmagnetic (Zn/Mg).

Nonvolatile magnetoelectric coupling in two-dimensional ferromagnetic-bilayer/ferroelectric van der Waals heterostructures

One of the promising research topics on two-dimensional (2D) van der Waals (vdW) material based devices is the nonvolatile electrical control of magnetism. Usually, it is very hard to tune ferromagnetic or antiferromagnetic ordering by ferroelectric polarization due to strong exchange coupling. The existence of vdW layer spacing, however, which is ubiquitous in 2D materials, makes interlayer magnetic exchange coupling much weaker than interlayer coupling. In this work, we design a multiferroic heterostructure composed of a CrOBr ferromagnetic bilayer and an In₂Se₃ ferroelectric monolayer. The weaker interlayer exchange coupling of the CrOBr bilayer makes it easier to be regulated by ferroelectric polarization, enabling reversible nonvolatile electric control of shifts between ferromagnetic and antiferromagnetic ordering. The unique electrically controlled interlayer magnetic coupling for tuning the overall magnetism may be available for the practical application of 2D vdW bilayer magnets in high-sensitivity sensors and high-density data storage.

PASP: Property analysis and simulation package for materials

We have developed a software package, namely, PASP (Property Analysis and Simulation Package for materials), to analyze the structural, electronic, magnetic, and thermodynamic properties of complex condensed matter systems. Our package integrates several functionalities including symmetry analysis, global structure searching methods, effective Hamiltonian methods, and Monte Carlo simulation methods. In conjunction with first-principles calculations, PASP has been successfully applied to diverse physical systems. In this paper, we give a brief introduction to its main features and underlying theoretical formulism. Some typical applications are provided to demonstrate the usefulness, high efficiency, and reliability of PASP. We expect that further developments will make PASP a general-purpose tool for material simulation and property calculation of condensed matters.

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.

Voltage controlled Néel vector rotation in zero magnetic field

Multi-functional thin films of boron (B) doped Cr2O3 exhibit voltage-controlled and nonvolatile Néel vector reorientation in the absence of an applied magnetic field, H. Toggling of antiferromagnetic states is demonstrated in prototype device structures at CMOS compatible temperatures between 300 and 400 K. The boundary magnetization associated with the Néel vector orientation serves as state variable which is read via magnetoresistive detection in a Pt Hall bar adjacent to the B:Cr2O3 film. Switching of the Hall voltage between zero and non-zero values implies Néel vector rotation by 90 degrees. Combined magnetometry, spin resolved inverse photoemission, electric transport and scanning probe microscopy measurements reveal B-dependent TN and resistivity enhancement, spin-canting, anisotropy reduction, dynamic polarization hysteresis and gate voltage dependent orientation of boundary magnetization. The combined effect enables H = 0, voltage controlled, nonvolatile Néel vector rotation at high-temperature. Theoretical modeling estimates switching speeds of about 100 ps making B:Cr2O3 a promising multifunctional single-phase material for energy efficient nonvolatile CMOS compatible memory applications.

Dzyaloshinskii-Moriya-like interaction in ferroelectrics and antiferroelectrics

The Dzyaloshinskii-Moriya interaction (DMI) between two magnetic moments m_i and m_j is of the form [Formula: see text]. It originates from spin-orbit coupling, and is at the heart of fascinating phenomena involving non-collinear magnetism, such as magnetic topological defects (for example, skyrmions) as well as spin-orbit torques and magnetically driven ferroelectricity, that are of significant fundamental and technological interest. In sharp contrast, its electric counterpart, which is an electric DMI characterized by its [Formula: see text] strength and describing an interaction between two polar displacements u_i and u_j, has rarely been considered, despite the striking possibility that it could also generate new features associated with non-collinear patterns of electric dipoles. Here we report first-principles simulations combined with group theoretical symmetry analysis which not only demonstrate that electric DMI does exist and has a one-to-one correspondence with its magnetic analogue, but also reveals a physical source for it. These findings can be used to explain and/or design phenomena of possible technological importance in ferroelectrics and multiferroics.

0D/1D organic ferroelectrics/multiferroics for ultrahigh density integration: Helical hydrogen-bonded chains, multi-mode switching, and proton synaptic transistors

In recent years, room-temperature ferroelectricity has been experimentally confirmed in a series of two-dimensional (2D) materials. Theoretically, for isolated ferroelectricity in even lower dimensions such as 1D or 0D, the switching barriers may still ensure the room-temperature robustness for ultrahigh-density non-volatile memories, which has yet been scarcely explored. Here, we show ab initio designs of 0D/1D ferroelectrics/multiferroics based on functionalized transition-metal molecular sandwich nanowires (SNWs) with intriguing properties. Some functional groups such as -COOH will spontaneously form into robust threefold helical hydrogen-bonded chains around SNWs with considerable polarizations. Two modes of ferroelectric switching are revealed: when the ends of SNWs are not hydrogen-bonded, the polarizations can be reversed via ligand reorientation that will reform the hydrogen-bonded chains and alter their helicity; when both ends are hydrogen-bonded, the polarizations can be reversed via proton transfer without changing the helicity of chains. The combination of those two modes makes the system the smallest proton conductor with a moderate migration barrier, which is lower compared with many prevalent proton-conductors for higher mobility while still ensuring the robustness at ambient conditions. This desirable feature can be utilized for constructing nanoscale artificial ionic synapses that may enable neuromorphic computing. In such a design of synaptic transistors, the migration of protons through those chains can be controlled and continuously change the conductance of MXene-based post-neuron for nonvolatile multilevel resistance. The success of mimicking synaptic functions will make such designs promising in future high-density artificial neutral systems.

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.

Prediction of two-dimensional ferromagnetic ferroelectric VOF2 monolayer

Nowadays, designing and searching for materials with multiple functional characteristics are the keys to achieving high-performance electronic devices. Among many candidates, two-dimensional multiferroic materials have great potential to be applied in highly integrated magnetoelectric devices, such as high-density non-volatile memories. Here, we predict a two-dimensional material, VOF₂ monolayer, to possess intrinsic ferroelectric and ferromagnetic properties. The VOF₂ monolayer owns the largest in-plane ferroelectric polarization (332 pC m^-1) in the family of VOX₂ (X: halogen) oxyhalides. Different from other VOX₂ monolayers whose magnetic ground states are antiferromagnetic or noncollinear spiral textures, the VOF₂ monolayer owns a robust ferromagnetic ground state, which is rare but highly desirable. Our theoretical prediction provides a good candidate and starting point for the further pursuit of more two-dimensional multiferroic materials with high-performance magnetoelectricity.

Hexagonal rare-earth manganites and ferrites: a review of improper ferroelectricity, magnetoelectric coupling, and unusual domain walls

Hexagonal rare-earth manganites and ferrites are well-known improper ferroelectrics with low-temperature antiferromagnetism/weak ferromagnetism. In recent decades, new multi-functional device concepts and applications have provoked the exploration for multiferroics which simultaneously possess ferroelectric and magnetic orders. As a promising platform for multiferroicity, hexagonal manganites and ferrites are attracting great research interest among the fundamental scientific and technological communities. Moreover, the novel type of vortex-like ferroelectric domain walls are locked to the antiphase structural domain walls, providing an extra degree of freedom to tune the magnetoelectric coupling and other properties such as conductance. Here, we summarize the main experimental achievements and up-to-date theoretical understanding of the ferroelectric, magnetic, and magnetoelectric properties, as well as the intriguing domain patterns in hexagonal rare-earth manganites and ferrites. Recent work on non-stoichiometric compounds will also be briefly introduced.

Ferroelectrically tunable magnetism in BiFeO3/BaTiO3 heterostructure revealed by the first-principles calculations

The perovskite oxide interface has attracted extensive attention as a platform for achieving strong coupling between ferroelectricity and magnetism. In this work, robust control of magnetoelectric (ME) coupling in the BiFeO3/BaTiO3 (BFO/BTO) heterostructure (HS) was revealed by using the first-principles calculation. Switching of the ferroelectric polarization of BTO induce large ME effect with significant changes on the magnetic ordering and easy magnetization axis, making up for the weak ME coupling effect of single-phase multiferroic BFO. In addition, the Dzyaloshinskii-Moriya interaction (DMI) and the exchange coupling constants J for the BFO part of the HSs are simultaneously manipulated by the ferroelectric polarization, especially the DMI at the interface is significantly enhanced, which is three or four times larger than that of the individual BFO bulk. This work paves the way for designing new nanomagnetic devices based on the substantial interfacial ME effect.

Magnetic and electric properties of single crystal MnI2

Multiferroic materials endowed with both dielectric and magnetic orders, are ideal candidates for a wide range of applications. In this work, we reported two phase transitions of MnI2at 3.45 K and 4 K by systemically measuring the magnetic-field and temperature-dependent magnetization of the MnI2thin flakes. Furthermore, we observed similar temperature and field-dependent behaviours for the magnetic susceptibility of MnI2and electronic capacitance of the Ag/MnI2/Ag devices below 3.5 K. Considering the related theory work, we discussed the relationship between the antiferromagnetic and ferroelectric orders in MnI2. Our work reveals the in-plane magnetic and electric properties of MnI2materials, which might be helpful for the further investigation and application of MnI2multiferroics in the future.

Domains and domain walls in multiferroics

Multiferroics are materials combining several ferroic orders, such as ferroelectricity, ferro- (or antiferro-) magnetism, ferroelasticity and ferrotoroidicity. They are of interest both from a fundamental perspective, as they have multiple (coupled) non-linear functional responses providing a veritable myriad of correlated phenomena, and because of the opportunity to apply these functionalities for new device applications. One application is, for instance, in non-volatile memory, which has led to special attention being devoted to ferroelectric and magnetic multiferroics. The vision is to combine the low writing power of ferroelectric information with the easy, non-volatile reading of magnetic information to give a “best of both worlds” computer memory. For this to be realised, the two ferroic orders need to be intimately linked via the magnetoelectric effect. The magnetoelectric coupling – the way polarization and magnetization interact – is manifested by the formation and interactions of domains and domain walls, and so to understand how to engineer future devices one must first understand the interactions of domains and domain walls. In this article, we provide a short introduction to the domain formation in ferroelectrics and ferromagnets, as well as different microscopy techniques that enable the visualization of such domains. We then review the recent research on multiferroic domains and domain walls, including their manipulation and intriguing properties, such as enhanced conductivity and anomalous magnetic order. Finally, we discuss future perspectives concerning the field of multiferroic domain walls and emergent topological structures such as ferroelectric vortices and skyrmions.