The coupling between ferroelectric and magnetic orders in multiferroic materials and the nature of magnetoelectric (ME) effects are enduring experimental challenges. In this work, we have studied the response of magnetization to ferroelectric switching in thin-film hexagonal YbFeO3, a prototypical improper multiferroic. The bulk ME decoupling and potential domain-wall ME coupling were revealed using x-ray magnetic circular dichroism (XMCD) measurements with in-situ ferroelectric polarization switching. Our Landau theory analysis suggests that the bulk ME-coupled ferroelectric switching path has a higher energy barrier than that of the ME-decoupled path; this extra barrier energy is also too high to be reduced by the magneto-static energy in the process of breaking single magnetic domains into multi-domains. In addition, the reduction of magnetization around the ferroelectric domain walls predicted by the Landau theory may induce the domain-wall ME coupling in which the magnetization is correlated with the density of ferroelectric domain walls. These results provide important experimental evidence and theoretical insights into the rich possibilities of ME couplings in hexagonal ferrites, such as manipulating the magnetic states by an electric field.
Magnetic, dielectric and calorimetric studies on 0.9BiFeO3-0.1BaTiO3 indicate strong magnetoelectric coupling. XRD studies reveal a very remarkable change in the rhombohedral distortion angle and a significant shift in the atomic positions at the magnetic Tc due to an isostructural phase transition. The calculated polarization using Rietveld refined atomic positions scales linearly with magnetization. Our results provide the first unambiguous evidence for magnetoelectric coupling of intrinsic multiferroic origin in a BiFeO3 based system.
Magnetoelectric, dielectric and magnetic susceptibility tensors of multiferroic TbMnO3 with cycloidal antiferromagnetic structure in external electric and magnetic fields have been investigated with taking into account dynamics of spin, electro-dipole and acoustic subsystems. All components of tensors depend on values of external electric and magnetic fields. The possibility of control of electrodynamic properties of multiferroic TbMnO3 with cycloidal antiferromagnetic structure by external electric and magnetic fields has been shown. The resonant interaction of spin, electro-dipole, electroma…
AlFeO3, GaFeO3 and Al0.5Ga0.5FeO3, all crystallizing in a non-centrosymmetric space group, are multiferroic and also exhibit magnetoelectric properties, with Al0.5Ga0.5FeO3 showing unusually large magnetocapacitance at 300 K.
The key physical property of multiferroic materials is the existence of a coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this Review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on the main stream physical mechanisms in both single phase multiferroics and magnetoelectric heterostructures. The most rece…
The antiferromagnetic domain structure of a multiferroic has been investigated in the presence of a ferroelectric domain structure. It has been demonstrated that an inhomogeneous magnetoelectric (flexomagnetoelectric) interaction leads to pinning of antiferromagnetic domain walls at the walls of the ferroelectric domains and to a change in the structure of antiferromagnetic domain walls.
Magnetoelectric effect in multiferroic metals via a direct spin-charge interaction
Key Lab of advanced optoelectronic quantum architecture and measurement (MOE), and School of Interdisciplinary Science, Beijing Institute of Technology（北京理工大学光电量子架构与测量教育部重点实验室，交叉科学研究院）
We study the magnetoelectric and electrocaloric response of strain-engineered, multiferroic SrMnO$_3$, using a phenomenological Landau theory with all parameters obtained from \emph{first-principles}-based calculations. This allows to make realistic and materials-specific predictions about the magnitude of the corresponding effects. We find that in the vicinity of a tetracritical point, where magnetic and ferroelectric phase boundaries intersect, an electric field has a huge effect on the antiferromagnetic order, corresponding to a magnetoelectric response several orders of magnitude larger th…
We report the first magnetic-field-dependent Raman scattering studies on Pb(Zr,Ti)O3-CoFe2O4 bilayer multiferroic system. The phonon frequencies of the nano-bilayers obviously change with magnetic field, which is absent in the single Pb(Zr,Ti)O3 films. The magnetostriction of the CoFe2O4 layer generates stress mechanically transferred to the Pb(Zr,Ti)O3 layer, resulting in the mode changes. The observed magnetic-field-induced softening of the soft mode in the Pb(Zr,Ti)O3 layer bears a striking resemblance to direct magnetoelectric output in the bilayers, providing evidence for stress-mediated …
The magnetoelectric effect and skyrmions are two fundamental phenomena in the field of condensed-matter physics. Here, using first-principles calculations and Monte-Carlo simulations, we propose that strong magnetoelectric coupling can be demonstrated in a multiferroic heterobilayer consisting of two-dimensional (2D) MnSTe and α-In2Se3. As the electric polarization in ferroelectric α-In2Se3 is switched, the creation and annihilation of topological magnetic phase can be achieved in this multiferroic heterobilayer, giving rise to the intriguing ferroelectrically controllable skyrmions. This feat…
We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to BiFeO3 (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions -- i.e., in absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions -- these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.
We present a unique example of giant magnetoelectric effect in a conventional multiferroic HoMnO3, where polarization is very large (~56 mC/m2) and the ferroelectric transition temperature is higher than the magnetic ordering temperature by an order. We attribute the uniqueness of the giant magnetoelectric effect to the ferroelectricity induced entirely by the off-center displacement of rare earth ions with large magnetic moments. This finding suggests a new avenue to design multiferroics with large polarization and higher ferroelectric transition temperature as well as large magnetoelectric e…
Electric susceptibility of antiferromagnetic multiferroics with cycloidal spin order at magnetoelectric effect associated with collinear component of spins
We explore computationally the formation of tri-layer superlattices as an alternative approach for combining ferroelectricity with magnetism to form magnetoelectric multiferroics. We find that the contribution to the superlattice polarization from tri-layering is small compared to typical polarizations in conventionalferroelectrics, and the switchable ferroelectric component is negligible. In contrast, we show that epitaxial strain and ``negative pressure'' can yield large, switchable polarizations that are compatible with the coexistence of magnetism, even in materials with no active ferroele…
The electric and magnetic properties of (BaTiO$_3$)$_n$/(CaMnO$_3$)$_n$ short-period superlattices are studied by the first-principles calculations. The local electric polarizations in the CaMnO$_3$ layers are significant, comparable to that in the BaTiO$_3$ layers. Remarkably, the electric polarization is almost doubled when the spin configuration changes from antiferromagnetic to ferromagnetic in the superlattices, indicating a giant magnetoelectric coupling. This enhancement of the magnetoelectric coupling is due to the suppression of the antiferrodistortive mode in the CaMnO$_3$ layers at …
Multiferroics offer exciting opportunities for electric-field control of magnetism. Unfortunately, single-phase multiferroics suitable for such applications at room temperature has not been discovered. Here, we propose the concept of a new type of multiferroics, namely, "asymmetric multiferroic". In asymmetric multiferroics, two locally stable ferroelectric states are not symmetrically equivalent, leading to different magnetic properties between these two states. Furthermore, we predict from first-principles that a Fe-Cr-Mo superlattice with the LiNbO3-type structure is such an asymmetric mult…
Inhomogeneous magnetoelectric effect in magnetization distribution heterogeneities (0-degree domain walls) appeared on crystal lattice defect of the multiferroic material has been investigated. Magnetic symmetry based predictions of kind of electrical polarization distribution in their volumes were used. It was found that magnetization distribution heterogeneity with any symmetry produces electrical polarization. Results were systemized in scope of micromagnetic structure chirality. It was shown that all 0-degree domain walls with time-noninvariant chirality have identical type of spatial dist…
We report on epitaxial growth of single-phase [Pb(Zr0.57Ti0.43)O3]0.8[Pb(Fe2/3W1/3)O3]0.2 (PZT-PFW) solid-solution thin films using pulsed laser deposition. X-ray diffraction measurements reveal that the films have a tetragonal structure. The films exhibit ferroelectric properties and weak ferromagnetic responses at room temperature. Magnetoelectric effects were investigated; the nonlinear magnetoelectric coefficient was measured and found to be comparable to those of multiferroic hexagonal manganites, but at least two orders of magnitude smaller than that for polycrystalline PZT-PFW films.
Ultrasonic velocity measurements on the magnetoelectric multiferroic compound CuFeO2 reveal that the antiferromagnetic transition observed at TN1 = 14 K might be induced by an R-3m -> C2/m pseudoproper ferroelastic transition (G. Quirion, M. J. Tagore, M. L. Plumer, O. A. Petrenko, Phys. Rev. B 77, 094111 (2008)). In that case, the group theory states that the order parameter associated with the structural transition must belong to a two dimensional irreducible representation Eg (x^2 - y^2, xy). Since this type of transition can be driven by a Raman Eg mode, we performed Raman scattering measu…
Realizing topological magnetism and its electric control are intensive topics in the spintronics due to their promising applications in information storage and logic technologies. Here we unveil that both can be achieved in the two-dimensional (2D) magnetoelectric multiferroics. Using first-principles calculations, we show that strong Dzyaloshinskii-Moriya interaction (DMI), which is the key ingredient for the formation of exotic chiral magnetism, could be induced in 2D multiferroics with vertical electric polarization via Rashba effect. We verify that such significant DMI can promote sub-10 n…
Materials that combine magnetic and ferroelectric properties have generated increasing interest over the last few years, due to both their diverse properties and their potential utility in new types of magnetoelectric device applications. In this review we discuss recent progress in the study of such magnetoelectric multiferroics which has been achieved using computational first-principles methods based on density functional theory. In particular, we show how first-principles methods have been successfully used to explain various properties of multiferroic materials and to predict novel effect…
In this article, we perform the symmetry analysis of perovskite-based multiferroics: bismuth ferrite (BiFeO3)-like, orthochromites (RCrO3), and Ruddlesden-Popper perovskites (Ca3Mn2O7-like), being the typical representatives of multiferroics of the trigonal, rhombic, and tetragonal crystal families and explore the effect of crystallographic distortions on magnetoelectric properties. We determine the principal order parameters for each of the considered structures and obtain their invariant combinations consistent with the particular symmetry. This approach allowed us to analyze the features of…
GaFeO3, AlFeO3 and related oxides are ferrimagnetic exhibiting magnetodielectric effect. There has been no evidence to date for ferroelectricity and hence multiferroicity in these oxides. We have investigated these oxides as well as oxides of the composition Al1-x-yGaxFe1+yO3 (x = 0.2, y = 0.2) for possible ferroelectricity by carrying out pyroelectric measurements. These measurements establish the occurrence of ferroelectricity at low temperatures below the Nèel temperature in these oxides. They also exhibit significant magnetoelectric effect. We have tried to understand the origin of ferroel…
A theoretical description of the sequence of magnetic phases in Co3TeO6 is presented. The strongly first-order character of the transition to the commensurate multiferroic ground state, induced by coupled order parameters corresponding to different wavevectors, is related to a large magnetoelastic effect with an exchange energy critically sensitive to the interatomic spacing. The monoclinic magnetic symmetry C2' of the multiferroic phase permits spontaneous polarization and magnetization as well as the linear magnetoelectric effect. The existence of weakly ferromagnetic domains is verified exp…
Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism and electricity. The discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this…
Electric and magnetic properties of multiferroic GdMn2O5 in external magnetic fields were investigated to map out the magnetoelectric phases in this material. Due to strong magnetoelectric coupling, the dielectric permittivity is highly sensitive to phase boundaries in GdMn2O5, which allowed to construct the field-temperature phase diagrams. Several phase transitions are observed which are strongly field-dependent with respect to field orientation and strength. The phase diagram for a magnetic field along the crystallographic a-axis corresponds well to a polarization step, as induced by 90 deg…
First-principles density functional calculations show that the $\textrm{SrRuO}_{3}/\textrm{PbTiO}_{3}/\textrm{SrRuO}_{3}$ multiferroic junction with asymmetric (RuO$_{2}$/PbO and TiO$_{2}$/SrO) interfaces has a large ferroelectric depolarizing field, whose switching changes the interface transmission probabilities for tunneling electrons, leading to electroresistance modulation over several orders of magnitude. The switching further affects the interface spin density, naturally driving magnetoresistance as well as modulated spin-dependent in-plane resistivity, which may be exploited in field-e…
Multiferroics with the coexistence of ferroelectric and ferromagnetic orders are ideal candidates for magnetoelectric applications. Unfortunately, only very few ferroelectric-ferromagnetic multiferroics (with low magnetic critical temperature) were discovered. Here we perform first principles calculations to investigate the effects of the epitaxial strain on the properties of BiMnO3 films grown along the pseudocubic [001] direction. Unlike the ground state with the centrosymmetric C2/c space group in bulk, we reveal that the tensile epitaxial strain stabilizes the ferromagnetic and ferroelectr…
Multiferroics are materials where two or more ferroic orders coexist owing to the interplay between spin, charge, lattice and orbital degrees of freedom. The explosive expansion of multiferroics literature in recent years demon-strates the fast growing interest in this field. In these studies, the first-principles calculation has played a pioneer role in the experiment explanation, mechanism discovery and prediction of novel multiferroics or magnetoelectric materials. In this review, we discuss, by no means comprehensively, the extensive applications and successful achievements of first-princi…
In this work, we report the growth and functional characterizations of multiferroic TbMnO3 thin films grown on Nb-doped SrTiO3 (001) substrates using pulsed laser deposition. By performing detailed magnetic and ferroelectric properties measurements, we demonstrate that the multiferroicity of spin origin known in the bulk crystals can be successfully transferred to TbMnO3 thin films. Meanwhile, anomalous magnetic transition and unusual magnetoelectric coupling related to Tb moments are observed, suggesting a modified magnetic configuration of Tb in the films as compared to the bulk counterpart.…
Ferroelectricity in the incommensurate helical magnetic phase (below TN, 43K) of alpha CaCr2O4 has been confirmed by pyroelectric measurements. Magnetoelectric and magnetodielectric coupling exist below TN and are proportional to the square of magnetic field. From symmetry analysis, we suggest that the presence of an external electric field destabilizes the symmetrical 2221' phase and stabilizes 21' symmetry. This provides a unique system in which polarization varies as the fourth-degree of the order-parameter amplitude and exhibit a vanishingly small value below the first-order transition at …
Two-dimensional (2D) semiconducting multiferroics that can effectively couple magnetic and polarization (P) orders have great interest for both fundamental research and technological applications in nanoscale, which are, however, rare in nature. In this study, we propose a general mechanism to realize semiconducting 2D multiferroics via vdW heterojunction engineering, as demonstrated in a typical heterostructure consisting of magnetic bilayer CrI3 (bi-CrI3) and ferroelectric monolayer In2Se3. Interestingly, the novel indirect orbital coupling between Se 4p and Cr 3d orbitals, intermediated by …
The electronic valence state of Mn in Pb(Zr0.2Ti0.8)O3/La0.8Sr0.2MnO3 multiferroic heterostructures is probed by near edge x-ray absorption spectroscopy as a function of the ferroelectric polarization. We observe a temperature independent shift in the absorption edge of Mn associated with a change in valency induced by charge carrier modulation in the La0.8Sr0.2MnO3, demonstrating the electronic origin of the magnetoelectric effect. Spectroscopic, magnetic, and electric characterization shows that the large magnetoelectric response originates from a modified interfacial spin configuration, ope…
By means of symmetry analysis, density functional theory calculations, and Monte Carlo simulations we show that goethite, $α$-FeOOH, is a linear magnetoelectric below its Néel temperature $T_{\rm N}=400$ K. The experimentally observed magnetic field induced spin-flop phase transition results in either change of direction of electric polarization or its suppression. Calculated value of magnetoelectric coefficient is 0.24 $μ$C m$^{-2}$ T$^{-1}$. The abundance of goethite in nature makes it arguably the most widespread magnetoelectric material.
Magnetoelectric coupling in the polycrystalline antiferromagnets CuFe0.95Rh0.05O2 and CuFeO2 has been investigated. For both samples, electric polarization was observed in the absence of an applied external magnetic field demonstrating that for multiferroic research ceramics are worth to be studied. The observed magnetodielectric effect for CuFe0.95Rh0.05O2 in the electrically polar phase supports the existence of a noncollinear antiferromagnetic state. Interestingly, the electric polarization of this sample can be suppressed by a magnetic field. The temperature dependence of the relative magn…
Magnetic phase transitions in multiferroic bismuth ferrite (BiFeO3) induced by magnetic field, epitaxial strain, and composition modification are considered. These transitions from a spatially modulated spin spiral state to a homogenous antiferromagnetic one are accompanied by the release of latent magnetization and a linear magnetoelectric effect that makes BiFeO3-based materials efficient room-temperature single phase multiferroics.
Nowdays, multiferroic materials with magnetoelectric coupling have many real-world applications in the fields of novel memory devices. It is challenging is to create multiferroic materials with strongly coupled ferroelectric and ferrimagnetic orderings at room temperature. The single crystal of ferric selenide (Fe3Se4) shows type-II multiferroic due to the coexistence of ferroelectric as well as magnetic ordering at room temperature. We have investigated the lattice instability, electronic structure, ferroelectric, ferrimagnetic ordering and transport properties of ferroelectric metal Fe3Se4. …
In this article the mechanism of the linear magnetoelectric (ME) effect in the rhombohedral multiferroic BiFeO$_3$ is considered. The study is based on the symmetry approach of the GinzburgLandau type, in which polarization, antiferrodistortion, and antiferromagnetic momentum vectors are viewed as ordering parameters. We demonstrate that the linear ME effect in BFO is caused by reorientation of the antiferrodistortion vector in either electric or magnetic field. The numerical estimations, which show quantitative agreement with the results of the recent measurements in film samples, have been p…
Complex experimental and theoretical study of the magnetic, magnetoelectric, and magnetoelastic properties of neodymium iron borate NdFe3(BO3)4 along various crystallographic directions have been carried out in strong pulsed magnetic fields up to 230 kOe in a temperature range of 4.2-50 K. It has been found that neodymium iron borate, as well as gadolinium iron borate, is a multiferroic. It has much larger (above 3 10^(-4) C/m^2) electric polarization controlled by the magnetic field and giant quadratic magnetoelectric effect. The exchange field between the rare-earth and iron subsystems (~50 …
Multiferroic Properties of Electrospun CFO-BCTSn Nanocomposites for Magnetoelectric and Magnetic Field Sensing Applications
Jozef Stefan Institute（约瑟夫·斯蒂芬研究所）；University of Picardie Jules Verne（皮卡第朱尔斯·凡尔纳大学）；Cadi-Ayyad University, Faculty of Sciences and Technology（卡迪·阿亚德大学科学与技术学院）；University Mohammed VI Polytechnic (UM6P)（穆罕默德六世理工大学）；Aix-Marseille University - CNRS（艾克斯-马赛大学-法国国家科学研究中心）；Institute of Physics AS CR（捷克科学院物理研究所）
The direct magnetoelectric (ME) effect mediated by lattice strains induced in a ferroelectric film by a ferromagnetic substrate is evaluated using first-principles-based calculations. To that end, the strain sensitivity of ferroelectric polarization and the film permittivity are calculated as a function of the in-plane biaxial strain for Pb(Zr0.52Ti0.48)O3 films under various depolarizing fields. It is found that the ME voltage coefficient varies nonmonotonically with this strain and may reach giant values exceeding 100 Vcm-1 Oe-1 over a strain range that can be controlled through the electric…
The quantitative understanding of converse magnetoelectric effects, i.e., the variation of the magnetization as a function of an applied electric field, in extrinsic multiferroic hybrids is a key prerequisite for the development of future spintronic devices. We present a detailed study of the strain-mediated converse magnetoelectric effect in ferrimagnetic Fe3O4 thin films on ferroelectric BaTiO3 substrates at room temperature. The experimental results are in excellent agreement with numerical simulation based on a two-region model. This demonstrates that the electric field induced changes of …
Clear anomalies in the lattice thermal expansion (deviation from linear variation) and elastic properties (softening of the sound velocity) at the antiferromagnetic-to-paramagnetic transition are observed in the prototypical multiferroic BiFeO3 using a combination of picosecond acoustic pump-probe and high-temperature X-ray diffraction experiments. Similar anomalies are also evidenced using first-principles calculations supporting our experimental findings. Those calculations in addition to a simple Landau-like model we also developed allow to understand the elastic softening and lattice chang…
An effective model is developed to explain the phase diagram and the mechanism of magnetoelectric coupling in multiferroics, $RMn_2O_5$. We show that the nature of magnetoelectric coupling in $RMn_2O_5$ is a coupling between two Ising-type orders, namely, the ferroelectric order in the b axis, and the coupled magnetic order between two frustrated antiferromagnetic chains. The frustrated magnetic structure drives the system to a commensurate-incommensurate phase transition, which can be understood as a competition between a collinear or col-plane order stemming from the `order by disorder' mech…
A series of manganites Tb1-xHoxMnO3 (0<=x<=0.6) with orthorhombic structure are synthesized and detailed investigations on their multiferroicity are performed. Successive magnetic transitions upon temperature variation are evidenced for all samples, and both the Mn3+ spiral spin ordering and rare-earth spin ordering are suppressed with increasing x. Significant enhancement of both the polarization and magnetoelectric response within 0.2<x<0.4 is observed, which may be ascribed to the competition possibly existing between spiral and E-type spin orders. Theoretical calculation is given based on …
Single-phase multiferroic materials are usually considered useless because of the weak magnetoelectric effects, low operating temperature, and small electric polarization induced by magnetic orders. As a result, current studies on applications of the magnetoelectric effects are mainly focusing on multiferroic heterostructures and composites. Here we report a room-temperature giant effect in response to external magnetic fields in single-phase multiferroics. A low magnetic field of 1000 Oe applied on the spin-driven multiferroic hexaferrites BaSrCo2Fe11AlO22 and Ba0.9Sr1.1Co2Fe11AlO22 is able t…
We have identified three of the four magnetoelectric modes of multiferroic BiFeO$_3$ measured using THz spectroscopy. Excellent agreement with the observed peaks is obtained by including the effects of easy-axis anisotropy along the direction of the electric polarization. By distorting the cycloidal spin state, anisotropy splits the $Ψ_{\pm 1}$ mode into peaks at 20 and 21.5 cm$^{-1}$ and activates the lower $Φ_{\pm 2}$ mode at 27 cm$^{-1}$ (T=200 K). An electromagnon is identified with the upper $Ψ_{\pm 1}$ mode at 21.5 cm$^{-1}$. Our results also explain recent Raman and inelastic neutron-sc…
In this contribution to the special issue on magnetoelectrics and their applications, we focus on some single phase multiferroics theoretically predicted and/or experimentally discovered by the authors in recent years. In these materials, iron is the common core element. However, these materials are conceptually different from the mostly-studied BiFeO$_3$, since their ferroelectricity is improper. Our reviewed materials are not simply repeating one magnetoelectric mechanism, but cover multiple branches of improper ferroelectricity, including the magnetism-driven ferroelectrics, geometric ferro…
We present a theory for surface polaritons on ferroelectric-antiferromagnetic materials with canted spin structure. Canting is assumed to be due to a Dzyaloshinkii-Moriya interaction with the electric polarisation and weak ferromagnetism directed in the plane parallel to the surface. Surface and bulk modes for a semi-infinite film are calculated for the case of transverse magnetic polarisation. Example results are presented using parameters appropriate for BaMnF4. We find that the magnetoelectric interaction gives rise to "leaky" surface modes, i.e. pseudosurface waves that exist in the pass b…
Using first principles calculations, we study the microscopic origin of ferroelectricity (FE) induced by magnetic order in the orthorhombic HoMnO3. We obtain the largest ferroelectric polarization observed in the whole class of improper magnetic ferroelectrics to date. We find that the two proposed mechanisms for FE in multiferroics, lattice- and electronic-based, are simultaneously active in this compound: a large portion of the ferroelectric polarization arises due to quantum-mechanical effects of electron orbital polarization, in addition to the conventional polar atomic displacements. An i…
We study theoretically the multiferroic dynamics in a composite one-dimensional system consisting of BaTiO3 multiferroically coupled to an iron chain. The method treats the magnetization and the polarization as thermodynamic quantities describable via a combination of the Landau-Lifshits- Gilbert and the Ginzburg-Landau dynamics coupled via an additional term in the total free energy density. This term stems from the multiferroic interaction at the interface. For a wide range of strengths of this coupling we predict the possibility of obtaining a well-developed hysteresis in the ferromagnetic …
Multiferroic materials with coupled ferroelectric and ferromagnetic properties are important for multifunctional devices due to their potential ability of controlling magnetism via electric field, and vice versa. The recent discoveries of two-dimensional ferromagnetic and ferroelectric materials have ignited tremendous research interest and aroused hope to search for two-dimensional multiferroics. However, intrinsic two-dimensional multiferroic materials and, particularly, those with strong magnetoelectric couplings are still rare to date. In this paper, using first-principles simulations, we …
