Three-dimensional topological insulator films in contact with magnetic layers exhibit intriguing magneto-optical and magnetoelectric phenomena, but little is known beyond the linear response regime. We demonstrate that the presence of two electric fields parallel to the surface of the film induces a perpendicular AC polarization, whereas a static polarization can be induced by applying a single circularly polarized electromagnetic wave. These phenomena are determined by the second-order susceptibility, which also controls the manner in which the anomalous Hall current is modulated by a perpendicular AC electric field. If the modulation frequency is low, the Hall effect is topologically protected and the nonlinear response vanishes.
We theoretically study magnetoelectric effects in a heterostructure of a generic band insulator and a ferromagnet. In contrast to the kinetic magnetoelectric effect in metals, referred to as the Edelstein effect or the inverse spin galvanic effect, our mechanism relies on virtual interband transitions between the valence and conduction bands and therefore immune to disorder or impurity scattering. By calculating electric field-induced magnetization by the linear response theory, we reveal that the magnetoelectric effect shows up without specific parameter choices. The magnetoelectric effect qu…
Two-dimensional (2D) magnets have broad application prospects in the spintronics, but how to effectively control them with a small electric field is still an issue. Here we propose that 2D magnets can be efficiently controlled in a multiferroic heterostructure composed of 2D magnetic material and perovskite oxide ferroelectric (POF) whose dielectric polarization is easily flipped under a small electric field. We illustrate the feasibility of such strategy in the bilayer CrI3/BiFeO3(001) heterostructure by using the first-principles calculations. Different from the traditional POF multiferroic …
Magnetoelectric coupling between magnetic and electric dipoles is one of the cornerstones of modern physics towards developing the most energy-efficient magnetic data storage. Conventionally, magnetoelectric coupling is achieved in single-phase multiferroics or in magnetoelectric composite nanostructures consisting of ferromagnetic and ferroelectric/piezoelectric materials. Here, we demonstrate an electric-field-induced strain-mediated magnetoelectric effect in ultrathin CoFeB/MgO magnetic tunnel junction employing non-piezoelectric material, which is a vitally important structure for spintron…
Chromia is a magnetoelectric insulator whose bulk magnetoelectric susceptibility contains a non-zero pseudoscalar component, like that present in magnetized topological insulators. We reveal the dynamic axion field of chromia by measuring the temperature dependence of its non-linear magnetoelectric response using a lock-in technique with an AC electric field stimulus. The electric field dependence, magnetic field dependence, and temperature behavior of the second harmonic lock-in signal are all in agreement with theoretical expectations. Our results demonstrate that chromia magnetoelectric res…
Understanding the mechanisms of magnetoelectric (ME) coupling within multiferroic structures is paramount from a fundamental as well as an applied point of view. We report here that the magnetoelectric properties, as well as the magnetization, of BaTiO$_3$-BiFeO$_3$ superlattices can be tuned by varying the BiFeO$_3$ layer thickness. The magnetoelectric voltage coefficient ($α_{ME}$) reaches its maximum of 60.2 Vcm$^{-1}$Oe$^{-1}$ at 300 K, one of the highest values reported so far, for a sample with a BiFeO$_3$ thickness of 5 nm and a BaTiO$_3$ thickness of 10 nm. To gain deeper insight into …
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 …
The kinetic magnetoelectric effect is an orbital analogue of the Edelstein effect and offers an additional degree of freedom to control magnetisation via the charge current. Here we theoretically propose a gigantic kinetic magnetoelectric effect in topological insulators and interpret the results in terms of topological surface currents. We construct a theory of the kinetic magnetoelectric effect for a surface Hamiltonian of a topological insulator, and show that it well describes the results by direct numerical calculation. This kinetic magnetoelectric effect depends on the details of the sur…
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）
Ferromagnet-ferroelectric-metal superlattices are proposed to realize the large room-temperature magnetoelectric effect. Spin dependent electron screening is the fundamental mechanism at the microscopic level. We also predict an electric control of magnetization in this structure. The naturally broken inversion symmetry in our tri-component structure introduces a magnetoelectric coupling energy of $P M^2$. Such a magnetoelectric coupling effect is general in ferromagnet-ferroelectric heterostructures, independent of particular chemical or physical bonding, and will play an important role in th…
The existence of magnetostriction in bulk BiFeO3 is still a matter of investigation and it is also an issue to investigate the magnetostriction effect in nano BiFeO3. Present work demonstrates the existence of magnetostrictive strain in superparamagnetic BiFeO3 nanoparticles at room temperature and the magnetoelectric coupling properties in composite form with P(VDFTrFE). Despite few reports on the magnetostriction effect in bulk BiFeO3 evidenced by the indirect method, the direct method (strain gauge) was employed in this work to examine the magnetostriction of superparamagnetic BiFeO3. In ad…
Working in the crystal-momentum representation, we calculate the optical conductivity of noncentrosymmetric insulating crystals at first order in the wave vector of light. The time-even part of this tensor describes natural optical activity and the time-odd part describes nonreciprocal effects such as gyrotropic birefringence. The time-odd part can be uniquely decomposed into magnetoelectriclike and purely quadrupolar contributions. The magnetoelectriclike component reduces in the static limit to the traceless part of the frozen-ion static magnetoelectric polarizability while at finite frequen…
We extend the band theory of linear orbital magnetoelectric coupling to treat crystals under finite electric fields. Previous work established that the orbital magnetoelectric response of a generic insulator at zero field comprises three contributions that were denoted as local circulation, itinerant circulation, and Chern-Simons. We find that the expression for each of them is modified by the presence of a dc electric field. Remarkably, the sum of the three correction terms vanishes, so that the total coupling is still given by the same formula as at zero field. This conclusion is confirmed b…
Poly(vinylidenefluoride-co-trifluoroethylene) (P(VDF-TrFE)) based pyroelectric as well as magnetoelectric materials offer great promises for energy harvesting for flexible and wearable applications. Hence, this work focus on solar energy harvesting as well as magnetoelectric phenomenon in two phase nanocomposite film where the constituting phases are manganese ferrite (MnFe2O4) nanoparticles and P(VDF-TrFE) polymer. Composite films have been prepared using solution casting technique. X-ray diffraction result shows higher crystallinity of these films. The ferroelectric, magnetic and magnetoelec…
The electric manipulation of antiferromagnets has become an area of great interest recently for zero-stray-field spintronic devices, and for their rich spin dynamics. Generally, the application of antiferromagnetic media for information memories and storage requires a heterostructure with a ferromagnetic layer for readout through the exchange-bias field. In magnetoelectric and multiferroic antiferromagnets, the exchange coupling exerts an additional impediment (energy barrier) to magnetization reversal by the applied magnetoelectric energy. We proposed and verified a method to overcome this ba…
Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously sho…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discu…
We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing to calculate th…
The Ginzburg-Landau free energy of a conventional superconductor coupled to a helimagnet is microscopically derived using functional field integral techniques. We show that the spin texture leads to a Lifshitz invariant in the free energy, which couples the momentum density of the superconducting condensate to the magnetization of the helimagnet. For helimagnets with a conical texture, the Lifshitz invariant yields a spatial modulation of the superconducting phase along the helical wavevector of the magnetic texture. Based on self-consistent numerical calculations, we verify the theoretical fo…
We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and anti-skyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show th…
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell theory arises when we study the effects of EM energy propagation and consider group velocity of the waves in a ME medium. The energy balance equation reveals unusual topolo…
Although several multiferroic materials/heterostructures have been extensively studied, finding strong magnetoelectric couplings for the electric field control of the magnetization remains challenging. Here, a novel interfacial magnetoelectric coupling based on three components (ferroelectric dipole, magnetic moment, and antiferromagnetic order) is analytically formulated. As an extension of carrier-mediated magnetoelectricity, the new coupling is shown to induce an electric-magnetic hysteresis loop. Realizations employing BiFeO$_3$ bilayers grown along the [$111$] axis are proposed. Without i…
A graphene bilayer shows an unusual magnetoelectric response whose magnitude is controlled by the valley-isospin density, making it possible to link magnetoelectric behavior to valleytronics. Complementary to previous studies, we consider the effect of static homogeneous electric and magnetic fields that are oriented parallel to the bilayer's plane. Starting from a tight-binding description and using quasi-degenerate perturbation theory, the low-energy Hamiltonian is derived including all relevant magnetoelectric terms whose prefactors are expressed in terms of tight-binding parameters. We con…
Three-dimensional topological insulators or axion insulators exhibit the topological magnetoelectric effect, which is isotropic with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here we study the finite-size effect of topological magnetoelectric effect, and find the magnetoelectric coefficients are anisotropic, namely $α_{xx}\neqα_{zz}$. Both of them are shown to converge to a quantized value when the thickness of topological insulator film $d$ increases reaching the three-dimensional bulk limit. The nonzero value of $(α_{xx}-α_{zz})\propto1/d$ could be measured b…
In this letter, we demonstrate switching of nanomagnets through RKKY interactions in topological insulator-based magnetoelectric devices. The switching speed is dependent on the size of the ferromagnets.
It is argued that in magnetoelectrics with diagonal magnetoelectric coupling there should be a monopole-like distribution of magnetization around electric charge. It may lead to nontrivial transport properties of such materials, to understand which the picture of magnetic monopoles attached to electric charges may be very useful.
Geometry-Driven Nonlinear Orbital Magnetoelectric Effect
University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）；Shenzhen University（深圳大学）；Quantum Science Center of Guangdong-Hongkong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；The University of Hong Kong（香港大学）
Topological insulators with a time reversal symmetry breaking perturbation near the surface present a magnetoelectric response that is quantized when the frequency of the probing fields is much smaller than the surface gap induced by the perturbation. In this work we describe the intrinsic finite frequency magnetoelectric response of topological insulators for frequencies of the order and larger than the surface gap, including the experimentally relevant case where the system is metallic. This response affects physical observable quantities and will give rise to new finite frequency phenomena …
Topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value…
Reprogrammable magnonic logic in a multiferroic heterostructure via magnetoelectric coupling
Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay（阿尔伯特·费尔特实验室，法国国家科学研究中心，泰雷兹集团，巴黎萨克雷大学）；Faculty of Information Technology and Bionics, Pázmány Peter Catholic University（帕兹马尼·彼得天主教大学信息与仿生技术学院）；Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay（纳米科学与工程中心，法国国家科学研究中心，巴黎萨克雷大学）；Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay（固体物理实验室，法国国家科学研究中心，巴黎萨克雷大学）；Institute of Applied Physics, University of Münster（明斯特大学应用物理研究所）
Since the initial isolation of few-layer graphene, a plethora of two-dimensional atomic crystals has become available, covering almost all known materials types including metals, semiconductors, superconductors, ferro- and antiferromagnets. These advances have augmented the already existing variety of two-dimensional materials that are routinely realized by quantum confinement in bulk-semiconductor heterostructures. This review focuses on the type of material for which two-dimensional realizations are still being actively sought: magnetoelectrics. We present an overview of current theoretical …
Axion insulator is an exotic magnetic topological insulator with zero Chern number but a nonzero quantized Chern-Simons magnetoelectric coupling. A conclusive experimental evidence for axion insulators is still lacking due to the small signal of topological magnetoelectric effect (TME). Here we show that the dynamical magnetoelectric coupling can be induced by the \emph{out-of-plane} surface magnetization dynamics in axion insulator thin films, which further generates a polarization current in the presence of an external magnetic field in the same direction. Such a current is finite in the bul…
The magnetoelectricity of garnets is considered by means of a symmetry and quantum mechanical combined analysis. It is shown, that the magnetoelectric effect is not realized in most garnets although the necessary condition of the crystal magnetic structure antisymmetry in them is held at low temperatures. Nevertheless, the effect can be observed in some garnets as well as other odd effects, namely, piezomagnetic effect, magnetic field evoked piezoelectric one, etc. It is also discovered that magnetic fields can induce specific antiferroelectric structures in garnet crystals and produce electri…
It has been proposed that topological insulators can be best characterized not as surface conductors, but as bulk magnetoelectrics that -- under the right conditions-- have a universal quantized magnetoelectric response coefficient $e^2/2h$. However, it is not clear to what extent these conditions are achievable in real materials that can have disorder, finite chemical potential, residual dissipation, and even inversion symmetry. This has led to some confusion and misconceptions. The primary goal of this work is to illustrate exactly under what real life scenarios and in what context topologic…
The magnetoelectric response in inversion-breaking two dimensional Dirac systems induced by strain is analyzed. It is shown that, in the same way that the piezoelectric response in these materials is related to the valley Chern number, the strain-induced magnetoelectric effect is related both to the non trivial Berry curvature and the derivative of the orbital magnetic moment per valley. This phenomenon allows to locally induce and control charge densities by an external magnetic field in strained zones of the sample.
Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time-reversal symmetry, because the contributions of both bulk and surface states cancel each other. Instead, the characteristic response of a TI is a nonlinear magnetoelectric effect. Field theoretic aspects of the nonlinear magnetoelectric response and numerical calculations for experimentally relevant geometries are discussed. Distinct from this effect, the magnetoelectric coupli…
Resonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problem in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like "artificial atoms", meta-atoms, with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta-atoms is not associated with the near-field manipulation properties…
