Magnetoelectric near fields

Critical behavior of sputter-deposited magnetoelectric antiferromagnetic Cr$_2$O$_3$ films near Néel temperature

Chromium(III) oxide is a classical collinear antiferromagnet with a linear magnetoelectric effect. We are presenting the measurements of the magnetoelectric susceptibility $α$ of a sputter-deposited 500-nm film and a bulk single-crystal of Cr$_\mathrm{2}$O$_\mathrm{3}$. We investigated the magnetic phase-transition and the critical exponent $β$ of the sublattice magnetization near Néel temperature. For the films, an exponent of 0.49(1) was found below 293 K, and changed to 1.06(4) near the Néel temperature of 298 K. For the single-crystal, the exponent was constant at 0.324(4). We investigated…

磁电电磁学中的对称性与磁电超原子

Symmetry in magnetoelectric electromagnetism and magnetoelectric meta-atoms

该研究针对磁电过程的时空对称性破缺问题，提出由磁性绝缘体制成的磁电超原子可产生磁电场，其与电磁系统通过磁电虚拟光子相互作用，且磁电量子真空态可在微波腔中检测，丰富了磁电量子电动力学的基础研究。

Electric-field-induced strain-mediated magnetoelectric effect in CoFeB-MgO magnetic tunnel junctions

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…

Orbital magnetoelectric coupling at finite electric field

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…

Impact of magnetization and hyperfine field distribution on high magnetoelectric coupling strength in BaTiO$_3$-BiFeO$_3$ multilayers

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 …

Finite-size effects on the magnetoelectric response of field-driven ferroelectric/ferromagnetic chains

We study theoretically the coupled multiferroic dynamics of one-dimensional ferroelectric/ferromagnet chains driven by harmonic magnetic and electric fields as a function of the chain length. A linear magnetoelectric coupling is dominated by the spin-polarized screening charge at the interface. We performed Monte-Carlo simulations and calculations based on the coupled Landau-Lifshitz-Gilbert and Landau-Khalatnikov equations showing that the net magnetization and the total polarization of thin heterostructures, i.e. with up to ten ferroelectric and ferromagnetic sites counted from the interface…

Magnetoelectric oscillations in quasi-2D ferrite disk particles

In this paper we show that magnetic-dipolar-mode (MDM) oscillations of a quasi-2D ferrite disk are characterized by unique symmetry features with topological phases resulting in appearance of the magnetoelectric (ME) properties. The entire ferrite disk can be characterized as a pair of two, electric and magnetic, coupled eigen moments. However, there is no a "glued pair" of two dipoles. An external electromagnetic field in the near-field region "views" such a ME particle, as a system with a normally oriented eigen electric moment and an in-plane rotating eigen magnetic dipole moment.

Magnetoelectric effect of a conducting sphere near a planar topological insulator

When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular…

Theory of orbital magnetoelectric response

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…

Search for the magnetic monopole at a magnetoelectric surface

We show, by solving Maxwell's equations, that an electric charge on the surface of a slab of a linear magnetoelectric material generates an image magnetic monopole below the surface provided that the magnetoelectric has a diagonal component in its magnetoelectric response. The image monopole, in turn, generates an ideal monopolar magnetic field outside of the slab. Using realistic values of the electric- and magnetic- field susceptibilties, we calculate the magnitude of the effect for the prototypical magnetoelectric material Cr$_2$O$_3$. We use low energy muon spin rotation to measure the str…

Effect of nano-size on magnetostriction of BiFeO3 and exceptional magnetoelectric coupling properties of BiFeO3_P(VDF-TrFE) polymer composite films for magnetic field sensor application

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…

Orbital magnetoelectric coupling in band insulators

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…

Finite frequency magnetoelectric response of three dimensional Topological Insulators

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 …

Inversion of ferrimagnetic magnetization by ferroelectric switching via a novel magnetoelectric coupling

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…

非线性磁电耦合中的异常霍尔效应

Anomalous Hall effect from nonlinear magnetoelectric coupling

本研究通过非线性磁电耦合机制揭示了异常霍尔效应的起源，并通过第一性原理计算确定了Cr₂O₃和CoF₂为潜在材料。

Azimuthally unidirectional transport of energy in magnetoelectric fields. Topological Lenz effect

Magnetic dipolar modes (MDMs) in a quasi 2D ferrite disk are microwave energy eigenstate oscillations with topologically distinct structures of rotating fields and unidirectional power flow circulations. At the first glance, this might seem to violate the law of conservation of an angular momentum, since the microwave structure with an embedded ferrite sample is mechanically fixed. However, an angular momentum is seen to be conserved if topological properties of electromagnetic fields in the entire microwave structure are taken into account. In this paper we show that due to the topological ac…

Electric field modulated topological magnetoelectric effect in Bi$_2$Se$_3$

Topological insulators have been predicted to exhibit a variety of interesting phenomena including a quantized magnetoelectric response and novel spintronics effects due to spin textures on their surfaces. However, experimental observation of these phenomena has proved difficult due to the finite bulk carrier density which may overwhelm the intrinsic topological responses that are expressed at the surface. Here, we demonstrate a novel ionic gel gating technique to tune the chemical potential of Bi$_{2}$Se$_{3}$ thin films while simultaneously performing THz spectroscopy. We can tune the carrie…

Magnetoelectric coupling in a ferroelectric/ferromagnetic chain revealed by ferromagnetic resonance

Understanding the multiferroic coupling is one of the key issues in the feld of multiferroics. As shown here theoretically, the ferromagnetic resonance (FMR) renders possible an access to the magnetoelectric coupling coefficient in composite multiferroics. This we evidence by a detailed analysis and numerical calculations of FMR in an unstrained chain of BaTiO3 in the tetragonal phase in contact with Fe, including the effect of depolarizing field. The spectra of the absorbed power in FMR are found to be sensitive to the orientation of the interface electric polarization and to an applied stati…

Vector Potential and Surface Magnetic Field in Magnetoelectric Antiferromagnetic Materials

A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. For antiferromagnetic materials, the study reveals a unique relation between the macroscopic potential and the orientation-dependent magnetic quadrupole, as a result of the different crystalline and magnetic symmetries. In particular, at surfaces and interfaces of a truncated bulk without inversion and time-reversal symmetries, the average vector potential exhibits a discontinuity, which results in an interfacial magnetic field. In general, ho…

Equilibrium spin currents and magnetoelectric effect in magnetic nanostructures

We discuss the problem of equilibrium spin currents in ferromagnets with inhomogeneous magnetization. Using simple microscopic models we explain the physical origin of equilibrium spin currents. Next we derive the equilibrium spin current from the Hamiltonian with a gauge field associated with local rotations in the spin space. Several examples of magnetic systems are studied in details, and the persistent spin current is found to exist in the ground state of these systems. We also demonstrate the possibility to measure the equilibrium spin current using the magnetoelectrically induced electri…

磁性纳米膜与纳米线皱褶诱导的磁电效应

Magnetoelectricity induced by rippling of magnetic nanomembranes and wires

提出在常规铁磁基态绝缘体中通过纳米尺度弯曲几何结构打破反演对称性产生线性磁电耦合的新方法，证明可控皱褶和锯齿形铁磁线能分别激活磁电单极子与触发磁环形矩耦合。

Nonlinear Magneto-Optical and Magnetoelectric Phenomena in Topological Insulator Heterostructures

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 perpend…

Low-energy magnetoelectric control of domain states in exchange-coupled heterostructures

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…

The symmetry and magnetoelectric effects in garnet crystals and films

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…

双叶黎曼面拓扑逆磁电效应

Double-leaf Riemann surface topological converse magnetoelectricity

本研究将拓扑引入多铁性领域，在二维GdI₂单层中发现基于自旋相关d-p杂化的双叶黎曼面拓扑逆磁电效应，可电调控180°自旋反转，还设计了更多候选材料推动相关应用。

The topological magnetoelectric effect in semiconductor nanostructures: quantum wells, wires, dots and rings

Electrostatic charges placed near the interface between ordinary and topological insulators induce magnetic fields, through the so-called topological magnetoelectric effect. Here, we present a numerical implementation of the associated Maxwell equations. The resulting model is simple, fast and quantitatively as accurate as the image charge method, but with the advantage of providing easy access to elaborate geometries when pursuing specific effects. The model is used to study how magnetoelectric fields are influenced by the dimensions and the shape of the most common semiconductor nanostructur…

Magnetoelectric effects in superconducting nanowires with Rashba spin-orbit coupling

Recent experiments in semiconductor nanowires with a spin-orbit coupling and proximity-induced superconductivity exhibit signatures of Majorana bound states predicted to exist in the topological phase. In this work we predict that these nanowire systems exhibit unconventional magnetoelectric effects showing a sharp crossover behavior at the topological phase transition. We find that magnetic fields with a component parallel to the spin-orbit field can give rise to currents in equilibrium. Surprisingly, also fields perpendicular to the spin-orbit field may induce currents and can be employed in…

磁场诱导的块体磁电螺旋磁体Cu$_2$OSeO$_3$中的手性孤子晶格

Magnetic field-induced chiral soliton lattice in the bulk magnetoelectric helimagnet Cu$_2$OSeO$_3$

本研究通过小角中子散射实验，在块体磁电螺旋磁体Cu$_2$OSeO$_3$中观察到由磁场诱导的手性孤子晶格，揭示了其非简谐性质及磁相互作用复杂性，为电场控制的自旋电子器件应用提供新见解。

Magnetoelectric classification of skyrmions

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…

Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state

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…

Magnetoelectricity in two-dimensional materials

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 …

Magnetoelectric effect in topological insulator films beyond the linear response regime

We study the response of topological insulator films to strong magnetic and electric fields beyond the linear response theory. As a model, we use the three-dimensional lattice Wilson-Dirac Hamiltonian where we simultaneously introduce both magnetic field through the Peierls substitution and electric field as a potential energy depending on lattice coordinate. We compute the electron energy spectrum by numerically diagonalizing this Hamiltonian and obtain quantized magnetoelectric polarizability. In addition, we find that the magnetoelectric effect vanishes as the film width decreases due to th…

Direct control of the skyrmion phase stability by electric field in a magnetoelectric insulator

Magnetic skyrmions are topologically protected spin-whirl quasiparticles currently considered as promising components for ultra-dense memory devices. In the bulk they form lattices that are stable over just a few Kelvin below the ordering temperature. This narrow stability range presents a key challenge for applications, and finding ways to tune the SkL stability over a wider phase space is a pressing issue. Here we show experimentally that the skyrmion phase in the magnetoelectric insulator ${\text{Cu}_2 \text{O} \text{Se} \text{O}_3}$ can either expand or shrink substantially depending on th…

利用磁场调控共振自旋光电流；应用于磁电氧化物Cr2O3

Controlling resonant spin photocurrent using magnetic field; application to a magnetoelectric oxide Cr2O3

本文通过非线性响应理论研究了磁电氧化物Cr2O3中由线偏振和圆偏振电磁波通过单磁振子过程产生磁振子自旋光电流的机制，揭示了其对静态磁场的独特依赖关系，为实验验证提供了可行途径。

Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect

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…

Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field $E$ at $E/B \ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E \ll 1$).

Patterns and Thresholds of Magnetoelectric Switching in Spin Logic Devices

In the quest to develop spintronic logic, it was discovered that magnetoelectric switching results in lower energy and shorter switching time than other mechanisms. Magnetoelectric (ME) field due to exchange bias at the interface with a multi-ferroic (such as BiFeO3) is well suited for 180 degree switching of magnetization. The ME field is determined by the direction of canted magnetization in BiFeO3 which can point at an angle to the plane, to which voltage is applied. Dependence of switching time and the threshold of ME field on its angles was determined by micromagnetic simulations. Switchi…

Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems

Profiles of the spin and orbital angular momentum accumulations induced by a longitudinally applied electric field are explored in nanoribbons of $p$-band systems with a honeycomb lattice. We show that nanoribbons with zigzag borders can exhibit orbital magnetoelectric effects. More specifically, we have found that purely orbital magnetization oriented perpendicularly to the ribbon may be induced in these systems by means of the external electric field, when sublattice symmetry is broken. The effect is rather general and may occur in other multi-orbital materials.

Electrically tunable and reversible magnetoelectric coupling in strained bilayer graphene

The valleys in hexagonal two-dimensional systems with broken inversion symmetry carry an intrinsic orbital magnetic moment. Despite this, such systems possess zero net magnetization unless additional symmetries are broken, since the contributions from both valleys cancel. A nonzero net magnetization can be induced through applying both uniaxial strain to break the rotational symmetry of the lattice and an in-plane electric field to break time-reversal symmetry owing to the resulting current. This creates a magnetoelectric effect whose strength is characterized by a magnetoelectric susceptibili…

磁电分形、磁电参数共振与Hopf分岔

Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation

本文研究磁电耦合的磁性纳米粒子动力学，发现强非线性下微小耦合引发混沌，弱非线性下可增强磁振荡，并观察到Hopf分岔与磁电分形。

Strong spintronic magnetoelectric effect in layered magnetic metamaterial

It is shown that external magnetic field or magnetization induces electric polarization of microscopic isolated magnetic/non-magnetic hybrid structures due to the spin-dependent electron redistribution and mutual capacity. The magnetoelectric effect can be very strong, for instance the change of electric polarization reaches $100$ $μC/m^{2}$ at a constant magnetic field of only $1.5$ Tesla in the case of $100$ $÷$ $10$ nanometer structures which tightly fill the space, composing a metamaterial. The effect does not require using exotic compounds. Based on the obtained results we suggest a numbe…

Magnetoelectric effect in cylindrical topological insulators

Topological insulators (TIs) exhibit a quantized magnetoelectric response when time-reversal symmetry is broken on its surface. This unusual electromagnetic (EM) response is a unique macroscopic manifestation of the quantum Hall effect on the TI surface and it is described by a quantized Chern-Simons theory. In this paper, we construct the Green's function (GF) describing the EM response of two topological media separated by a cylindrical interface. This GF, in the appropriate limits, describes the magnetoelectric effect of both i) a cylindrical TI surrounded by a dielectric fluid, and ii) a T…

Theory of the Strain-Induced Magnetoelectric Effect in Planar Dirac Systems

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.

Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetildeα$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetildeα$ is for Cr_2O_3…