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 the magnetoelectric response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear magnetoelectric tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the `Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, `Kubo' term, involves the first-order change in the orbitals and gives isotropic as well as anisotropic contributions to the response. In ordinary magnetoelectric insulators both terms are generally present, while in strong Z2 topological insulators only the former type is allowed, and is quantized. In order to validate the theory we have calculated under periodic boundary conditions the linear magnetoelectric coupling for a 3-D tight-binding model of an ordinary magnetoelectric insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.
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）
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.
While it is often assumed that the orbital response is suppressed and short-ranged due to strong crystal field potential and orbital quenching, we show that the orbital magnetoelectric response can be remarkably long-ranged in ferromagnets. In a bilayer consisting of a nonmagnet and a ferromagnet, spin injection from the interface results in spin accumulation and torque in the ferromagnet, which rapidly oscillate and decay by spin dephasing. In contrast, we find that even when an external electric field is applied only on the nonmagnet, we find substantially long-ranged orbital magnetoelectric…
Magnetization can be induced by an electric field in systems without inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$. This phenomenon is called the magnetoelectric (ME) effect. The spin ME effect has been actively studied in multiferroics. The orbital ME effect also exists and has been mainly discussed in topological insulators at zero temperature. In this paper, we study the intrinsic orbital ME response in metals at finite temperature using the Kubo formula. The intrinsic response originates from the Fermi sea and does not depend on the dissipation. Especially in sy…
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…
Superconducting magnetoelectric effect, which is the current-induced magnetization in a superconductor, mainly focused on the spin magnetization in previous studies, but ignore the effect of the orbital magnetic moments carried by the paired Bloch electrons. In this work, we show that orbital magnetic moments in superconductors can induce large orbital magnetization in the presence of a current. We constructed a unified description for the current-induced spin and orbital magnetization across the superconductivity normal metal phase transition. We find that in a superconductor with uniform pai…
Topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all the surface states. Here, we theoretically propose that the axion insulators with a simple ferromagnetic configuration, such as MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize TME. In a designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical …
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）
The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag (ZZ) edges may exhibit a sizeable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of MoS$_2$ in the trigonal (H) structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric fi…
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…
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…
Non-volatile Orbital magnetoelectric effect in a two-dimensional electron gas
CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；Grenoble-INP（格勒诺布尔国立理工学院）；SPINTEC（自旋电子学与自旋器件实验室）；Laboratoire Albert Fert（阿尔伯特·费特实验室）；Thales（泰雷兹集团）；Université Paris-Saclay（巴黎萨克雷大学）；Photon Science Division, Paul Scherrer Institut（保罗谢尔研究所光子科学部）；Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS)（斯特拉斯堡材料物理与化学研究所）；Université de Strasbourg（斯特拉斯堡大学）；Department of Applied Physics, Indian Institute of Information Technology Vadodara（瓦多德拉印度信息技术学院应用物理系）；Dipartimento di Fisica, Università di Cagliari（卡利亚里大学物理系）；CNR-IOM（意大利国家研究委员会无机材料与光化学研究所）；Dipartimento di Fisica “E. R. Caianiello,” Universitá di Salerno（萨莱诺大学E.R.凯亚涅洛物理系）；Faculty of Environmental Life, Natural Science and Technology, Okayama University（冈山大学环境生命自然科学与技术学部）
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 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…
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…
We predict that antiferromagnetic bilayers formed from van der Waals (vdW) materials, like bilayer CrI$_3$, have a strong magnetoelectric response that can be detected by measuring the gate voltage dependence of Faraday or Kerr rotation signals, total magnetization, or anomalous Hall conductivity. Strong effects are possible in single-gate geometries, and in dual-gate geometries that allow internal electric fields and total carrier densities to be varied independently. We comment on the reliability of density-functional-theory estimates of interlayer magnetic interactions in van der Waals bila…
Twisted graphene systems have draw significant attention due to the discoveries of various correlated and topological phases. In particular, recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible interesting correlation effects of this class of alternating twisted graphene systems. In this work we consider generic alternating twisted multilayer graphene (ATMG) systems with $M$-$L$-$N$ stacking configurations, in which the $M$ ($L$) graphene layers and the $L$ ($N$) layers a…
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…
We develop a comprehensive theory for magnetoelectricity in magnetically ordered quasi-2D systems whereby in thermal equilibrium an electric field can induce a magnetization $m$ and a magnetic field can induce a polarization. This effect requires that both space-inversion and time-reversal symmetry are broken. Antiferromagnetic (AFM) order plays a central role in this theory. We define a Néel operator $τ$ such that a nonzero expectation value $\langle τ\rangle$ signals AFM order, in the same way $m$ signals ferromagnetic (FM) order. While $m$ is even under space inversion and odd under time re…
A quantized version of the magnetoelectric effect, known as the topological magnetoelectric effect, can exist in a time-reversal invariant topological insulator with all its surface states gapped out by magnetism. This topological phase, called the axion insulator phase, has been theoretically proposed but is still lack of conclusive experimental evidence due to the small signal of topological magnetoelectric effect. In this work, we propose that the dynamical in-plane magnetization in an axion insulator can generate a "pseudo-electric field", which acts on the surface state of topological ins…
Topological insulator (TI) thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect (QAHE) when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric (QTME) response when the magnetizations have opposing orientations (axion insulator phase) and the films are sufficiently thick. We present a unified picture of both effects that associates deviations from exact quantization of the QTME caused by finite thickness with non-locality in the side-wall current response function. Using realistic tight-binding model…
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.
A semiclassical theory for the orbital magnetization due to adiabatic evolutions of Bloch electronic states is proposed. It renders a unified theory for the periodic-evolution pumped orbital magnetization and the orbital magnetoelectric response in insulators by revealing that these two phenomena are the only instances where the induced magnetization is gauge invariant. This theory also accounts for the electric-field induced intrinsic orbital magnetization in two-dimensional metals and Chern insulators. We illustrate the orbital magnetization pumped by microscopic local rotations of atoms, wh…
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…
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…
We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into …
We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric an…
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 coupling of electrons in a three-dimensional solid can be effectively described by axion electrodynamics. Here we report the discovery of the fractional magnetoelectric effect in chiral anomalous semimetals of the three-dimensional massless Wilson fermions, which have linear dispersions at the energy crossing point, and break the chiral symmetry at generic momenta. In the presence of electric and magnetic fields, the time-reversal and parity symmetry breaking give rise to the quarter-quantized topological magnetoelectric effect, which is directly related to the winding numb…
The effect of quantum coherence involving macroscopic degree of freedom, and occurring in systems far larger than individual atoms are one of the topical fields in modern physics. Because of material dispersion, a phenomenological approach to macroscopic quantum electrodynamics, where no canonical formulation is attempted, is used. The problem becomes more complicated when geometrical forms of a material structure have to be taken into consideration. Magnetic dipolar mode (MDM) oscillations in a magnetically saturated quasi 2D ferrite disk are macroscopically quantized states. In this ferrimag…
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…
