Electrical polarization and orbital magnetization: the modern theories

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals

We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.

The shape effect and its consequences for polar surfaces and for heterogeneous catalysis

In this paper we develop the shape effect, which is relevant for crystalline materials whose size is larger than that of the thermodynamic limit. According to this effect the electronic properties of one surface of a crystal depend upon all of its surfaces, i.e. on the overall shape. At first, qualitative mathematical arguments are presented for the existence of this effect based on the conditions for the stability of polar surfaces. Our treatment explains why such surfaces are observed even though earlier theory indicated that they should not exist. Then, models are developed from which it is found computationally that changing the shape of a polar crystal can substantially alter the magnitude of its surface charges. Apart from surface charges, it follows that the crystal shape will also significantly affect bulk properties, most notably polarization and piezoelectric responses. Additional model calculations show a strong shape effect on the activation energy for heterogeneous catalysis primarily through local surface charges rather than a non-local/long range electrostatic potential.

Computational Electromagnetics: A Miscellany

The paper presents a miscellany of unorthodox and, in some cases, paradoxical or controversial items related to computational and applied electromagnetics. The topics include a definition of the magnetic source field via a line integral, losses in electric power transmission vs. losses in photonics, homogenization of periodic electromagnetic structures, spurious modes, models of plasmonic media, and more. It is hoped that this assortment of subjects will be of interest to a broad audience of scientists and engineers.

Magnetically Induced Polarization in Centrosymmetric Bonds

We reveal the microscopic origin of electric polarization P[over →] induced by noncollinear magnetic order. We show that in Mott insulators, such P[over →] is given by all possible combinations of position operators r[over →][over ^]_{ij}=(r[over →]_{ij}^{0},r[over →]_{ij}) and transfer integrals t[over ^]_{ij}=(t_{ij}^{0},t_{ij}) in the bonds, where r[over →]_{ij}^{0} and t_{ij}^{0} are spin-independent contributions in the basis of Kramers doublet states, while r[over →]_{ij} and t_{ij} stem solely from the spin-orbit interaction. Among them, the combination t_{ij}^{0}r[over →]_{ij}, which couples to the spin current, remains finite in the centrosymmetric bonds, thus yielding finite P[over →] in the case of noncollinear arrangement of spins. The form of the magnetoelectric coupling, which is controlled by r[over →]_{ij}, appears to be rich and is not limited to the phenomenological law P[over →]∼ε_{ij}×[e_{i}×e_{j}] with ε_{ij} being the bond vector connecting the spins e_{i} and e_{j}. Using density-functional theory, we illustrate how the proposed mechanism works in the spiral magnets CuCl_{2}, CuBr_{2}, CuO, and α-Li_{2}IrO_{3}, providing a consistent explanation for the available experimental data.

Phonon Magnetic Moment from Electronic Topological Magnetization

The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by the lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a k resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yang's monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gapped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where nontopological contribution is also important. Our results agree with recent observations in experiments.

Electric-field-based Poisson-Boltzmann theory: Treating mobile charge as polarization

Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of an electrolyte can then be treated as a composite nonuniform dielectric body. Writing the electrostatic interactions as an integral over electric-field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua [J. L. Ericksen, Arch. Rational Mech. Anal. 183, 299 (2007)AVRMAW0003-952710.1007/s00205-006-0042-4]. The Maxwell field equations are enforced by extending the set of variational parameters by a vector potential representing the dielectric displacement which is fully transverse in a dielectric system without embedded external charge. The electric-field energy density in this representation is a function of the vector potential and the sum of ionic and solvent polarization making the mutual screening explicit. Transverse polarization is accounted for by construction, lifting the restriction to longitudinal polarization inherent in the electrostatic potential based formulation of Poisson-Boltzmann mean field theory.

Magneto-electric multiferroics: designing new materials from first-principles calculations

In parallel with the revival of interest for magneto-electric multiferroic materials in the beginning of the century, first-principles simulations have grown incredibly in efficiency during the last two decades. Density functional theory calculations, in particular, have so become a must-have tool for physicists and chemists in the multiferroic community. While these calculations were originally used to support and explain experimental behaviour, their interest has progressively moved to the design of novel magneto-electric multiferroic materials. In this article, we mainly focus on oxide perovskites, an important class of multifunctional material, and review some significant advances to which contributed first-principles calculations. We also briefly introduce the various theoretical developments that were at the core of all these advances.

Gas sensors based on mass-sensitive transducers part 1: transducers and receptors-basic understanding

The scientific interest in gas sensors is continuously increasing because of their environmental, medical, industrial, and domestic applications. This has resulted in an increasing number of investigations being reported in the literature and communicated at conferences. The present review, organized in two parts, addresses the peculiarities of gas sensors based on mass-sensitive transducers, starting with their structure and functionality and progressing to implementation and specific use. In this first part of the review, we discuss the constructional peculiarities and operation regions and the physical and chemical processes governing the reception and transduction functions and the way in which they influence the sensor sensing parameters/features. Scientific outcomes and trends in research into gas sensors based on mass sensitive transducers are also considered.

Spectral dynamics of shift current in ferroelectric semiconductor SbSI

Photoexcitation in solids brings about transitions of electrons/holes between different electronic bands. If the solid lacks an inversion symmetry, these electronic transitions support spontaneous photocurrent due to the geometric phase of the constituting electronic bands: the Berry connection. This photocurrent, termed shift current, is expected to emerge on the timescale of primary photoexcitation process. We observe ultrafast evolution of the shift current in a prototypical ferroelectric semiconductor antimony sulfur iodide (SbSI) by detecting emitted terahertz electromagnetic waves. By sweeping the excitation photon energy across the bandgap, ultrafast electron dynamics as a source of terahertz emission abruptly changes its nature, reflecting a contribution of Berry connection on interband optical transition. The shift excitation carries a net charge flow and is followed by a swing over of the electron cloud on a subpicosecond timescale. Understanding these substantive characters of the shift current with the help of first-principles calculation will pave the way for its application to ultrafast sensors and solar cells.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

Size-scaling behaviour of the electronic polarizability of one-dimensional interacting systems

Electronic polarizability of finite chains is accurately calculated from the total energy variation of the system produced by small but finite static electric fields applied along the chain direction. Normalized polarizability, that is, polarizability divided by chain length, diverges as the second power of length for metallic systems but approaches a constant value for insulating systems. This behaviour provides a very convenient way to characterize the wave-function malleability of finite systems as it avoids the need of attaching infinite contacts to the chain ends. Hubbard model calculations at half filling show that the method works for a small U  =  1 interaction value that corresponds to a really small spectral gap of 0.005 (hopping t  =  -1 is assumed). Once successfully checked, the method has been applied to the long-range hopping model of Gebhard and Ruckenstein showing 1/r hopping decay (Gebhard and Ruckenstein 1992 Phys. Rev. Lett. 68 244; Gebhard et al 1994 Phys. Rev. B 49 10926). Metallicity for U values below the reported metal-insulator transition is obtained but the surprise comes for U values larger than the critical one (when a gap appears in the spectral density of states) because a steady increase of the normalized polarizability with size is obtained. This critical size-scaling behaviour can be understood as corresponding to a molecule which polarizability is unbounded. We have checked that a real transfer of charge from one chain end to the opposite occurs as a response to very small electric fields in spite of the existence of a large gap of the order of U for one-particle excitations. Finally, ab initio quantum chemistry calculations of realistic poly-acetylene chains prove that the occurrence of such critical behaviour in real systems is unlikely.

Orbital Edelstein Effect as a Condensed-Matter Analog of Solenoids

We theoretically study current-induced orbital magnetization in a chiral crystal. This phenomenon is an orbital version of the Edelstein effect. We propose an analogy between the current-induced orbital magnetization and an Ampère field in a solenoid in classical electrodynamics. To quantify this effect, we define a dimensionless parameter from the response coefficients relating a current density with an orbital magnetization. This dimensionless parameter can be regarded as a number of turns within a unit cell when the crystal is regarded as a solenoid, and it represents how "chiral" the crystal is. By focusing on the dimensionless parameter, one can design a band structure that realizes the induction of large orbital magnetization. In particular, a Weyl semimetal with all of the Weyl nodes close to the Fermi energy can have a large value for this dimensionless parameter, which can exceed that of a classical solenoid.

Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous response to an external electric field of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.

Large Bulk Photovoltaic Effect and Spontaneous Polarization of Single-Layer Monochalcogenides

We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effective three-dimensional shift current (∼100  μA/V^{2}), larger than has been previously observed in other polar systems. Moreover, we show that the integral of the shift-current tensor is correlated to the large spontaneous effective three-dimensional electric polarization (∼1.9  C/m^{2}). Our calculations indicate that the shift current will be largest in the visible spectrum, suggesting that these monochalcogenides may be promising for polar optoelectronic devices. A Rice-Mele tight-binding model is used to rationalize the shift-current response for these systems, and its dependence on polarization, in general terms with implications for other polar materials.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.

Persistence of strong and switchable ferroelectricity despite vacancies

Vacancies play a pivotal role in affecting ferroelectric polarization and switching properties, and there is a possibility that ferroelectricity may be utterly eliminated when defects render the system metallic. However, sufficient quantitative understandings of the subject have been lacking for decades due to the fact that vacancies in ferroelectrics are often charged and polarization in charged systems is not translationally invariant. Here we perform first-principles studies to investigate the influence of vacancies on ferroelectric polarization and polarization switching in prototypical BaTiO₃ of tetragonal symmetry. We demonstrate using the modern theory of polarization that, in contrast to common wisdom, defective BaTiO₃ with a large concentration of vacancies (or , or ) possesses a strong nonzero electric polarization. Breaking of Ti-O bonds is found to have little effect on the magnitude of polarization, which is striking. Furthermore, a previously unrecognized microscopic mechanism, which is particularly important when vacancies are present, is proposed for polarization switching. The mechanism immediately reveals that (i) the switching barrier in the presence of is small with ΔE = 8.3 meV per bulk formula cell, and the polarization is thus switchable even when vacancies exist; (ii) The local environment of vacancy is surprisingly insignificant in polarization switching. These results provide profound new knowledge and will stimulate more theoretical and experimental interest on defect physics in FEs.

Maxwell Garnett approximation (advanced topics): tutorial

In the second part of this tutorial, we consider several advanced topics related to the Maxwell Garnett approximation.

Interface Magnetoelectric Coupling in Co/Pb(Zr,Ti)O3

Magnetoelectric coupling at multiferroic interfaces is a promising route toward the nonvolatile electric-field control of magnetization. Here, we use optical measurements to study the static and dynamic variations of the interface magnetization induced by an electric field in Co/PbZr0.2Ti0.8O3 (Co/PZT) bilayers at room temperature. The measurements allow us to identify different coupling mechanisms. We further investigate the local electronic and magnetic structure of the interface by means of transmission electron microscopy, soft X-ray magnetic circular dichroism, and density functional theory to corroborate the coupling mechanism. The measurements demonstrate a mixed linear and quadratic optical response to the electric field, which results from a magneto-electro-optical effect. We propose a decomposition method of the optical signal to discriminate between different components involved in the electric field-induced polarization rotation of the reflected light. This allows us to extract a signal that we can ascribe to interface magnetoelectric coupling. The associated surface magnetization exhibits a clear hysteretic variation of odd symmetry with respect to the electric field and nonzero remanence. The interface coupling is remarkably stable over a wide frequency range (1-50 kHz), and the application of a bias magnetic field is not necessary for the coupling to occur. These results show the potential of exploiting interface coupling with the prospect of optimizing the performance of magnetoelectric memory devices in terms of stability, as well as fast and dissipationless operation.

Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure

We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular to the applied current.

Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques

Recent experiments on current-induced domain-wall motion in chiral domain walls reveal important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the twist torque moment, which probes the internal twist of wavepackets in chiral magnets in a similar way as the orbital moment probes the wavepacket's internal self-rotation. We propose to interpret the Berry phase theory of DMI as a theory of spiralization in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Co/Pt(111), O/Co/Pt(111) and Al/Co/Pt(111) magnetic bi- and trilayers and show that the DMI is highly anisotropic in these systems.

Structure, energetics, and electronic states of III-V compound polytypes

Recently several hexagonal polytypes such as 2H, 4H, and 6H have been discovered for conventional III-V semiconductor compounds in addition to the cubic 3C zinc-blende polytype by investigating nanorods grown in the [111] direction in different temperature regimes. Also III-mononitrides crystallizing in the hexagonal 2H wurtzite structure under ambient conditions can be deposited in zinc-blende geometry using various growth techniques. The polytypic crystal structures influence the local electronic properties and the internal electric fields due to the spontaneous polarization in non-cubic crystals.In this paper we give a comprehensive review on the thermodynamic, structural, and electronic properties of twelve Al, Ga, and In antimonides, arsenides, phosphides, and nitrides as derived from ab initio calculations. Their lattice parameters, energetic stability, and characteristic band structure energies are carefully discussed and related to the atomic geometries of the polytypes. Chemical trends are investigated. Band offsets between polytypes and their consequences for heterocrystalline structures are derived. The described properties are discussed in the light of available experimental data and previous computations. Despite several contradictory results in the literature, a unified picture of the III-V polytypes and their heterocrystalline structures is developed.

Orbital magnetization as a local property

The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions--either periodic or open. While P--owing to its "quantum" indeterminacy--is not a bulk property in this sense, M is. We provide its r-space expression for any insulator, even with a nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory.

Lyddane-Sachs-Teller relationship in linear magnetoelectrics

In a linear magnetoelectric the lattice is coupled to electric and magnetic fields; both affect the longitudinal-transverse splitting of zone-center optical phonons on equal footing. A response matrix relates the macroscopic fields (D, B) to (E, H) at infrared frequencies. It is shown that the response matrices at frequencies 0 and ∞ fulfill a generalized Lyddane-Sachs-Teller relationship. The right-hand side member of such relationship is expressed in terms of weighted averages over the longitudinal and transverse excitations of the medium, and assumes a simple form for a harmonic crystal.

Towards a bulk theory of flexoelectricity

Flexoelectricity is the linear response of polarization to a strain gradient. Here we address the simplest class of dielectrics, namely, elemental cubic crystals, and we prove that therein there is no extrinsic (i.e., surface) contribution to flexoelectricity in the thermodynamic limit. The flexoelectric tensor is expressed as a bulk response of the solid, manifestly independent of surface configurations. Furthermore, we prove that the flexoelectric responses induced by a long-wavelength phonon and by a uniform strain gradient are identical.