Nonreciprocal Directional Dichroism Research Articles

Magnetochiral tunneling in paramagnetic Co1/3NbS2

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co1/3NbS2, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up an avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets.

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Visualization of antiferromagnetic domains by nonreciprocal directional dichroism and related optical responses

Nonreciprocal directional dichroism (NDD) is a phenomenon in which the optical absorption is changed by reversing the direction of light propagation or the sign of the magnetic order parameters. While the NDD has mostly been observed in materials with macroscopic magnetization, recent experiments have shown that the NDD can be induced by a specific antiferromagnetic (AFM) spin structure that breaks both space-inversion and time-reversal symmetries. This opens the possibility of visualizing the spatial distribution of AFM domains via the NDD effect. This article reviews the basic features of the NDD, a brief history of the NDD in AFM materials, and recent achievements in visualizing AFM domains via the NDD and related optical responses, and finally provides a perspective on applications of this method for future AFM spintronics research.

Nonreciprocal microwave response at room temperature in multiferroic Y-type hexaferrite BaSrCo2Fe11AlO22

We investigated the microwave response in room-temperature multiferroic BaSrCo2Fe11AlO22. Microwave absorption ascribed to magnetic resonances was observed in the frequency range from 6 to 20 GHz. When the ferroelectric polarization is aligned by the electric and magnetic fields, the magnitude depends on the sign of the microwave propagation vector that indicates the nonreciprocal directional dichroism (NDD). The phenomenon can be observed even at room temperature, the sign can be controlled by the external electric and magnetic fields, and the magnitude of NDD attained is approximately 11% at 300 K and 28% at 200 K. Such microwave properties will open the avenue of practical applications for future wireless communications.

Nonreciprocal Directional Dichroism in Magnetoelectric Spin Glass.

Optical absorption spectra in the visible and near-infrared light were measured for magnetoelectric spin glass Ni_{0.4}Mn_{0.6}TiO_{3} under various field-cooled conditions. Despite the absence of long-range magnetic-dipole order, this spin-glass system exhibits nonreciprocal directional dichroism (NDD) at zero external field after a magnetoelectric field-cooled procedure. This result is distinct from previous studies on NDD in systems with magnetic toroidal moments induced either by long-range magnetic-dipole order or by applying crossed electric and magnetic fields. The present Letter conclusively demonstrates that the observed NDD originates from magnetoelectrically induced ferroic order of magnetic toroidal moments without conventional magnetic-dipole order.

Chirality‐Dependent Magnetoelectric Responses in a Magnetic‐Field‐Induced Ferroelectric Phase of Pb(TiO)Cu4(PO4)4

AbstractMagnetoelectric multiferroic materials can exhibit a variety of functional properties such as electric field control of magnetization and nonreciprocal electromagnetic responses. Such a magnetoelectric response may be further enriched by the combination of the magnetoelectric order and a peculiar crystallographic order, such as crystal chirality. Recently, it was reported that a chiral‐lattice magnet Pb(TiO)Cu4(PO4)4 showing a magnetoelectric quadrupole order in its ground state exhibits anomalous chirality‐induced tilt of magnetization vector with respect to an applied magnetic field. In this progress report, additional results that advance the understanding of chirality‐induced tilt of magnetization vector are presented. It is found that chirality‐induced tilt of the magnetization vector also exists in a magnetic‐field‐induced ferroelectric (FI‐FE) phase of this compound that is stabilized in magnetic fields higher than 16 tesla. The resulting transverse component of the magnetization can be switched with an applied electric field through a polarization reversal. The analysis indicates that this transverse component is as large as ≈0.014 μB per f.u, suggesting that the tilting angle of the magnetization in the FI‐FE phase is much larger than that in the low‐field phase. Also, as another research progress, electric field control of nonreciprocal directional dichroism in the FI‐FE phase is demonstrated.

Nonreciprocal directional dichroism at telecom wavelengths

Magnetoelectrics with ultra-low symmetry and spin-orbit coupling are well known to display a number of remarkable properties including nonreciprocal directional dichroism. As a polar and chiral magnet, Ni3TeO6 is predicted to host this effect in three fundamentally different configurations, although only two have been experimentally verified. Inspired by the opportunity to unravel the structure-property relations of such a unique light-matter interaction, we combined magneto-optical spectroscopy and first-principles calculations to reveal nonreciprocity in the toroidal geometry and compared our findings with the chiral configurations. We find that formation of Ni toroidal moments is responsible for the largest effects near 1.1 eV—a tendency that is captured by our microscopic model and computational implementation. At the same time, we demonstrate deterministic control of nonreciprocal directional dichroism in Ni3TeO6 across the entire telecom wavelength range. This discovery will accelerate the development of photonics applications that take advantage of unusual symmetry characteristics.

Shedding Light on Nonreciprocal Directional Dichroism at High Magnetic Fields in a Multiferroic Material

Large optical nonreciprocal directional dichroism, coupled with an antiferromagnetic order parameter, is observed in a high magnetic field via magneto-optical spectroscopy combined with a pulse magnet technique.

Nonreciprocal Directional Dichroism in a Magnetic-Field-Induced Ferroelectric Phase of Pb(TiO)Cu4(PO4)4

We study nonreciprocal directional dichroism (NDD) of magnetoelectric Pb(TiO)Cu4(PO4)4 in magnetic fields up to 49 T via magneto-optical spectroscopy in the (near-)visible range. Measuring the opti...

Selection rules and dynamic magnetoelectric effect of the spin waves in multiferroic BiFeO3

We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mostly determined by the orientation of the $\mathbf{q}$ vector with respect to the electromagnetic fields. We observed a magnetic field history dependent change in the strength and the frequency of the spin-wave modes, which we attributed to the change of the orientation and the length of the cycloidal $\mathbf{q}$ vector, respectively. Finally, we compared our experimental data with the results of linear spin-wave theory that reproduces the magnetic field dependence of the spin-wave frequencies and most of the selection rules, from which we identified the spin-polarization coupling terms relevant for the optical magnetoelectric effect.

InSitu Electric-Field Control of THz Nonreciprocal Directional Dichroism in the Multiferroic Ba_{2}CoGe_{2}O_{7}.

Nonreciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of noncentrosymmetric magnets. However, the insitu electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin excitations with comparable magnetic- and electric-dipole activity, and switchable electric polarization. We demonstrate the isothermal electric switch between domains of Ba_{2}CoGe_{2}O_{7} possessing opposite magnetoelectric susceptibilities. Combining THz spectroscopy and multiboson spin-wave analysis, we show that unbalancing the population of antiferromagnetic domains generates the nonreciprocal light absorption of spin excitations.

Electric Dipole Active Magnetic Resonance and Nonreciprocal Directional Dichroism in Magnetoelectric Multiferroic Materials in Terahertz and Millimeter Wave Regions

We review electric dipole active magnetic resonance and nonreciprocal directional dichroism in magnetoelectric multiferroic materials in terahertz and millimeter wave regions. Owing to dynamical magnetoelectric coupling generated by the spin-dependent electric polarization, magnetic resonance, which usually occurs owing to magnetic dipole transition, can be induced by the oscillating electric fields of electromagnetic wave. This electric dipole active magnetic resonance can be useful for microscopic investigations of magnetic excitation in unconventional spin systems. The magnetoelectric coupling also induces the nonreciprocal directional dichroism, which provides a novel functionality to materials as an optical diode, in teraheltz and microwave absorption by magnetic resonance. As examples, we describe the results of the high field ESR measurements of the triangular lattice antiferromagnet $$\hbox {CuFeO}_{\mathrm{2}}$$ and the interacting quantum spin dimer systems $$\hbox {TlCuCl}_{\mathrm{3}}$$ and $$\hbox {KCuCl}_{\mathrm{3}}$$ .

Nonreciprocal directional dichroism in multiferroics

Nonreciprocal directional dichroism in multiferroics, namely magnetoelectric coupling in the dynamic regime, is endowed with rich physics and promising applications, which are entangled with fundamental physical components, such as spin, orbital, lattice, charge, and topology. Such a linear nonreciprocal response behavior in the GHz-THz frequency range, represented by optical magnetoelectric effect and magnetochiral dichroism, occurs ubiquitously in material systems with the spontaneous breaking of space-time symmetry, and is subject to Onsager’s reciprocal theorem in the thermodynamic limit. Microscopically, these nonreciprocal responses are usually encoded by toroidization (chirality) and electromagnon (quasiparticle), thus establishing a comprehensive understanding of magnetoelectric coupling and irreversible dynamics. Herein, the basic mechanisms and emergent nonreciprocal directional dichroism in single-phase multiferroics are summarized. We expect that the present review will stimulate diverse possibilities toward nonreciprocal directional dichroism within and beyond multiferroics.

Nonreciprocal directional dichroism of a chiral magnet in the visible range

Nonreciprocal directional dichroism is an unusual light–matter interaction that gives rise to diode-like behavior in low-symmetry materials. The chiral varieties are particularly scarce due to the requirements for strong spin–orbit coupling, broken time-reversal symmetry, and a chiral axis. Here we bring together magneto-optical spectroscopy and first-principles calculations to reveal high-energy, broadband nonreciprocal directional dichroism in Ni3TeO6 with special focus on behavior in the metamagnetic phase above 52 T. In addition to demonstrating this effect in the magnetochiral configuration, we explore the transverse magnetochiral orientation in which applied field and light propagation are orthogonal to the chiral axis and, by so doing, uncover an additional configuration with a unique nonreciprocal response in the visible part of the spectrum. In a significant conceptual advance, we use first-principles methods to analyze how the Ni2+d-to-d on-site excitations develop magneto-electric character and present a microscopic model that unlocks the door to theory-driven discovery of chiral magnets with nonreciprocal properties.

Dynamical magnetoelectric phenomena of skyrmions in multiferroics

Abstract Magnetic skyrmions, nanoscopic spin vortices carrying a quantized topological number in chiral-lattice magnets, are recently attracting great research interest. Although magnetic skyrmions had been observed only in metallic chiral-lattice magnets such as B20 alloys in the early stage of the research, their realization was discovered in 2012 also in an insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . A characteristic of the insulating skyrmions is that they can host multiferroicity, that is, the noncollinear magnetization alignment of skyrmion induces electric polarizations in insulators with a help of the relativistic spin-orbit interaction. It was experimentally confirmed that the skyrmion phase in Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ is indeed accompanied by the spin-induced ferroelectricity. The resulting strong magnetoelectric coupling between magnetizations and electric polarizations can provide us with a means to manipulate and activate magnetic skyrmions by application of electric fields. This is in sharp contrast to skyrmions in metallic systems, which are driven through injection of electric currents. The magnetoelectric phenomena specific to the skyrmion-based multiferroics are attracting intensive research interest, and, in particular, those in dynamical regime are widely recognized as an issue of vital importance because their understanding is crucial both for fundamental science and for technical applications. In this article, we review recent studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulating chiral-lattice magnet Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . It is argued that the multiferroic skyrmions show unique resonant excitation modes of coupled magnetizations and polarizations, so-called electromagnon excitations, which can be activated both magnetically with a microwave magnetic field and electrically with a microwave electric field. The interference between these two activation processes gives rise to peculiar phenomena in the gigahertz regime. As its representative example, we discuss a recent theoretical prediction of unprecedentedly large nonreciprocal directional dichroism of microwaves in the skyrmion phase of Cu 2 OSeO 3 $\textrm{Cu}_2\textrm{OSeO}_3$ . This phenomenon can be regarded as a one-way window effect on microwaves, that is, the extent of microwave absorption changes significantly when its incident direction is reversed. This dramatic effect was indeed observed by subsequent experiments. These studies demonstrated that the multiferroic skyrmions can be a promising building block for microwave devices.

Local-Site Dependency of Magneto-Chiral Dichroism in Enantiopure One-Dimensional Copper(II)–Chromium(III) Coordination Polymers

Magneto-chiral dichroism (MChD) is a nonreciprocal directional dichroism emerged by applying a magnetic field to chiral materials, which provides a clear distinction between light propagating paral...

Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole.

We identify the quantum metric dipole as the geometric origin of the nonreciprocal directional dichroism which describes the change in the refractive index upon reversing the light propagation direction. Specifically, we find that the static limit of the nonreciprocal directional dichroism corresponds to a quadrupolar transport current from the quantum metric dipole, in response to a quadrupolar electric field. Moreover, at a finite frequency, we demonstrate that the steepest slope of the averaged quantum metric dipole gives rise to a peak in the differential refractive index between counterpropagating lights. Finally, we illustrate both features in a low-energy model.

Strong magnetochiral dichroism for visible light emission in a rationally designed paramagnetic enantiopure molecule

Magnetochiral dichroism (MChD) in chiral materials is a nonreciprocal directional dichroism producing optical absorption/emission differences for unpolarized (or linearly polarized) light propagating parallel and antiparallel to a magnetic field; this is an intriguing optical phenomenon enabled by coupling between chirality and magnetism. Since ubiquitous unpolarized light can be coupled with chirality of materials in a magnetic field, MChD has been attracting attention as a potential source for asymmetric photochemical reactions and as an application source for novel magneto-optical devices. However, it has been weakly observed in the visible light region, which is of the order of ${10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}1}%$ for the corresponding signal, and prevents further applications. In this study, we demonstrate a strong MChD for visible light emission based on the microscopic mechanism in a terbium(III) chiral complex with highly symmetrical nona-coordinated geometry. The MChD signal reaches $\ensuremath{\sim}16%$ at 14 T of the luminescence intensity, involving the development of magnetization under magnetic fields.

Directional dichroism in the paramagnetic state of multiferroics: A case study of infrared light absorption in Sr2CoSi2O7 at high temperatures

The coexisting magnetic and ferroelectric orders in multiferroic materials give rise to a handful of novel magnetoelectric phenomena, such as the absorption difference for the opposite propagation directions of light called the non-reciprocal directional dichroism (NDD). Usually these effects are restricted to low temperature, where the multiferroic phase develops. In this paper we report the observation of NDD in the paramagnetic phase of Sr2CoSi2O7 up to temperatures more than ten times higher than its N\'eel temperature (7 K) and in fields up to 30 T. The magnetically induced polarization and NDD in the disordered paramagnetic phase is readily explained by the single-ion spin-dependent hybridization mechanism, which does not necessitate correlation effects between magnetic ions. The Sr2CoSi2O7 provides an ideal system for a theoretical case study, demonstrating the concept of magnetoelectric spin excitations in a paramagnet via analytical as well as numerical approaches. We applied exact diagonalization of a spin cluster to map out the temperature and field dependence of the spin excitations, as well as symmetry arguments of the single ion and lattice problem to get the spectrum and selection rules.

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M is retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M, based on linear response theory and the Green's function method; the results are used to study the system optical properties. First, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Second, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α×q). In the presence of M, which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M. For α∥M, these components yield the Faraday effect for the Faraday configuration q∥M and the Cotton-Mouton effect for the Voigt configuration (q⊥M). When α and M are noncollinear, M- and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the Voigt configuration. In these nonreciprocal optical phenomena, a “toroidal moment,” α×M, and a “quadrupole moment,” αiMj+Miαj, play central roles. These phenomena are strongly enhanced at the spin-split transition edge in the electron band.