Magnetic control of crystal chirality and the existence of a large magneto-optical dichroism effect in CuB2O4

Enhanced gyrotropic birefringence and natural optical activity on electromagnon resonance in a helimagnet

Spontaneous symmetry breaking in crystalline solid often produces exotic nonreciprocal phenomena. As one such example, the unconventional optical rotation with nonreciprocity, which is termed gyrotropic birefringence, is expected to emerge from the magnetoelectric coupling. However, the fundamental nature of gyrotropic birefringence remains to be examined. Here w`e demonstrate the gyrotropic birefringence enhanced by the dynamical magnetoelectric coupling on the electrically active magnon resonance, i.e. electromagnon, in a multiferroic helimagnet. The helical spin order having both polarity and chirality is found to cause the giant gyrotropic birefringence in addition to the conventional gyrotropy, i.e. natural optical activity. It is demonstrated that the optical rotation of gyrotropic birefringence can be viewed as the nonreciprocal rotation of the optical principal axes, while the crystallographic and magnetic anisotropies are intact. The independent control of the nonreciprocal linear (gyrotropic birefringence) and circular (natural optical activity) birefringence/dichroism paves a way for the optically active devices.

Helicity-dependent resonant X-ray scattering in CuB2O4

Exploitation of X-ray circular polarized beams to study forbidden Bragg reflections and new information that could be obtained in these experiments are discussed. It is shown that the intensities of such reflections can be different for the right- and left-circular polarizations (i.e. exhibiting circular dichroism) even for the dipole-dipole resonant transitions involved in the scattering process. This difference can be observed only in crystals having no center of inversion. Here, this approach is used to study helicity-dependent resonant diffraction in copper metaborate CuB₂O₄ single crystal, which is non-centrosymmetric but achiral. Nonetheless, a strong circular dichroism has been observed for hh0 forbidden reflections in the vicinity of the Cu K-edge. This effect is shown to originate from dipolar transitions in Cu atoms occupying the 8(d) Wyckoff position only.

Electric field control of natural optical activity in a multiferroic helimagnet

Controlling the chiral degree of freedom in matter has long been an important issue for many fields of science. The spin-spiral order, which exhibits a strong magnetoelectric coupling, gives rise to chirality irrespective of the atomic arrangement of matter. Here, we report the resonantly enhanced natural optical activity on the electrically active magnetic excitation, that is, electromagnon, in multiferroic cupric oxide. The electric field control of the natural optical activity is demonstrated through magnetically induced chirality endowed with magnetoelectric coupling. These optical properties inherent to multiferroics may lead to optical devices based on the control of chirality.

Nonreciprocal charge transport up to room temperature in bulk Rashba semiconductor α-GeTe

Nonmagnetic Rashba systems with broken inversion symmetry are expected to exhibit nonreciprocal charge transport, a new paradigm of unidirectional magnetoresistance in the absence of ferromagnetic layer. So far, most work on nonreciprocal transport has been solely limited to cryogenic temperatures, which is a major obstacle for exploiting the room-temperature two-terminal devices based on such a nonreciprocal response. Here, we report a nonreciprocal charge transport behavior up to room temperature in semiconductor α-GeTe with coexisting the surface and bulk Rashba states. The combination of the band structure measurements and theoretical calculations strongly suggest that the nonreciprocal response is ascribed to the giant bulk Rashba spin splitting rather than the surface Rashba states. Remarkably, we find that the magnitude of the nonreciprocal response shows an unexpected non-monotonical dependence on temperature. The extended theoretical model based on the second-order spin-orbit coupled magnetotransport enables us to establish the correlation between the nonlinear magnetoresistance and the spin textures in the Rashba system. Our findings offer significant fundamental insight into the physics underlying the nonreciprocity and may pave a route for future rectification devices.

Canting angle dependence of single-chain magnet behaviour in chirality-introduced antiferromagnetic chains of acetate-bridged manganese(III) salen-type complexes

Canted antiferromagnetism (AFM) is considered an effective tool for designing single-chain magnets (SCMs) in homometallic chain systems. The family of manganese(iii) (MnIII) salen-type Schiff-base complexes is an outstanding building-unit candidate for designing SCMs because such complexes possess relatively large uniaxial magnetic anisotropy in the out-of-plane direction. However, SCM behaviour in simple alternating chains based on monomeric MnIII salen-type complexes has not been studied extensively. Herein, we report the SCM behaviour of canted AFM in an alternating chain of an acetate-bridged MnIII salen-type complex.

Magnetochiral Dichroism in a Collinear Antiferromagnet with No Magnetization

We show the directional dichroism in a collinear antiferromagnet MnTiO_{3}. The dichroism between two distinctive antiferromagnetic states with opposite signs of staggered magnetic moments can be regarded as magnetochiral dichroism in the absence of external fields. Electric-field reversal of antiferromagnetic domain causes a change in the absorption intensity of unpolarized light around 2.15 eV. The difference in optical absorption between two antiferromagnetic states is reversed for the light propagating in the opposite direction. The absorption coefficient displays a hysteretic behavior for a cycle of sweeping the external electric or magnetic field.

Controlled transformation of skyrmions and antiskyrmions in a non-centrosymmetric magnet

Control of topological spin textures in magnetic systems may enable future spintronic applications. Magnetic field pulses can switch the vortex polarity¹ or the winding number of magnetic bubbles². Thermal energy can reverse the helicity of skyrmions³ and induce the transformation between meron and skyrmion by modifying the in-plane anisotropy^4,5. Among the various topological spin textures, skyrmions^6,7 and antiskyrmions^8-10 are nanometric spin-whirling structures carrying integer topological charges (N) of -1 and +1 (refs. ^7,11,12), respectively, and can be observed in real space^8,13. They exhibit different dynamical properties under current flow^14-18, for example, opposite signs for the topological Hall effect. Here we observe, in real space, transformations among antiskyrmions, non-topological (NT) bubbles and skyrmions (with N of +1, 0 and -1, respectively) and their lattices in a non-centrosymmetric Heusler magnet, Mn_1.4Pt_0.9Pd_0.1Sn, with D_2d symmetry. Lorentz transmission electron microscopy images under out-of-plane magnetic fields show a square lattice of square-shaped antiskyrmions near the Curie temperature and a triangular lattice of elliptically deformed skyrmions with opposite helicities at lower temperatures. The clockwise and counter-clockwise helicities of the skyrmions originate from Dzyaloshinskii-Moriya interactions with opposite signs along the [100] and [010] directions, respectively. A variation of the in-plane magnetic field induces a topological transformation from antiskyrmions to NT-bubbles and to skyrmions, which is accompanied by a change of the lattice geometry. We also demonstrate control of the helicity of skyrmions by variations of the in-plane magnetic field. These results showcase the control of the topological nature of spin configurations in complex magnetic systems.

Dynamical magnetoelectric phenomena of skyrmions in multiferroics

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.

Recent advances in studies on the magneto-chiral dichroism of organic compounds

Magneto-chiral dichroism is described in terms of devices and synthesis, and is a clue to explain the homochirality of life.

Nonreciprocal Refraction of Light in a Magnetoelectric Material

In magnetoelectric materials, where the time-reversal and space-inversion symmetries are simultaneously broken, optical properties can differ between the opposite propagation directions of light. We report on an experimental observation of nonreciprocal trajectory of a light ray in magnetoelectric material CuB_{2}O_{4}. The light is refracted in different ways between the opposite propagation directions of light. We find a nonreciprocal refraction at the interface between a matter with macroscopic toroidal moment and vacuum. The resultant nonreciprocal deflection of the light is 0.005 deg, which is quantitatively explained using Fermat's principle.

Anomalous Nonreciprocal Electrical Transport on Chiral Magnetic Order

Nonreciprocal flow of conduction electrons is systematically investigated in a monoaxial chiral helimagnet CrNb_{3}S_{6}. We found that such directional dichroism of the electrical transport phenomena, called the electrical magnetochiral (EMC) effect, occurs in a wide range of magnetic fields and temperatures. The EMC signal turns out to be considerably enhanced below the magnetic ordering temperature, suggesting a strong influence of the chiral magnetic order on this anomalous EMC transport property. The EMC coefficients are separately evaluated in terms of crystalline and magnetic contributions in the magnetic phase diagram.

Identification of Antiferromagnetic Domains Via the Optical Magnetoelectric Effect

The ultimate goal of multiferroic research is the development of a new-generation nonvolatile memory devices, where magnetic bits are controlled via electric fields with low energy consumption. Here, we demonstrate the optical identification of magnetoelectric (ME) antiferromagnetic (AFM) domains in the LiCoPO_{4} exploiting the strong absorption difference between the domains. This unusual contrast, also present in zero magnetic field, is attributed to the dynamic ME effect of the spin-wave excitations, as confirmed by our microscopic model, which also captures the characteristics of the observed static ME effect. The control and the optical readout of AFM/ME domains, demonstrated here, will likely promote the development of ME and spintronic devices based on AFM insulators.

Octacyanidotungstate(IV) Coordination Chains Demonstrate a Light-Induced Excited Spin State Trapping Behavior and Magnetic Exchange Photoswitching

A huge increase in the magnetization of two coordination chains based on tetravalent octacyanidometalates (W^IV and Mo^IV ) is observed on irradiation with 436 nm light, while no such behavior is observed for the Nb^IV analogue. A photomagnetic response based solely on [W^IV (CN)₈ ]^4- is demonstrated for the first time. The observed behavior is attributed to the light-induced excited spin state trapping (LIESST) effect at the octacyanidometalate, and to the resulting magnetic exchange ON/OFF photoswitching between the Mn^II center and the photoinduced high-spin (S=1) W^IV or Mo^IV centers.

Magnetoelectrical control of nonreciprocal microwave response in a multiferroic helimagnet

The control of physical properties by external fields is essential in many contemporary technologies. For example, conductance can be controlled by a gate electric field in a field effect transistor, which is a main component of integrated circuits. Optical phenomena induced by an electric field such as electroluminescence and electrochromism are useful for display and other technologies. Control of microwave propagation is also important for future wireless communication technology. Microwave properties in solids are dominated mostly by magnetic excitations, which cannot be easily controlled by an electric field. One solution to this problem is to use magnetically induced ferroelectrics (multiferroics). Here we show that microwave nonreciprocity, that is, different refractive indices for microwaves propagating in opposite directions, could be reversed by an external electric field in a multiferroic helimagnet Ba₂Mg₂Fe₁₂O₂₂. This approach offers an avenue for the electrical control of microwave properties.

Control of microwave propagation is important for future communication technology. Here, Iguchi et al. report the reversal of microwave nonreciprocity by an external electric field in a multiferroic helimagnet Ba₂Mg₂Fe₁₂O₂₂.

One-Way Transparency of Light in Multiferroic CuB(2)O(4)

We experimentally demonstrate one-way transparency of light in multiferroic CuB(2)O(4). The material is rendered transparent for light propagating in one direction, while opaque for light propagating in the opposite direction. The novel transparency results from a destructive interference of the electric dipole and magnetic dipole transitions. The realization of the effect has been accomplished by the application of a high magnetic field and the proper selection of the propagation direction of light in agreement with our quantum mechanical formulation of nonreciprocal directional dichroism.

Dynamical magnetoelectric phenomena of multiferroic skyrmions

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.

Optical Diode Effect at Spin-Wave Excitations of the Room-Temperature Multiferroic BiFeO_{3}

Multiferroics permit the magnetic control of the electric polarization and the electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an electric voltage would provide a huge technological advantage. Dynamic or optical ME effects are equally interesting, because they give rise to unidirectional light propagation as recently observed in low-temperature multiferroics. This phenomenon, if realized at room temperature, would allow the development of optical diodes which transmit unpolarized light in one, but not in the opposite, direction. Here, we report strong unidirectional transmission in the room-temperature multiferroic BiFeO_{3} over the gigahertz-terahertz frequency range. The supporting theory attributes the observed unidirectional transmission to the spin-current-driven dynamic ME effect. These findings are an important step toward the realization of optical diodes, supplemented by the ability to switch the transmission direction with a magnetic or electric field.

Microwave Magnetochiral Effect in Cu_{2}OSeO_{3}

We theoretically find that in the multiferroic chiral magnet Cu_{2}OSeO_{3} resonant magnetic excitations are coupled to the collective oscillation of the electric polarization, and thereby attain simultaneous activity to the ac magnetic field and ac electric field. Because of the interference between these magnetic and electric activation processes, this material hosts a gigantic magnetochiral dichroism for microwaves, that is, a directional dichroism at gigahertz frequencies in the Faraday geometry. The absorption intensity of a microwave differs by as much as ~30% depending on whether its propagation direction is parallel or antiparallel to the external magnetic field.

Control of magnetism by electric fields

The electrical manipulation of magnetism and magnetic properties has been achieved across a number of different material systems. For example, applying an electric field to a ferromagnetic material through an insulator alters its charge-carrier population. In the case of thin films of ferromagnetic semiconductors, this change in carrier density in turn affects the magnetic exchange interaction and magnetic anisotropy; in ferromagnetic metals, it instead changes the Fermi level position at the interface that governs the magnetic anisotropy of the metal. In multiferroics, an applied electric field couples with the magnetization through electrical polarization. This Review summarizes the experimental progress made in the electrical manipulation of magnetization in such materials, discusses our current understanding of the mechanisms, and finally presents the future prospects of the field.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Magneto-chiral dichroism of artificial light-harvesting antenna

We have demonstrated the presence of magneto-chiral dichroism (MChD) of chiral J-aggregates of zinc chlorins. To the best of our knowledge, this is the first observation of MChD in artificial light-harvesting antennas.

Enhanced directional dichroism of terahertz light in resonance with magnetic excitations of the multiferroic Ba2CoGe2O7 oxide compound

We propose that concurrently magnetic and ferroelectric, i.e., multiferroic, compounds endowed with electrically active magnetic excitations (electromagnons) provide a key to producing large directional dichroism for long wavelengths of light. By exploiting the control of ferroelectric polarization and magnetization in a multiferroic oxide Ba(2)CoGe(2)O(7), we demonstrate the realization of such a directional light-switch function at terahertz frequencies in resonance with the electromagnon absorption. Our results imply that this hidden potential is present in a broad variety of multiferroics.

Comment on 'Calculated chiral and magneto-electric dichroic signals for copper metaborate (CuB(2)O(4)) in an applied magnetic field'

Contrary to a claim by Lovesey and Staub (2009 J. Phys.: Condens. Matter 21 142201), a careful treatment of symmetry shows that the application of a magnetic field along a twofold axis can induce the crystallographic chirality in a tetragonal system with the point group [Formula: see text] like CuB(2)O(4). The chirality is reversed by a 90° rotation of the magnetic field around the c axis.

Reply to comment on 'Calculated chiral and magneto-electric dichroic signals for copper metaborate (CuB(2)O(4)) in an applied magnetic field'

From the dawn of modern electromagnetism it has been known that a magnetic field is not handed (chiral). Arima and Saito (2009 J. Phys.: Condens. Matter 21 498001) persist with unwisdom in their repeated claim to have observed control of chirality using a magnetic field by and in itself. In our reply to their claim, we demonstrate damning errors in all challenges in the comment levelled at our analysis of the observation reported by Saito et al (2008 Phys. Rev. Lett. 101 117402) and made on a crystal of copper metaborate.

Periodic rotation of magnetization in a non-centrosymmetric soft magnet induced by an electric field

The control of magnetism with an electric field is a challenging area with the potential to affect fields related to magnetic data storage, sensors and magnetic random access memory. Although there are some successful examples of such control based on the use of magnetic metals and semiconductors, energy loss caused by current flow is a problem that needs to be addressed. In particular, the repeatable control of magnetization with an electric field can be disturbed by joule heat loss. In this regard, non-centrosymmetric insulating magnets are good candidates for controlling magnetization without energy loss, in which the linear magnetoelectric effect has an essential role. Moreover, such magnets exhibit an unconventional magneto-optical effect, which allows the time-resolved detection of the magnetization direction. Here, we show a periodic oscillation of the magnetization direction by +/-20 degrees in a non-centrosymmetric soft magnet (Cu,Ni)B(2)O(4), which is induced by an a.c. electric field of 2 kHz. The present study provides a strategy for identifying materials in which the magnetization direction can be modulated at high speed with an electric field.

Calculated chiral and magneto-electric dichroic signals for copper metaborate (CuB(2)O(4)) in an applied magnetic field

Expressions for dichroic signals in terms of electron multipoles have been used to analyse optical data gathered on a crystal of copper metaborate in the presence of a magnetic field. Calculated signals comply with the established crystal and magnetic structures of CuB(2)O(4), and respect the global symmetries of parity-even and parity-odd dichroic signals in full. We have success in describing five different experiments in total. The claim by Saito et al (2008 Phys. Rev. Lett. 101 117402) that they observe magnetic control of crystal chirality in one of their five experiments is challenged.