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

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates ofΔ f ν = 0.57 , GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.

Nonvolatile Switching of Large Nonreciprocal Optical Absorption at Shortwave Infrared Wavelengths

We report large nonreciprocal optical absorption at shortwave infrared (SWIR) wavelengths in the magnetoelectric (ME) antiferromagnet (AFM) LiNiPO_{4}. The difference in absorption coefficients for light propagating in opposite directions, divided by the sum, reaches up to ∼40% at 1450 nm. Moreover, the nonreciprocity is switched by a magnetic field in a nonvolatile manner. Using symmetry considerations, we reveal that the large nonreciprocal absorption is attributed to Ni^{2+} d-d transitions through the spin-orbit coupling. Furthermore, we propose that an even larger nonreciprocity can be achieved for a Ni-based ME AFM where electric dipoles of every NiO_{6} unit and Ni^{2+} spins are orthogonal and, respectively, form a collinear arrangement. This study provides a pathway toward nonvolatile switchable one-way transparency of SWIR light.

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.

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.

Unity-order magnetochiral effects exhibited by a single metamolecule

A numerical study predicts that a single metamolecule with magnetism and chirality has giant magnetochiral (MCh) effects at microwave frequencies. The magnetism is provided by the ferromagnetic resonance of ferrite under dc bias magnetic fields, while the chirality is provided by the spiral arrangement of dielectric cubes with Mie resonance. The dielectric and magnetic resonances interfere in the metamolecule, resulting in a two-order of magnitude enhancement of the MCh effect compared with that reported in previous studies. This prediction is verified experimentally. A unity-order directional difference in the refractive index caused by the MCh effect is also demonstrated. This study is a significant milestone in the practical use of the MCh effect.

Lead-Free Aurivillius Phase Bi2LaNb1.5Mn0.5O9: Structure, Ferroelectric, Magnetic, and Magnetodielectric Effects

Aurivillius phase Bi₂LaNb_1.5Mn_0.5O₉, derived from ferroelectric PbBi₂Nb₂O₉ by simultaneous substitution of the A-site and B-site cations, was synthesized using a molten-salt method. Here, we discuss the structure-property relationships in detail. X-ray and neutron diffraction show that Bi₂LaNb_1.5Mn_0.5O₉ adopts an A2₁am orthorhombic crystal structure. Rietveld refinement analysis, supported by Raman spectroscopy, indicates that the Bi³⁺ ions occupy the bismuth oxide blocks, La³⁺ ions occupy the perovskite A-site, and Nb⁵⁺/Mn³⁺ ions occupy the perovskite B-site. Ferroelectric ordering takes place at 535 K, which coexists with local ferromagnetic order below 65 K. The cation disorder on the B-site results in relaxor-ferroelectric behavior, and the short-range ferromagnetic order can be attributed to Mn³⁺/Mn⁴⁺ double-exchange. Magnetodielectric coupling measured at 5 K and 100 kHz in a field of 5 T suggests the existence of intrinsic spin-lattice coupling with a magnetodielectric coefficient of 0.20%. These findings will provide significant impetus for further research into potential devices based on the magnetodielectric effect in Aurivillius materials.

Visualizing rotation and reversal of the Néel vector through antiferromagnetic trichroism

Conventional magnetic memories rely on bistable magnetic states, such as the up and down magnetization states in ferromagnets. Increasing the number of stable magnetic states in each cell, preferably composed of antiferromagnets without stray fields, promises to achieve higher-capacity memories. Thus far, such multi-stable antiferromagnetic states have been extensively studied in conducting systems. Here, we report on a striking optical response in the magnetoelectric collinear antiferromagnet Bi₂CuO₄, which is an insulating version of the representative spintronic material, CuMnAs, with four stable Néel vector orientations. We find that, due to a magnetoelectric effect in a visible range, which is enhanced by a peculiar local environment of Cu ions, absorption coefficient takes three discrete values depending on an angle between the propagation vector of light and the Néel vector—a phenomenon that we term antiferromagnetic trichroism. Furthermore, using this antiferromagnetic trichroism, we successfully visualize field-driven reversal and rotation of the Néel vector.

Antiferromagnets have great promise for use in spin-based electronics; however, detecting the Neel vector is challenging due to the lack of a net magnetization. Here, Kimura et al demonstrate an intriguing optical response, where the optical absorption depends on the angle of the Neel vector.

Coexistence of Magnetoelectric and Antiferroelectric-like Orders in Mn3Ta2O8

In materials showing a linear magnetoelectric (ME) effect, unconventional functionalities can be anticipated such as electric control of magnetism and nonreciprocal optical responses. Thus, the search for new linear ME materials is of interest in materials science. Here, using a recently proposed design principle of linear ME materials, which is based on the combination of local structural asymmetry and collinear antiferromagnetism, we demonstrate that an anion-deficient fluorite derivative, Mn₃Ta₂O₈, is a new linear ME material. This is evidenced by the onset of magnetic-field-induced electric polarization in its collinear antiferromagnetic phase below T_N = 24 K. Furthermore, we also find an antiferroelectric-like phase transition at T_S = 55 K, which is attributable to an off-center displacement of magnetic Mn²⁺ ions. The present study shows that Mn₃Ta₂O₈ is a rare material that exhibits both ME and antiferroelectric-like transitions. Thus, Mn₃Ta₂O₈ may provide an opportunity to investigate the physics associated with complicated interactions between magnetic (spin) and electric dipole degrees of freedom.

Magneto-Electric Directional Anisotropy in Polar Soft Ferromagnets of Two-Dimensional Organic-Inorganic Hybrid Perovskites

Two-dimensional organic-inorganic hybrid perovskites (2D-OIHPs) are attracting interest due to their structural tunability and rich functional characteristics, such as ferroelectricity and ferromagnetism. Here, we report the chiral-polar ferromagnetic 2D-OIHP copper chlorides with discernable electric polarization in the inorganic layers. In these systems, the magneto-electric (ME) correlation has been clearly observed by measuring a magneto-electric directional anisotropy (MEA), in which an optical absorption coefficient changes with reversal of the light propagating direction. We have found that the MEA can be induced by a low magnetic field of about 50 mT, reflecting soft magnetic nature. The present results suggest a new paradigm for designing functional ME multiferroics, which effectively couples magnetic and electric properties.

Nonreciprocal second harmonic generation in a magnetoelectric material

Mirror symmetries are of particular importance because they are connected to fundamental properties and conservation laws. Spatial inversion and time reversal are typically associated to charge and spin phenomena, respectively. When both are broken, magnetoelectric cross-coupling can arise. In the optical regime, a difference between forward and backward propagation of light may result. Usually, this nonreciprocal response is small. We show that a giant nonreciprocal optical response can occur when transferring from linear to nonlinear optics, specifically second harmonic generation (SHG). CuB₂O₄ exhibits SHG transmission changes by almost 100% upon reversal of a magnetic field of just ±10 mT. The observed nonreciprocity results from an interference between magnetic-dipole and electric-dipole SHG. Although the former is inherently weaker than the latter, a resonantly enhanced magnetic-dipole transition has a comparable amplitude as a nonresonant electric-dipole transition, thus maximizing the nonreciprocity. Multiferroics and magnetoelectrics are an obvious materials platform to exhibit nonreciprocal nonlinear optical functionalities.

Nonreciprocity of spin waves in the conical helix state

Nonreciprocity emerges in nature and in artificial objects from various physical origins, being widely utilized in contemporary technologies as exemplified by diode elements in electronics. While most of the nonreciprocal phenomena are realized by employing interfaces where the inversion symmetry is trivially lifted, nonreciprocal transport of photons, electrons, magnons, and possibly phonons also emerge in bulk crystals with broken space inversion and time reversal symmetries. Among them, directional propagation of bulk magnons (i.e., quanta of spin wave excitation) is attracting much attention nowadays for its potentially large nonreciprocity suitable for spintronic and spin-caloritronic applications. Here, we demonstrate nonreciprocal propagation of spin waves for the conical spin helix state in Cu₂OSeO₃ due to a combination of dipole and Dzyaloshinskii-Moriya interactions. The observed nonreciprocal spin dispersion smoothly connects to the hitherto known magnetochiral nonreciprocity in the field-induced collinear spin state; thus, all the spin phases show diode characteristics in this chiral insulator.

Metastable growth and infrared spectra of CuB2O4:Ni single crystals

The formation of CuB2O4:Ni crystals in fluxes based on Li2WO4–Bi2O3–WO3 has been studied. A distinctive feature of the used flux growing mode is the metastable nature of nucleation. IR reflection and transmission spectra are presented.

Wide spectral range ultrafast pump-probe magneto-optical spectrometer at low temperature, high-magnetic and electric fields

We developed a table-top setup to perform magneto-optical pump-probe measurements with the possibility to independently tune the photon-energy of both pump and probe beams in the 0.5 eV-3.5 eV range. Our apparatus relies on a commercial turn-key amplified laser system, able to generate light pulses with duration shorter than or comparable to 100 fs throughout the whole spectral range. The repetition rate of the source can be modified via the computer in the 1 kHz to 1 MHz range. A commercial balanced detector is connected to a high-frequency digitizer, allowing for a highly-sensitive detection scheme: rotations of the probe polarization as small as 70 μdeg can be measured. Additionally, a DC magnetic field as high as 9 T and voltages in the kV regime can be applied on the sample. A cryostat allows us to precisely set the temperature of the specimen in the 4 K-420 K interval. We prove the performance of our setup by measuring the ultrafast demagnetization of a cobalt crystal as a function of a wide variety of experimental parameters.

Electrical Switching of the Nonreciprocal Directional Microwave Response in a Triplon Bose-Einstein Condensate

We present a microwave electron spin resonance study of the quantum spin dimer system TlCuCl_{3}, which shows the magnetic-field-induced ordering with both antiferromagnetic spin order and ferroelectricity by the Bose-Einstein condensation (BEC) of triplon quasiparticles. Our main achievement is an electrical switching of the nonreciprocal directional microwave response in the triplon BEC phase. High-speed directional control of microwave absorption by applying an electric field has been accomplished in this Letter. The strength of the observed nonreciprocal microwave response well agrees with the calculation based on Kubo theory with the parameters, evaluated from the static electric polarization in this material.

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.

Single-phase multiferroics: new materials, phenomena, and physics

Multiferroics, where multiple ferroic orders coexist and are intimately coupled, promise novel applications in conceptually new devices on one hand, and on the other hand provide fascinating physics that is distinctly different from the physics of high-T_C superconductors and colossal magnetoresistance manganites. In this mini-review, we highlight the recent progress of single-phase multiferroics in the exploration of new materials, efficient roadmaps for functionality enhancement, new phenomena beyond magnetoelectric coupling, and underlying novel physics. In the meantime, a slightly more detailed description is given of several multiferroics with ferrimagnetic orders and double-layered perovskite structure and also of recently emerging 2D multiferroics. Some emergent phenomena such as topological vortex domain structure, non-reciprocal response, and hybrid mechanisms for multiferroicity engineering and magnetoelectric coupling in various types of multiferroics will be briefly reviewed.

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.

Poling of an artificial magneto-toroidal crystal

Although ferromagnetism is known to be of enormous importance, the exploitation of materials with a compensated (for example, antiferromagnetic) arrangement of long-range ordered magnetic moments is still in its infancy. Antiferromagnetism is more robust against external perturbations, exhibits ultrafast responses of the spin system¹ and is key to phenomena such as exchange bias^2,3, magnetically induced ferroelectricity⁴ or certain magnetoresistance phenomena⁵. However, there is no conjugate field for the manipulation of antiferromagnetic order, hindering both its observation and direct manipulation. Only recently, direct poling of a particular antiferromagnet was achieved with spintronic approaches⁶. An interesting alternative to antiferromagnetism is ferrotoroidicity-a recently established fourth form of ferroic order^7,8. This is defined as a vortex-like magnetic state with zero net magnetization, yet with a spontaneously occurring toroidal moment⁹. As a hallmark of ferroic order, there must be a conjugate field that can manipulate the order parameter. For ferrotoroidic materials, this is a toroidal field-a magnetic vortex field violating both space-inversion and time-reversal symmetry analogous to the toroidal moment¹⁰. However, the nature and generation of the toroidal field remain elusive for conventional crystalline systems. Here, we demonstrate the creation of an artificial crystal^11,12 consisting of mesoscopic planar nanomagnets with a magneto-toroidal-ordered ground state. Effective toroidal fields of either sign are applied by scanning a magnetic tip over the crystal. Thus, we achieve local control over the orientation of the toroidal moment despite its zero net magnetization.

Nonreciprocal responses from non-centrosymmetric quantum materials

Directional transport and propagation of quantum particle and current, such as electron, photon, spin, and phonon, are known to occur in the materials system with broken inversion symmetry, as exemplified by the diode in semiconductor p-n junction and the natural optical activity in chiral materials. Such a nonreciprocal response in the quantum materials of noncentrosymmetry occurs ubiquitously when the time-reversal symmetry is further broken by applying a magnetic field or with spontaneous magnetization, such as the magnetochiral effect and the nonreciprocal magnon transport or spin current in chiral magnets. In the nonlinear regime responding to the square of current and electric field, even a more variety of nonreciprocal phenomena can show up, including the photocurrent of topological origin and the unidirectional magnetoresistance in polar/chiral semiconductors. Microscopically, these nonreciprocal responses in the quantum materials are frequently encoded by the quantum Berry phase, the toroidal moment, and the magnetoelectric monopole, thus cultivating the fertile ground of the functional topological materials. Here, we review the basic mechanisms and emergent phenomena and functions of the nonreciprocal responses in the noncentrosymmetric quantum materials.

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.