Optical Magnetoelectric Resonance in a Polar Magnet (Fe,Zn)_{2}Mo_{3}O_{8} with Axion-Type Coupling

Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials1-4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin-orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds.

Optical Tellegen metamaterial with spontaneous magnetization

The nonreciprocal magnetoelectric effect, also known as the Tellegen effect, promises a number of groundbreaking phenomena connected to fundamental (e.g., electrodynamics of axion and relativistic matter) and applied physics (e.g., magnetless isolators). We propose a three-dimensional metamaterial with an isotropic and resonant Tellegen response in the visible frequency range. The metamaterial is formed by randomly oriented bi-material nanocylinders in a host medium. Each nanocylinder consists of a ferromagnet in a single-domain magnetic state and a high-permittivity dielectric operating near the magnetic Mie-type resonance. The proposed metamaterial requires no external magnetic bias and operates on the spontaneous magnetization of the nanocylinders. By leveraging the emerging magnetic Weyl semimetals, we further show how a giant bulk effective magnetoelectric effect can be achieved in a proposed metamaterial, exceeding that of natural materials by almost four orders of magnitude.

Direct observation of topological magnon polarons in a multiferroic material

Magnon polarons are novel elementary excitations possessing hybrid magnonic and phononic signatures, and are responsible for many exotic spintronic and magnonic phenomena. Despite long-term sustained experimental efforts in chasing for magnon polarons, direct spectroscopic evidence of their existence is hardly observed. Here, we report the direct observation of magnon polarons using neutron spectroscopy on a multiferroic Fe2Mo3O8 possessing strong magnon-phonon coupling. Specifically, below the magnetic ordering temperature, a gap opens at the nominal intersection of the original magnon and phonon bands, leading to two separated magnon-polaron bands. Each of the bands undergoes mixing, interconverting and reversing between its magnonic and phononic components. We attribute the formation of magnon polarons to the strong magnon-phonon coupling induced by Dzyaloshinskii-Moriya interaction. Intriguingly, we find that the band-inverted magnon polarons are topologically nontrivial. These results uncover exotic elementary excitations arising from the magnon-phonon coupling, and offer a new route to topological states by considering hybridizations between different types of fundamental excitations.

Antiferromagnetic to Ferrimagnetic Phase Transition and Possible Phase Coexistence in Polar Magnets (Fe1-xMnx)2Mo3O8 (0 ≤ x ≤ 1)

In the present work, the magnetic properties of a single crystal (Fe_1-xMn_x)₂Mo₃O₈ (0 ≤ x ≤ 1) have been studied by performing extensive measurements. A detailed magnetic phase diagram is built up, in which the antiferromagnetic state dominates for x ≤ 0.25 and the ferrimagnetic phase arises for x ≥ 0.3. Meanwhile, a sizeable electric polarization of spin origin is commonly observed in all samples, no matter what the magnetic state is. For the samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops are revealed, while the remnant magnetization and coercive field can be tuned drastically by simply varying the Mn content or temperature. A possible coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be responsible for the remarkable modulation of magnetic properties in the samples.

Topological spintronics and magnetoelectronics

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.

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.

In Situ 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 in situ 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.

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Imaging antiferromagnetic antiphase domain boundaries using magnetic Bragg diffraction phase contrast

Manipulating magnetic domains is essential for many technological applications. Recent breakthroughs in Antiferromagnetic Spintronics brought up novel concepts for electronic device development. Imaging antiferromagnetic domains is of key importance to this field. Unfortunately, some of the basic domain types, such as antiphase domains, cannot be imaged by conventional techniques. Herein, we present a new domain projection imaging technique based on the localization of domain boundaries by resonant magnetic diffraction of coherent X rays. Contrast arises from reduction of the scattered intensity at the domain boundaries due to destructive interference effects. We demonstrate this approach by imaging antiphase domains in a collinear antiferromagnet Fe₂Mo₃O₈, and observe evidence of domain wall interaction with a structural defect. This technique does not involve any numerical algorithms. It is fast, sensitive, produces large-scale images in a single-exposure measurement, and is applicable to a variety of magnetic domain types.

Imaging the antiferromagnetic (AFM) domains facilitates the understanding and design of AFM spintronics but is still challenging. Here the authors show an imaging approach for antiphase domains in AFM Fe₂Mo₃O₈ by resonantly scattered coherent soft X-rays, which is also applicable to collinear antiferromagnets.

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.

Orientation-Dependent Optical Magnetoelectric Effect in Patterned BaTiO3/La0.67Sr0.33MnO3 Heterostructures

The optical magnetoelectric effect has been widely investigated, but obtaining the large and tunable optical magnetoelectric effect at room temperature is still a big challenge. We here design ferroelectric/ferromagnetic heterostructures with various orientations, which are composed of titanate BaTiO₃ and manganese oxide La_0.67Sr_0.33MnO₃. This artificial bilayer structure presents room-temperature ferroelectric and ferromagnetic properties. After patterning a 4 μm grating structure on the bilayer thin film, the optical magnetoelectric effect for near-infrared light is investigated systematically through the Bragg diffraction method. The relative change of diffracted light intensity of the order n = 1 has a strong dependence on the magnetization and polarization of the thin films, whether the superlattice is irradiated in reflection or transmission geometries. For (100)- and (111)-oriented samples, both show the room-temperature optical magnetoelectric effect, while the (111)-oriented thin film has a stronger optical magnetoelectric effect. These results pave the way for designing next-generation optical magnetoelectric devices based on the ferroelectric/ferromagnetic structure.

High-Temperature Terahertz Optical Diode Effect without Magnetic Order in Polar FeZnMo_{3}O_{8}

We present a terahertz spectroscopic study of polar ferrimagnet FeZnMo_{3}O_{8}. Our main finding is a giant high-temperature optical diode effect, or nonreciprocal directional dichroism, where the transmitted light intensity in one direction is over 100 times lower than intensity transmitted in the opposite direction. The effect takes place in the paramagnetic phase with no long-range magnetic order in the crystal, which contrasts sharply with all existing reports of the terahertz optical diode effect in other magnetoelectric materials, where the long-range magnetic ordering is a necessary prerequisite. In FeZnMo_{3}O_{8}, the effect occurs resonantly with a strong magnetic dipole active transition centered at 1.27 THz and assigned as electron spin resonance between the eigenstates of the single-ion anisotropy Hamiltonian. We propose that the optical diode effect in paramagnetic FeZnMo_{3}O_{8} is driven by single-ion terms in magnetoelectric free energy.