Skyrmions Subtractor Based on Dzyaloshinskii-Moriya Interaction Gate

Skyrmions are increasingly favored in developing various spintronic devices as efficient information carriers. The proposed voltage-controlled Dzyaloshinskii-Moriya interaction (VCDM) offers an additional means to manipulate the movement of skyrmions. In this study, we investigated how the skyrmions behave when passing through the VCDM gate in ferromagnetic nanotracks driven by current. Our findings suggest that reducing the strength of the Dzyaloshinskii-Moriya interaction (DMI) can more effectively block skyrmions, while increasing the DMI strength can more effectively attract them. This indicates that the motion behavior of skyrmions can be controlled by changing the shape of the VCDM gate, thereby demonstrating the effectiveness of VCDM gates in controlling skyrmion motion. Due to the ability of VCDM gates to block skyrmions, we have designed a robust subtractor based on skyrmions. These results provide valuable insights for the development of future skyrmion-based devices using the DMI method.

Chemical pressure induced spin reorientation in the magnetic structure ofCa3Mn2-xSnxO7(x=0,0.03,0.05)

The effect of partially substituting Tin (Sn) at the Manganese (Mn) site ofCa3Mn2O7, viz.Ca3Mn2-xSnxO7withx=0.03,0.05, on its structural and magnetic properties have been investigated using synchrotron diffraction, neutron diffraction, and bulk magnetization measurements. It is observed that with a substitution ofx=0.03, the minor (≈8%) tetragonal (I4/mmm) structural phase that is present in the predominantly orthorhombic (Cmc21) undopedCa3Mn2O7, completely disappears. The compounds order antiferromagnetically, the ordering temperature decreases with increasing Sn-content, indicating a weakening of the antiferromagnetic exchange interactions. Interestingly, in the ordered state, the spin magnetic moments which were aligned along thea-axis of the unit cell in the undoped compound, are observed to have reoriented with their major components lying in theb - cplane in the Sn-doped compounds. The above influence of Sn-doping is seen to be stemming from a significant modification of the octahedral rotation and tilt mode geometry in the unit cell, that is known to be responsible for driving ferroelectricity in these compounds.

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Unusual Dzyaloshinskii-Moriya Interaction in Graphene/Fe3GeTe2 Van der Waals Heterostructure

Dzyaloshinskii-Moriya interaction (DMI) is shown to induce a topologically protected chiral spin texture in magnetic/nonmagnetic heterostructures. In the context of van der Waals spintronic devices, graphene emerges as an excellent candidate material. However, due to its negligible spin-orbit interaction, inducing DMI to stabilize topological spins when coupled to 3d-ferromagnets remains challenging. Here, it is demonstrated that, despite these challenges, a sizeable Rashba-type spin splitting followed by significant DMI is induced in graphene/Fe3GeTe2. This is made possible due to an interfacial electric field driven by charge asymmetry together with the broken inversion symmetry of the heterostructure. These findings reveal that the enhanced DMI energy parameter, resulting from a large effective electron mass in Fe3GeTe2, remarkably contributes to stabilizing non-collinear spins below the Curie temperature, overcoming the magnetic anisotropy energy. These results are supported by the topological Hall effect, which coexists with the non-trivial breakdown of Fermi liquid behavior, confirming the interplay between spins and non-trivial topology. This work paves the way toward the design and control of interface-driven skyrmion-based devices.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material displays competing magnetic interactions and features nonlinear optical responses with the capability of generating coherent photons. The incommensurate magnetic ground state of CaMnTeO6 with an unusually large spin rotation angle of 127°(1) indicates that the anisotropic interlayer exchange is strong and competing with the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) µB, extracted from low-temperature heat capacity and neutron diffraction measurements, is only 46% of the expected value of the static moment 3 µB. This reduction indicates the presence of strong quantum fluctuations in the half-integer spin S = 3/2 CaMnTeO6 magnet, which is rare. By comparing the spin-polarized band structure, chemical bonding, and physical properties of AMnTeO6 (A = Ca, Sr, Pb), how quantum-chemical interpretation can illuminate insights into the fundamentals of magnetic exchange interactions, providing a powerful tool for modulating spin dynamics with atomically precise control is demonstrated.

Spontaneous Atomic-Scale Polar Skyrmions and Merons on a SrTiO3 (001) Surface: Defect Engineering for Emerging Topological Orders

The emergence of nontrivial topological order in condensed matter has been attracting a great deal of attention owing to its promising technological applications in novel functional nanodevices. In ferroelectrics, the realization of polar topological order at an ultimately small scale is extremely challenging due to the lack of chiral interaction and the critical size of the ferroelectricity. Here, we break through these limitations and demonstrate that the ultimate atomic-scale polar skyrmion and meron (∼2 nm) can be induced by engineering oxygen vacancies on the SrTiO3 (001) surface based on first-principles calculations. The paraelectric-to-antiferrodistortive phase transition leads to a novel topological transition from skyrmion to meron, indicating phase-topology correlations. We also discuss accumulating and driving polar skyrmions based on the oxygen divacancy model; these results and the recent discovery of defect engineering techniques suggest the possibility of arithmetic operations on topological numbers through the natural self-organization and diffusion features of oxygen vacancies.

Intrinsic edge states and strain-tunable spin textures in the Janus 1T-VTeCl monolayer

Using first-principles calculations and micro-magnetic simulations, we investigate the electronic structures, the effect of biaxial strain on the topological characteristics, magnetic anisotropy energy (MAE), Dzyaloshinskii-Moriya interaction (DMI) and spin textures in the Janus 1T phase VTeCl (1T-VTeCl) monolayer. Our results show that 1T-VTeCl has an intrinsic edge state, and a topological phase transition with a sizeable band gap is achieved by applying biaxial strain. Interestingly, the MAE can be switched from the in-plane to the off-plane with a compressive strain of -5%. Microscopically, the origin of MAE is mainly associated with the large spin-orbit coupling (SOC) from the heavy nonmagnetic Te atoms rather than that from the V atoms. Furthermore, the induced DMI (0.09 meV) can occur stabilizing magnetic merons without applying temperatures and magnetic fields. Then, the skyrmions, frustrated antiferromagnetism and vortex are induced after applying a suitable compressive strain. Our study provides compelling evidence that the 1T-VTeCl monolayer with topological properties holds great potential for application in spintronic devices, as well as information storage devices based on different magnetic phases achievable through strain engineering.

Spin-Chirality-Driven Multiferroicity in van der Waals Monolayers

Driven by the expected contribution of two-dimensional multiferroic systems with strong magnetoelectric coupling to the development of multifunctional nanodevices, here we propose, by means of first-principles calculations, vanadium-halide monolayers as a new class of spin-chirality-driven van der Waals multiferroics. The frustrated 120-deg magnetic structure in the triangular lattice induces a ferroelectric polarization perpendicular to the spin-spiral plane, whose sign is switched by a spin-chirality change. It follows that, in the presence of an applied electric field perpendicular to the monolayers, one magnetic chirality can be stabilized over the other, thereby allowing the long-sought electrical control of spin textures. Moreover, we demonstrate the remarkable role of spin-lattice coupling on magnetoelectricity, which adds to the expected contribution of spin-orbit interaction determined by an anion. Indeed, such compounds exhibit sizeable spin-driven structural distortions, thereby promoting the investigation of multifunctional spin-electric-lattice couplings.

Regulation of interfacial Dzyaloshinskii-Moriya interaction in ferromagnetic multilayers

Interfacial Dzyaloshinskii-Moriya interaction (i-DMI) exists in the film materials with inversion symmetry breaking, which can stabilize a series of nonlinear spin structures and control their chirality, such as Néel-type domain wall, magnetic skyrmion and spin spiral. In addition, the strength and chirality of i-DMI are directly related to the dynamic behavior of these nonlinear spin structures. Therefore, regulating the strength and chirality of i-DMI not only has an important scientific significance for enriching spintronics and topological physics, but also has a significant practical value for constructing a new generation of memorizer, logic gate, and brain-like devices with low-power. This review summarizes the research progress on the regulation of i-DMI in ferromagnetic films and provides some prospects for future research.

Dipolar skyrmions and antiskyrmions of arbitrary topological charge at room temperature

Magnetic skyrmions are localized, stable topological magnetic textures that can move and interact with each other like ordinary particles when an external stimulus is applied. The efficient control of the motion of spin textures using spin-polarized currents opened an opportunity for skyrmionic devices such as racetrack memory and neuromorphic or reservoir computing. The coexistence of skyrmions with high topological charge in the same system promises further possibilities for efficient technological applications. In this work, we directly observe dipolar skyrmions and antiskyrmions with arbitrary topological charge in Co/Ni multilayers at room temperature. We explore the dipolar-stabilized spin objects with topological charges of up to 10 and characterize their nucleation process, their energy dependence on the topological charge and the effect of the material parameters on their stability. Furthermore, our micromagnetic simulations demonstrate spin-transfer-induced motion of these spin objects, which is important for their potential device application.

The influence of antiferromagnetic spin cantings on the magnetic helix pitch in cubic helimagnets

In cubic helimagnets MnSi and Cu2OSeO3with their nearly isotropic magnetic properties, the magnetic structure undergoes helical deformation, which is almost completely determined by the helicoid wavenumberk=D/J, where magnetization field stiffnessJis associated with isotropic spin exchange, andDis a pseudoscalar value characterizing the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. Another magnetic feature of these crystals, also caused by the DM interactions, are antiferromagnetic spin cantings, similar to the ferromagnetic cantings responsible for the phenomenon of weak ferromagnetism. Here we show that cantings can strongly influence the helical order through the value of the parameterD. Changing the cantings in a strong magnetic field is predicted to affect the magnon spectrum of the crystals.

Strain-Induced Reversible Motion of Skyrmions at Room Temperature

Magnetic skyrmions are topologically protected swirling spin textures with great potential for future spintronic applications. The ability to induce skyrmion motion using mechanical strain not only stimulates the exploration of exotic physics but also affords the opportunity to develop energy-efficient spintronic devices. However, the experimental realization of strain-driven skyrmion motion remains a formidable challenge. Herein, we demonstrate that the inhomogeneous uniaxial compressive strain can induce the movement of isolated skyrmions from regions of high strain to regions of low strain at room temperature, which was directly observed using an in situ Lorentz transmission electron microscope with a specially designed nanoindentation holder. We discover that the uniaxial compressive strain can transform skyrmions into a single domain with in-plane magnetization, resulting in the coexistence of skyrmions with a single domain along the direction of the strain gradient. Through comprehensive micromagnetic simulations, we reveal that the repulsive interactions between skyrmions and the single domain serve as the driving force behind the skyrmion motion. The precise control of skyrmion motion through strain provides exciting opportunities for designing advanced spintronic devices that leverage the intricate interplay between strain and magnetism.

Task-adaptive physical reservoir computing

Reservoir computing is a neuromorphic architecture that may offer viable solutions to the growing energy costs of machine learning. In software-based machine learning, computing performance can be readily reconfigured to suit different computational tasks by tuning hyperparameters. This critical functionality is missing in 'physical' reservoir computing schemes that exploit nonlinear and history-dependent responses of physical systems for data processing. Here we overcome this issue with a 'task-adaptive' approach to physical reservoir computing. By leveraging a thermodynamical phase space to reconfigure key reservoir properties, we optimize computational performance across a diverse task set. We use the spin-wave spectra of the chiral magnet Cu2OSeO3 that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to different computational reservoir responses. The task-adaptive approach is applicable to a wide variety of physical systems, which we show in other chiral magnets via above (and near) room-temperature demonstrations in Co8.5Zn8.5Mn3 (and FeGe).

Transition between distinct hybrid skyrmion textures through their hexagonal-to-square crystal transformation in a polar magnet

Magnetic skyrmions, topological vortex-like spin textures, garner significant interest due to their unique properties and potential applications in nanotechnology. While they typically form a hexagonal crystal with distinct internal magnetisation textures known as Bloch- or Néel-type, recent theories suggest the possibility for direct transitions between skyrmion crystals of different lattice structures and internal textures. To date however, experimental evidence for these potentially useful phenomena have remained scarce. Here, we discover the polar tetragonal magnet EuNiGe3 to host two hybrid skyrmion phases, each with distinct internal textures characterised by anisotropic combinations of Bloch- and Néel-type windings. Variation of the magnetic field drives a direct transition between the two phases, with the modification of the hybrid texture concomitant with a hexagonal-to-square skyrmion crystal transformation. We explain these observations with a theory that includes the key ingredients of momentum-resolved Ruderman-Kittel-Kasuya-Yosida and Dzyaloshinskii-Moriya interactions that compete at the observed low symmetry magnetic skyrmion crystal wavevectors. Our findings underscore the potential of polar magnets with rich interaction schemes as promising for discovering new topological magnetic phases.

Gate-Controlled Chiral Recognition and Spin Assessment with All-Electric Hybrid Quantum Wire-Based Transistors

The search for inexpensive and all-electric tunable methods for portable and fast recognition and discrimination between various chiral enantiomers, mainly those found in the gas phase, has been one of the most challenging tasks in the field of analytical chemistry. The current article reports on a chiral sensitive electric architecture (CSEA) of a helical polyaniline (PANI)@carbon nanotube (CNT) hybrid quantum-wire based field effect transistor (FET) platform. The CSEA architecture exhibits gate-controlled-channel-chirality modulation for the selective distinction of Limonene (S(+)/R(-)) at ≈12 V intervals. Typical gate-modulated selectivity of S(+)-Limonene and R(-)-Limonene using two opposite helically turned hybrids, namely as, S-PANI@CNT and R-PANI@CNT are 6.5 and 2.8, respectively. Theoretical analysis and modelling relates the gas-phase chiral quantum probe with spin-channel modulation in CNT by Rashba spin-orbit interaction. This is achieved by applied gate voltage, CNT's unique curved surface, adsorbed chiral adatom induced scattering center on the curved graphitic lattice and helicoid field from a synthetically prepared helical PANI@CNT hybrid interface.

Bloch-type magnetic skyrmions in two-dimensional lattices

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

High-density, spontaneous magnetic biskyrmions induced by negative thermal expansion in ferrimagnets

Magnetic skyrmions are topologically protected quasiparticles that are promising for applications in spintronics. However, the low stability of most magnetic skyrmions leads to either a narrow temperature range in which they can exist, a low density of skyrmions, or the need for an external magnetic field, which greatly limits their wide application. In this study, high-density, spontaneous magnetic biskyrmions existing within a wide temperature range and without the need for a magnetic field were formed in ferrimagnets owing to the existence of a negative thermal expansion of the lattice. Moreover, a strong connection between the atomic-scale ferrimagnetic structure and nanoscale magnetic domains in Ho(Co,Fe)3 was revealed via in situ neutron powder diffraction and Lorentz transmission electron microscopy measurements. The critical role of the negative thermal expansion in generating biskyrmions in HoCo3 based on the magnetoelastic coupling effect is further demonstrated by comparing the behavior of HoCo2.8Fe0.2 with a positive thermal expansion.

Controllable Skyrmionic Phase Transition between Néel Skyrmions and Bloch Skyrmionic Bubbles in van der Waals Ferromagnet Fe3-δ GeTe2

The van der Waals (vdW) ferromagnet Fe3-δ GeTe2 has garnered significant research interest as a platform for skyrmionic spin configurations, that is, skyrmions and skyrmionic bubbles. However, despite extensive efforts, the origin of the Dzyaloshinskii-Moriya interaction (DMI) in Fe3-δ GeTe2 remains elusive, making it challenging to acquire these skyrmionic phases in a controlled manner. In this study, it is demonstrated that the Fe content in Fe3-δ GeTe2 has a profound effect on the crystal structure, DMI, and skyrmionic phase. For the first time, a marked increase in Fe atom displacement with decreasing Fe content is observed, transforming the original centrosymmetric crystal structure into a non-centrosymmetric symmetry, leading to a considerable DMI. Additionally, by varying the Fe content and sample thickness, a controllable transition between Néel-type skyrmions and Bloch-type skyrmionic bubbles is achieved, governed by a delicate interplay between dipole-dipole interaction and the DMI. The findings offer novel insights into the variable skyrmionic phases in Fe3-δ GeTe2 and provide the impetus for developing vdW ferromagnet-based spintronic devices.

Weyl nodal lines, Weyl points and the tunable quantum anomalous Hall effect in two-dimensional multiferroic metal oxynitride: Tl2NO2

The investigation of two-dimensional (2D) multiferroic and topological quantum phases is a significant topic in current condensed matter physics. In this study, we discover quantum topological phases in the multiferroic material Tl2NO2. We observe that its ferroelectric (FE) phase displays a ferromagnetic ground state with magnetization favoring in-plane orientation. In the absence of spin-orbit coupling (SOC), a Weyl nodal loop around the Fermi level is evident, representing a 1D band crossing between spin-up and spin-down states. When spin-orbit coupling is taken into account, setting the magnetization in-plane, the Weyl nodal loop becomes gapped. Additionally, a pair of 2D Weyl nodes appear on the high-symmetry path, protected by a vertical mirror symmetry allowed by the magnetization. Remarkably, we prove that the Weyl nodes are situated at the topological phase transition between two quantum anomalous Hall (QAH) phases with opposite Chern numbers. Therefore, by adjusting the magnetization, it is possible to switch the propagation direction of chiral edge states. Furthermore, from its ferroelectric state to a paraelectric state, the time-reversal symmetry breaking nodal line is transformed into a Weyl point, achieving 100% spin polarization. Particularly, the Weyl points remain robust against SOC when the vertical mirror symmetry is preserved. Importantly, we also demonstrate that the Weyl point also represents the transition point where the QAH phase changes the sign of its Chern number. Overall, our study provides new insights into the study of multiferroic and topological phenomena in 2D materials and offers a potential avenue for controlling QAH phases.

Ferroelectrically tunable magnetic skyrmions in two-dimensional multiferroics

Magnetic skyrmions are topologically protected entities that are promising for information storage and processing. Currently, an essential challenge for future advances of skyrmionic devices lies in achieving effective control of skyrmion properties. Here, through first-principles and Monte-Carlo simulations, we report the identification of nontrivial topological magnetism in two-dimensional multiferroics of Co2NF2. Because of ferroelectricity, monolayer Co2NF2 exhibits a large Dzyaloshinskii-Moriya interaction. This together with exchange interaction can stabilize magnetic skyrmions with the size of sub-10 nm under a moderate magnetic field. Importantly, arising from the magnetoelectric coupling effect, the chirality of magnetic skyrmions is ferroelectrically tunable, producing the four-fold degenerate skyrmions. When interfacing with monolayer MoSe2, the creation and annihilation of magnetic skyrmions, as well as phase transition between skyrmion and skyrmion lattice, can be realized in a ferroelectrically controllable fashion. A dimensionless parameter κ' is further proposed as the criterion for stabilizing magnetic skyrmions in such multiferroic lattices. Our work greatly enriches the two-dimensional skyrmionics and multiferroics research.

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Light-Induced Metastable Hidden Skyrmion Phase in the Mott Insulator Cu2 OSeO3

The discovery of a novel long-lived metastable skyrmion phase in the multiferroic insulator Cu2 OSeO3 visualized with Lorentz transmission electron microscopy for magnetic fields below the equilibrium skyrmion pocket is reported. This phase can be accessed by exciting the sample non-adiabatically with near-infrared femtosecond laser pulses and cannot be reached by any conventional field-cooling protocol, referred as a hidden phase. From the strong wavelength dependence of the photocreation process and via spin-dynamics simulations, the magnetoelastic effect is identified as the most likely photocreation mechanism. This effect results in a transient modification of the magnetic free energy landscape extending the equilibrium skyrmion pocket to lower magnetic fields. The evolution of the photoinduced phase is monitored for over 15 min and no decay is found. Because such a time is much longer than the duration of any transient effect induced by a laser pulse in a material, it is assumed that the newly discovered skyrmion state is stable for practical purposes, thus breaking ground for a novel approach to control magnetic state on demand at ultrafast timescales and drastically reducing heat dissipation relevant for next-generation spintronic devices.

Ferroelectric solitons crafted in epitaxial bismuth ferrite superlattices

In ferroelectrics, complex interactions among various degrees of freedom enable the condensation of topologically protected polarization textures. Known as ferroelectric solitons, these particle-like structures represent a new class of materials with promise for beyond-CMOS technologies due to their ultrafine size and sensitivity to external stimuli. Such polarization textures have scarcely been demonstrated in multiferroics. Here, we present evidence for ferroelectric solitons in (BiFeO₃)/(SrTiO₃) superlattices. High-resolution piezoresponse force microscopy and Cs-corrected high-angle annular dark-field scanning transmission electron microscopy reveal a zoo of topologies, and polarization displacement mapping of planar specimens reveals center-convergent/divergent topological defects as small as 3 nm. Phase-field simulations verify that some of these structures can be classed as bimerons with a topological charge of ±1, and first-principles-based effective Hamiltonian computations show that the coexistence of such structures can lead to non-integer topological charges, a first observation in a BiFeO₃-based system. Our results open new opportunities in multiferroic topotronics.

CP2 skyrmions and skyrmion crystals in realistic quantum magnets

Magnetic skyrmions are nanoscale topological textures that have been recently observed in different families of quantum magnets. These objects are called CP¹ skyrmions because they are built from dipoles-the target manifold is the 1D complex projective space, CP¹ ≅ S². Here we report the emergence of magnetic CP² skyrmions in a realistic spin-1 model, which includes both dipole and quadrupole moments. Unlike CP¹ skyrmions, CP² skyrmions can also arise as metastable textures of quantum paramagnets, opening a new road to discover emergent topological solitons in non-magnetic materials. The quantum phase diagram of the spin-1 model also includes magnetic field-induced CP² skyrmion crystals that can be detected with regular momentum- (diffraction) and real-space (Lorentz transmission electron microscopy) experimental techniques.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

Realization and Current-Driven Dynamics of Fractional Hopfions and Their Ensembles in a Helimagnet FeGe

3D topological spin textures-hopfions-are predicted in helimagnetic systems but are not experimentally confirmed thus far. By utilizing an external magnetic field and electric current in the present study, 3D topological spin textures are realized, including fractional hopfions with nonzero topological index, in a skyrmion-hosting helimagnet FeGe. Microsecond current pulses are employed to control the dynamics of the expansion and contraction of a bundle composed of a skyrmion and a fractional hopfion, as well as its current-driven Hall motion. This research approach has demonstrated the novel electromagnetic properties of fractional hopfions and their ensembles in helimagnetic systems.

Nonreciprocal Phonon Propagation in a Metallic Chiral Magnet

The phonon magnetochiral effect (MChE) is the nonreciprocal acoustic and thermal transports of phonons caused by the simultaneous breaking of the mirror and time-reversal symmetries. So far, the phonon MChE has been observed only in a ferrimagnetic insulator Cu_{2}OSeO_{3}, where the nonreciprocal response disappears above the Curie temperature of 58 K. Here, we study the nonreciprocal acoustic properties of a room-temperature ferromagnet Co_{9}Zn_{9}Mn_{2} for unveiling the phonon MChE close to room temperature. Surprisingly, the nonreciprocity in this metallic compound is enhanced at higher temperatures and observed up to 250 K. This clear contrast between insulating Cu_{2}OSeO_{3} and metallic Co_{9}Zn_{9}Mn_{2} suggests that metallic magnets have a mechanism to enhance the nonreciprocity at higher temperatures. From the ultrasound and microwave-spectroscopy experiments, we conclude that the magnitude of the phonon MChE of Co_{9}Zn_{9}Mn_{2} mostly depends on the Gilbert damping, which increases at low temperatures and hinders the magnon-phonon hybridization. Our results suggest that the phonon nonreciprocity could be further enhanced by engineering the magnon band of materials.

Solution epitaxy of polarization-gradient ferroelectric oxide films with colossal photovoltaic current

Solution growth of single-crystal ferroelectric oxide films has long been pursued for the low-cost development of high-performance electronic and optoelectronic devices. However, the established principles of vapor-phase epitaxy cannot be directly applied to solution epitaxy, as the interactions between the substrates and the grown materials in solution are quite different. Here, we report the successful epitaxy of single-domain ferroelectric oxide films on Nb-doped SrTiO3 single-crystal substrates by solution reaction at a low temperature of ~200 oC. The epitaxy is mainly driven by an electronic polarization screening effect at the interface between the substrates and the as-grown ferroelectric oxide films, which is realized by the electrons from the doped substrates. Atomic-level characterization reveals a nontrivial polarization gradient throughout the films in a long range up to ~500 nm because of a possible structural transition from the monoclinic phase to the tetragonal phase. This polarization gradient generates an extremely high photovoltaic short-circuit current density of ~2.153 mA/cm2 and open-circuit voltage of ~1.15 V under 375 nm light illumination with power intensity of 500 mW/cm2, corresponding to the highest photoresponsivity of ~4.306×10-3 A/W among all known ferroelectrics. Our results establish a general low-temperature solution route to produce single-crystal gradient films of ferroelectric oxides and thus open the avenue for their broad applications in self-powered photo-detectors, photovoltaic and optoelectronic devices.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb₃ S₆  using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Current-Induced Reversible Split of Elliptically Distorted Skyrmions in Geometrically Confined Fe3 Sn2 Nanotrack

Skyrmions are swirling spin textures with topological characters promising for future spintronic applications. Skyrmionic devices typically rely on the electrical manipulation of skyrmions with a circular shape. However, manipulating elliptically distorted skyrmions can lead to numerous exotic magneto-electrical functions distinct from those of conventional circular skyrmions, significantly broadening the capability to design innovative spintronic devices. Despite the promising potential, its experimental realization so far remains elusive. In this study, the current-driven dynamics of the elliptically distorted skyrmions in geometrically confined magnet Fe3 Sn2 is experimentally explored. This study finds that the elliptical skyrmions can reversibly split into smaller-sized circular skyrmions at a current density of 3.8 × 1010 A m-2 with the current injected along their minor axis. Combined experiments with micromagnetic simulations reveal that this dynamic behavior originates from a delicate interplay of the spin-transfer torque, geometrical confinement, and pinning effect, and strongly depends on the ratio of the major axis to the minor axis of the elliptical skyrmions. The results indicate that the morphology is a new degree of freedom for manipulating the current-driven dynamics of skyrmions, providing a compelling route for the future development of spintronic devices.

Mirroring Skyrmions in Synthetic Antiferromagnets via Modular Design

Skyrmions are promising for the next generation of spintronic devices, which involves the production and transfer of skyrmions. The creation of skyrmions can be realized by a magnetic field, electric field, or electric current while the controllable transfer of skyrmions is hindered by the skyrmion Hall effect. Here, we propose utilizing the interlayer exchange coupling induced by the Ruderman-Kittel-Kasuya-Yoshida interactions to create skyrmions through hybrid ferromagnet/synthetic antiferromagnet structures. An initial skyrmion in ferromagnetic regions could create a mirroring skyrmion with an opposite topological charge in antiferromagnetic regions driven by the current. Furthermore, the created skyrmions could be transferred in synthetic antiferromagnets without deviations away from the main trajectories due to the suppression of the skyrmion Hall effect in comparison to the transfer of the skyrmion in ferromagnets. The interlayer exchange coupling can be tuned, and the mirrored skyrmions can be separated when they reach the desired locations. Using this approach, the antiferromagnetic coupled skyrmions can be repeatedly created in hybrid ferromagnet/synthetic antiferromagnet structures. Our work not only supplies a highly efficient approach to create isolated skyrmions and correct the errors in the process of skyrmion transport, but also paves the way to a vital information writing technique based on the motion of skyrmions for skyrmion-based data storage and logic devices.

Two temperature-induced 1D CuII chain enantiomeric pairs showing different magnetic properties and nonlinear optical responses

At different reaction temperatures, using Cu(NO₃)₂·3H₂O to react with enantiomerically pure N-donor ligands (L_S/L_R), respectively, two pairs of chiral one-dimensional (1D) Cu^II chain enantiomers formulated as [Cu(μ₂-NO₃)(NO₃)(L_S)]_n/[Cu(μ₂-NO₃)(NO₃)(L_R)]_n (S-1-Cu/R-1-Cu, formed at 40 °C with an NO₃^- group as a sole bridging ligand) and [Cu(μ₂-L_S)(NO₃)₂]_n/[Cu(μ₂-L_R)(NO₃)₂]_n (S-2-Cu/R-2-Cu, formed at 25 °C with L_S or L_R as a bridging ligand) were prepared, where L_S/L_R = (+)/(-)-4,5-pinenepyridyl-2-pyrazine. Interestingly, such a disparity in bridging ligands leads not only to their distinct structural features but also to their completely different magnetic couplings together with a large difference in their nonlinear optical responses. S-1-Cu with a 1D helical structure shows weak ferromagnetic coupling between Cu^II ions, while S-2-Cu with a 1D stairway-like structure presents weak antiferromagnetic coupling. In particular, they simultaneously possess both second- and third-harmonic generation (SHG and THG) responses in one molecule with large strength differences. More remarkably, S-1-Cu exhibits a very large THG response (162 × α-SiO₂), which is 22.5 times that of S-2-Cu, and the SHG strength of S-1-Cu is more than 3 times that of S-2-Cu. This work demonstrates that reaction temperature has a great impact on the self-assembled structures of coordination polymers and subsequently results in their large performance differences.

Lattice-Distortion-Induced Change in the Magnetic Properties in Br-Defect Host CsPbBr3 Perovskite Quantum Dots

Herein, we report temperature- and field-induced magnetic states in CsPbBr₃ perovskite quantum dots (PQDs) attributed to Br defects. We find that temperature-dependent structural distortion is the main source of various temperature-induced magnetic states in Br-defect host CsPbBr₃ PQDs. Comprehensively examined magnetization data through Arrott plots, Langevin and Brillouin function fitting, and structural analysis reveal the presence of various oxidation states (i.e., Pb⁰, Pb⁺, Pb²⁺, and Pb³⁺) yielding different magnetic states, such as diamagnetic states above 90 K, paramagnetic states below ≈90 K, and perhaps locally ordered states between 58 and 90 K. It is realized from theoretical fits that paramagnetic ions exist (i.e., superparamagnetic behavior) due to Br defects causing Pb⁺ (and/or Pb³⁺ ions) in the diamagnetic region. We anticipate that our findings will spur future research of the development of spin-optoelectronics, such as spin light-emitting diodes, and spintronics devices based on CsPbBr₃ PQDs.

Spontaneous Biskyrmion Lattice in a Centrosymmetric Rhombohedral Rare-Earth Magnet with Easy-Plane Anisotropy

Magnetic skyrmion and its derivatives have demonstrated fascinating topological behaviors with potential applications in future spintronic devices. Despite the recent progress, the spontaneous skyrmion lattice and successive topological transition in the magnets with easy-plane magnetic anisotropy are still elusive especially at room temperature. Here, in a centrosymmetric rhombohedral Nd₂Co₁₇ magnet with easy-plane magnetic anisotropy, spontaneous biskyrmions are observed over a wide temperature range across room temperature, and then evolve into enclosed in-plane domains with nanometric size due to the enhancement of the planar magnetic anisotropy. The spontaneous generation of the biskyrmion lattice and its evolution along different crystal orientations demonstrate the crucial role of intrinsic bi-anisotropy and demagnetization effects. This discovery provides a fundamental insight into the nature of topological magnetic textures in easy-plane anisotropy materials and suggests an arena to explore the topological states in rare-earth magnets as well as their applications in spintronics.

Spontaneous Topological States and Their Mutual Transformations in a Rare-Earth Ferrimagnet

Nontrivial chiral spin textures with nanometric sizes and novel characteristics (e.g., magnetic skyrmions) are promising for encoding information bits in future energy-efficient and high-density spintronic devices. Because of antiferromagnetic exchange coupling, skyrmions in ferrimagnetic materials exhibit many advantages in terms of size and efficient manipulation, which allow them to overcome the limitations of ferromagnetic skyrmions. Despite recent progress, ferrimagnetic skyrmions have been observed only in few films in the presence of external fields, while those in ferrimagnetic bulks remain elusive. This study reports on spontaneously generated zero-field ground-state magnetic skyrmions and their subsequent transformation into traditional magnetic bubbles via intermediate states of (bi-)target bubbles during a magnetic anisotropy change in the rare-earth ferrimagnetic crystal DyFe₁₁ Ti. Spontaneous reversible topological transformation driven by a temperature-induced spin reorientation transition is directly distinguished using Lorentz transmission electron microscopy. The spontaneous generation of magnetic skyrmions and successive topological transformations in ferrimagnetic DyFe₁₁ Ti are expected to advance the design of topological spin textures with versatile properties and potential applications in rare-earth magnets.

Skyrmion-skyrmion interaction induced by itinerant electrons in a ferromagnetic strip

Magnetic skyrmions are promising spin textures for building next-generation magnetic memories and spintronic devices. Nevertheless, one of the major challenges in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures in different geometries. Here we numerically study the skyrmion-skyrmion interaction potential that arises due to the dynamics of itinerant electrons coupled to the magnetic texture in a ferromagnetic background with racetrack geometry. We consider different topological textures (ferromagnetic (FM) and antiferromagnetic (AFM)), namely: skyrmions, antiskyrmions and biskyrmions. We show that at low electron filling, for sufficiently short separation, the skyrmions strongly couple each other yielding a bound-state bound by electronic dynamics. However, when the filling is increased, the interaction potential energy presents local minima at specific values of the skyrmion-skyrmion distance. Each of these local minima corresponds to energetically stable positions of skyrmions which are 'protected' by well-defined energy barriers. By inspecting the local charge density, we find that in the case of AFM skyrmions, the local antiferromagnetic nature prevents electronic penetration into the core, allowing the AFM skyrmions to be seen as infinite potential barriers for electrons.

Electric field writing and erasing of skyrmions in magnetoelectric Cu2OSeO3 with an ultralow energy barrier

Skyrmions are chiral magnetic textures with non-trivial topology, and due to their unique properties they are widely considered as promising information carriers in novel magnetic storage applications. While electric field writing/erasing and manipulation of skyrmions have been recently achieved, quantitative insights into the energetics of those phenomena remain scarce. Here, we report our in situ electric field writing/erasing of skyrmions in magnetoelectric helimagnet Cu₂OSeO₃ utilizing real-space and real-time Lorentz transmission electron macroscopy. Through the quantitavie analysis on our massive video data, we obtained a linear dependence of the number of skyrmions on the amplitude of the applied electric field, from which a local energy barried to write/erase skyrmions is estimated to be per skyrmion. Such an ultralow energy barrier implies the potential of precise control of skyrmions in future spintronics applications.

Distinguishing the Two-Component Anomalous Hall Effect from the Topological Hall Effect

In transport, the topological Hall effect (THE) presents itself as nonmonotonic features (or humps and dips) in the Hall signal and is widely interpreted as a sign of chiral spin textures, like magnetic skyrmions. However, when the anomalous Hall effect (AHE) is also present, the coexistence of two AHEs could give rise to similar artifacts, making it difficult to distinguish between genuine THE with AHE and two-component AHE. Here, we confirm genuine THE with AHE by means of transport and magneto-optical Kerr effect (MOKE) microscopy, in which magnetic skyrmions are directly observed, and find that genuine THE occurs in the transition region of the AHE. In sharp contrast, the artifact "THE" or two-component AHE occurs well beyond the saturation of the "AHE component" (under the false assumption of THE + AHE). Furthermore, we distinguish artifact "THE" from genuine THE by three methods: (1) minor loops, (2) temperature dependence, and (3) gate dependence. Minor loops of genuine THE with AHE are always within the full loop, while minor loops of the artifact "THE" may reveal a single loop that cannot fit into the "AHE component". In addition, the temperature or gate dependence of the artifact "THE" may also be accompanied by a polarity change of the "AHE component", as the nonmonotonic features vanish, while the temperature dependence of genuine THE with AHE reveals no such change. Our work may help future researchers to exercise caution and use these methods for careful examination in order to ascertain the genuine THE.

Chiral surface spin textures in Cu2OSeO3 unveiled by soft X-ray scattering in specular reflection geometry

Resonant elastic soft X-ray magnetic scattering (XRMS) is a powerful tool to explore long-periodic spin textures in single crystals. However, due to the limited momentum transfer range imposed by long wavelengths of photons in the soft x-ray region, Bragg diffraction is restricted to crystals with the large lattice parameters. Alternatively, small-angle X-ray scattering has been involved in the soft energy X-ray range which, however, brings in difficulties with the sample preparation that involves focused ion beam milling to thin down the crystal to below a few hundred nm thickness. We show how to circumvent these restrictions using XRMS in specular reflection from a sub-nanometer smooth crystal surface. The method allows observing diffraction peaks from the helical and conical spin modulations at the surface of a Cu   2 OSeO   3 single crystal and probing their corresponding chirality as contributions to the dichroic scattered intensity. The results suggest a promising way to carry out XRMS studies on a plethora of noncentrosymmetric systems hitherto unexplored with soft X-rays due to the absence of the commensurate Bragg peaks in the available momentum transfer range.

Magnetic Skyrmions with Unconventional Helicity Polarization in a Van Der Waals Ferromagnet

Skyrmion helicity, which defines the spin swirling direction, is a fundamental parameter that may be utilized to encode data bits in future memory devices. Generally, in centrosymmetric ferromagnets, dipole skyrmions with helicity of -π/2 and π/2 are degenerate in energy, leading to equal populations of both helicities. On the other hand, in chiral materials where the Dzyaloshinskii-Moriya interaction (DMI) prevails and the dipolar interaction is negligible, only a preferred helicity is selected by the type of DMI. However, whether there is a rigid boundary between these two regimes remains an open question. Herein, the observation of dipole skyrmions with unconventional helicity polarization in a van der Waals ferromagnet, Fe_{5- δ} GeTe₂ , is reported. Combining magnetometry, Lorentz transmission electron microscopy, electrical transport measurements, and micromagnetic simulations, the short-range superstructures in Fe_{5- δ} GeTe₂ resulting in a localized DMI contribution, which breaks the degeneracy of the opposite helicities and leads to the helicity polarization, is demonstrated. Therefore, the helicity feature in Fe_{5- δ} GeTe₂ is controlled by both the dipolar interaction and DMI that the former leads to Bloch-type skyrmions with helicity of ±π/2 whereas the latter breaks the helicity degeneracy. This work provides new insights into the skyrmion topology in van der Waals materials.

Tunable quantum gaps to decouple carrier and phonon transport leading to high-performance thermoelectrics

Thermoelectrics enable direct heat-to-electricity transformation, but their performance has so far been restricted by the closely coupled carrier and phonon transport. Here, we demonstrate that the quantum gaps, a class of planar defects characterized by nano-sized potential wells, can decouple carrier and phonon transport by selectively scattering phonons while allowing carriers to pass effectively. We choose the van der Waals gap in GeTe-based materials as a representative example of the quantum gap to illustrate the decoupling mechanism. The nano-sized potential well of the quantum gap in GeTe-based materials is directly visualized by in situ electron holography. Moreover, a more diffused distribution of quantum gaps results in further reduction of lattice thermal conductivity, which leads to a peak ZT of 2.6 at 673 K and an average ZT of 1.6 (323–723 K) in a GeTe system. The quantum gap can also be engineered into other thermoelectrics, which provides a general method for boosting their thermoelectric performance.

Defects are believed to always scatter carriers. Here, the authors find that the quantum gaps in GeTe-based materials do not scatter carriers, which decouple the carriers and phonons transport leading to high thermoelectric performance.

Origin of metamagnetism in skyrmion host Cu[Formula: see text]OSeO[Formula: see text]

Skyrmion host chiral Cu[Formula: see text]OSeO[Formula: see text] has attracted researchers due to several intriguing properties. Observation of metamagnetism in low-temperature and low-field makes the magnetic properties of Cu[Formula: see text]OSeO[Formula: see text] more complex. Here, we present an investigation on metamagnetism in Cu[Formula: see text]OSeO[Formula: see text] by analyzing its structural and magnetic properties. Study of magnetic properties reveal spin-flip of one of the Cu[Formula: see text] ions, embedded in square pyramidal CuO[Formula: see text] polyhedra, due to the development of strain in low-temperature and low-field regime. The spin-flip is found to be the main reason for field-induced first-order metamagnetic transition. Magnetic phase diagram of Cu[Formula: see text]OSeO[Formula: see text] has been constructed with the help of magnetization analyses. It is argued that the metamagnetic hysteretic field region may be low-temperature skyrmion phase with additional spiral and tilted-conical phases. A tricritical point has been observed in the phase diagram at which first-order metamagnetic hysteretic field range ceases to exist.

Skyrmion Echo in a System of Interacting Skyrmions

We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo).

Quantum Spin-Wave Theory for Non-Collinear Spin Structures, a Review

In this review, we trace the evolution of the quantum spin-wave theory treating non-collinear spin configurations. Non-collinear spin configurations are consequences of the frustration created by competing interactions. They include simple chiral magnets due to competing nearest-neighbor (NN) and next-NN interactions and systems with geometry frustration such as the triangular antiferromagnet and the Kagomé lattice. We review here spin-wave results of such systems and also systems with the Dzyaloshinskii–Moriya interaction. Accent is put on these non-collinear ground states which have to be calculated before applying any spin-wave theory to determine the spectrum of the elementary excitations from the ground states. We mostly show results obtained by the use of a Green’s function method. These results include the spin-wave dispersion relation and the magnetizations, layer by layer, as functions of T in 2D, 3D and thin films. Some new unpublished results are also included. Technical details and discussion on the method are shown and discussed.

Phase diagram of chiral magnets via Green's function method

In this paper, Green's function method is applied to study the ferromagnetic system with Dzyaloshinkii-Moriya (DM) interaction in both two-dimension (2D) and three-dimension chiral magnets. Relevant properties in 2D magnets are calculated, such as the susceptibility, correlation function and analytical expressions of phase boundary. Based on the theoretical results, a new phase is predicted in the window of strong DM interaction characterized by a negative winding number. In addition, helical state in pure 2D material only appears at zero temperature. The analysis on correlation function shows a special symmetry of transverse spin correlation, which corresponds to the skyrmion phase. The results also prove the instability of helical state and its lifetime is numerically computed. Different from 2D magnets, helical state in 3D exists in the window of a lower Zeeman energy and has a long lifetime. DM interaction also reduces Curie temperature because of the spatial symmetry breaking.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Qstate with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

Magnetoelectric Classification of Skyrmions

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and antiskyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the nonzero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity, and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.