Electric-field control of anomalous and topological Hall effects in oxide bilayer thin films

Topological Magneto-optical Effect from Skyrmions in Two-Dimensional Ferromagnets

Skyrmions in two-dimensional (2D) magnetic materials are considered as ideal candidates for information carriers in next-generation spintronic devices. However, conventional methods for elucidating the physical properties of skyrmions have limited the development of skyrmions in diverse 2D magnetic material systems due to their requirements for electrical conductivity. To overcome this limitation, we propose to utilize an optical method (magneto-optical Kerr technique) to detect the skyrmions in 2D magnetic materials. Herein, the graphene/Fe3GeTe2/graphene vertical van der Waals (vdW) heterostructure devices are fabricated to generate stabilized skyrmions by applying out-of-plane current. In combination with magnetic circular dichroism measurements, we observe topological-reflective magnetic circular dichroism (T-RMCD) effects in Fe3GeTe2 flakes and attribute the peak-shaped component in T-RMCD to the annihilation of skyrmion magnetic domains. Notably, the T-RMCD signal can maintain up to a temperature as high as the Curie temperature of Fe3GeTe2 flakes (∼200 K). Our work provides a universal, contactless, and nondestructive approach for studying the physical properties of skyrmions in 2D vdW magnetic materials while adding another degree of freedom to the modulation of skyrmions.

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.

Manipulating topological Hall-like signatures by interface engineering in epitaxial ruthenate/manganite heterostructures

Topologically protected non-trivial spin textures (e.g. skyrmions) give rise to a novel phenomenon called the topological Hall effect (THE) and have promising implications in future energy-efficient nanoelectronic and spintronic devices. Here, we have studied the Hall effect in SrRuO3/La0.42Ca0.58MnO3 (SRO/LCMO) bilayers. Our investigation suggests that pure SRO has hard and soft magnetic characteristics but the anomalous Hall effect (AHE) in SRO is governed by the high coercivity phase. We have shown that the proximity effect of a soft magnetic LCMO on SRO plays a critical role in interfacial magnetic coupling and transport properties in SRO. Upon reducing the SRO thickness in the bilayer, the proximity effect becomes the dominant feature, enhancing the magnitude and temperature range of THE-like signatures. The THE-like features in bilayers can be explained by a diffusive Berry phase transition model in the presence of an emergent magnetic state due to interface coupling. This work provides an alternative understanding of THE-like signatures and their manipulation in SRO-based heterostructures, bilayers and superlattices.

Electric-field control of reversible electronic and magnetic transitions in two-dimensional oxide monolayer magnets

Atomically thin oxide magnetic materials are highly desirable due to the promising potential to integrate two-dimensional (2D) magnets into next-generation spintronics. Therefore, 2D oxide magnetism is expected to be effectively tuned by the magnetic and electrical fields, holding prospective for future low-dissipation electronic devices. However, the electric-field control of 2D oxide monolayer magnetism has rarely been reported. Here, we present the realization of 2D monolayer magnetism in oxide (SrRuO3)1/(SrTiO3)N (N = 1, 3) superlattices that shows an efficient and reversible phase transition through electric-field controlled proton (H+) evolution. By using ionic liquid gating to modulate the proton concentration in (SrRuO3)1/(SrTiO3)1 superlattice, an electric-field induced metal-insulator transition was observed, along with gradually suppressed magnetic ordering and modulated magnetic anisotropy. Theoretical analysis reveals that proton intercalation plays a crucial role in both electronic and magnetic phase transitions. Strikingly, SrTiO3 layers can act as a proton sieve, which have a significant influence on proton evolution. Our work stimulates the tuning functionality of 2D oxide monolayer magnetism by voltage control, providing potential for future energy-efficient electronics.

Emergent quantum phenomena in atomically engineered iridate heterostructures

Over the last few years, researches in iridates have developed into an exciting field with the discovery of numerous emergent phenomena, interesting physics, and intriguing functionalities. Among the studies, iridate-based artificial structures play a crucial role owing to their extreme flexibility and tunability in lattice symmetry, chemical composition, and crystal dimensionality. In this article, we present an overview of the recent progress regarding iridate-based artificial structures. We first explicitly introduce several essential concepts in iridates. Then, we illustrate important findings on representative SrIrO3/SrTiO3 superlattices, heterostructures comprised of SrIrO3 and magnetic oxides, and their response to external electric-field stimuli. Finally, we comment on existing problems and promising future directions in this exciting field.

Néel Skyrmion Bubbles in La0.7Sr0.3Mn1-xRuxO3 Multilayers

Ferromagnetic La_0.7Sr_0.3Mn_1-xRu_xO₃ epitaxial multilayers with controlled variation of the Ru/Mn content were synthesized to engineer canted magnetic anisotropy and variable exchange interactions, and to explore the possibility of generating a Dzyaloshinskii-Moriya interaction. The ultimate aim of the multilayer design is to provide the conditions for the formation of domains with nontrivial magnetic topology in an oxide thin film system. Employing magnetic force microscopy and Lorentz transmission electron microscopy in varying perpendicular magnetic fields, magnetic stripe domains separated by Néel-type domain walls as well as Néel skyrmions smaller than 100 nm in diameter were observed. These findings are consistent with micromagnetic modeling, taking into account a sizable Dzyaloshinskii-Moriya interaction arising from the inversion symmetry breaking and possibly from strain effects in the multilayer system.

Light-Induced Mott-Insulator-to-Metal Phase Transition in Ultrathin Intermediate-Spin Ferromagnetic Perovskite Ruthenates

Light control of emergent quantum phenomena is a widely used external stimulus for quantum materials. Generally, perovskite strontium ruthenate SrRuO₃ has an itinerant ferromagnetism with a low-spin state. However, the phase of intermediate-spin (IS) ferromagnetic metallic state has never been seen. Here, by means of UV-light irradiation, a photocarrier-doping-induced Mott-insulator-to-metal phase transition is shown in a few atomic layers of perovskite IS ferromagnetic SrRuO_{3- δ} . This new metastable IS metallic phase can be reversibly regulated due to the convenient photocharge transfer from SrTiO₃ substrates to SrRuO_{3- δ} ultrathin films. These dynamical mean-field theory calculations further verify such photoinduced electronic phase transformation, owing to oxygen vacancies and orbital reconstruction. The optical manipulation of charge-transfer finesse is an alternative pathway toward discovering novel metastable phases in strongly correlated systems and facilitates potential light-controlled device applications in optoelectronics and spintronics.

Reversal of Anomalous Hall Effect and Octahedral Tilting in SrRuO3 Thin Films via Hydrogen Spillover

The perovskite SrRuO₃ (SRO) is a strongly correlated oxide whose physical and structural properties are strongly intertwined. Notably, SRO is an itinerant ferromagnet that exhibits a large anomalous Hall effect (AHE) whose sign can be readily modified. Here, a hydrogen spillover method is used to tailor the properties of SRO thin films via hydrogen incorporation. It is found that the magnetization and Curie temperature of the films are strongly reduced and, at the same time, the structure evolves from an orthorhombic to a tetragonal phase as the hydrogen content is increased up to ≈0.9 H per SRO formula unit. The structural phase transition is shown, via in situ crystal truncation rod measurements, to be related to tilting of the RuO₆ octahedral units. The significant changes observed in magnetization are shown, via density functional theory (DFT), to be a consequence of shifts in the Fermi level. The reported findings provide new insights into the physical properties of SRO via tailoring its lattice symmetry and emergent physical phenomena via the hydrogen spillover technique.

Controllable Itinerant Ferromagnetism in Weakly Correlated 5d SrIrO3

The weakly correlated nature of 5d oxide SrIrO₃ determines its rare ferromagnetism, and the control of its magnetic order is even less studied. Tailoring structure distortion is currently a main route to tune the magnetic order of 5d iridates, but only for the spatially confined insulating counterparts. Here, we have realized ferromagnetic order in metallic SrIrO₃ by construction of SrIrO₃/ferromagnetic-insulator (LaCoO₃) superlattices, which reveal a giant coercivity of ∼10 T and saturation field of ∼25 T with strong perpendicular magnetic anisotropy. The Curie temperature of SrIrO₃ can be controlled by engineering interface charge transfer, which is confirmed by Hall effect measurements collaborating with EELS and XAS. Besides, the noncoplanar spin texture is captured, which is caused by interfacial Dzyaloshinskii-Moriya interactions as well. These results indicate controllable itinerant ferromagnetism and an emergent topological magnetic state in strong spin-orbit coupled semimetal SrIrO₃, showing great potential to develop efficient spintronic devices.

Gradient-Induced Dzyaloshinskii-Moriya Interaction

The Dzyaloshinskii-Moriya interaction (DMI) that arises in the magnetic systems with broken inversion symmetry plays an essential role in topological spintronics. Here, by means of atomistic spin calculations, we study an intriguing type of DMI (g-DMI) that emerges in the films with composition gradient. We show that both the strength and chirality of g-DMI can be controlled by the composition gradient even in the disordered system. The layer-resolved analysis of g-DMI unveils its additive nature inside the bulk layers and clarifies the linear thickness dependence of g-DMI observed in experiments. Furthermore, we demonstrate the g-DMI-induced chiral magnetic structures, such as spin spirals and skyrmions, and the g-DMI driven field-free spin-orbit torque (SOT) switching, both of which are crucial toward practical device application. These results elucidate the underlying mechanisms of g-DMI and open up a new way to engineer the topological magnetic textures.

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.

Electric field-induced switching of anomalous Nernst conductivity in the 2D MoTe2/VSe2 heterostructure

Generation of a transverse electric current by a longitudinal charge or heat current is receiving extensive research efforts because of its potential applications in information-processing devices. Therefore, we investigated the electric field-dependent Curie temperature, anomalous Hall conductivity (AHC), and anomalous Nernst conductivity (ANC) of the 2H-MoTe₂/1T-VSe₂ heterostructure. The MoTe₂/VSe₂ heterostructure had a Curie temperature of 270 K and the Curie temperature was substantially increased to 355 K under an electric field. We obtained the electric field-induced switching of the AHC in the electron-doped system, whereas no switching was found in the hole-doped system. Also, the electric field-dependent ANC of the MoTe₂/VSe₂ heterostructure was investigated. The electric field-dependence of the ANC was more prominent in the electron-doped system. We obtained a large ANC of 2.3 A K^-1 m^-1 when the electric field was applied from VSe₂ to MoTe₂ layers and this was switched to -0.6 A K^-1 m^-1 with an opposite electric field. This finding may indicate that the 2D MoTe₂/VSe₂ heterostructure can be used for potential applications in energy conversion and spintronic devices.

Emergent Topological Hall Effect from Exchange Coupling in Ferromagnetic Cr2Te3/Noncoplanar Antiferromagnetic Cr2Se3 Bilayers

The topological Hall effect has been observed in magnetic materials of complex spin structures or bilayers of trivial magnets and strong spin-orbit-coupled systems. In view of current attention on dissipationless topological electronics, the occurrence of the topological Hall effect in new systems or by an unexpected mechanism is fascinating. Here, we report a robust topological Hall effect generated in bilayers of a ferromagnet and a noncoplanar antiferromagnet, from the interfacial Dzyaloshinskii-Moriya interaction due to the exchange coupling of magnetic layers. Molecular beam epitaxy has been utilized to fabricate heterostructures of a ferromagnetic metal Cr₂Te₃ and a noncoplanar antiferromagnet Cr₂Se₃. A significant topological Hall effect at low temperature implies the development of nontrivial spin chirality, and density functional theory calculations explain the correlation of the Dzyaloshinskii-Moriya interaction increase and inversion symmetry breaking at the interface. The presence of noncoplanar ordering in the antiferromagnet plays a pivotal role in producing the topological Hall effect. Our results suggest that the exchange coupling in ferromagnet/noncoplanar antiferromagnet bilayers could be an alternative mechanism toward topologically protected magnetic structures.

Topological Hall effect in SrRuO3thin films and heterostructures

Transition metal oxides hold a wide spectrum of fascinating properties endowed by the strong electron correlations. In 4dand 5doxides, exotic phases can be realized with the involvement of strong spin-orbit coupling (SOC), such as unconventional magnetism and topological superconductivity. Recently, topological Hall effects (THEs) and magnetic skyrmions have been uncovered in SrRuO₃thin films and heterostructures, where the presence of SOC and inversion symmetry breaking at the interface are believed to play a key role. Realization of magnetic skyrmions in oxides not only offers a platform to study topological physics with correlated electrons, but also opens up new possibilities for magnetic oxides using in the low-power spintronic devices. In this review, we discuss recent observations of THE and skyrmions in the SRO film interfaced with various materials, with a focus on the electric tuning of THE. We conclude with a discussion on the directions of future research in this field.

Soft-Magnetic Skyrmions Induced by Surface-State Coupling in an Intrinsic Ferromagnetic Topological Insulator Sandwich Structure

A magnetic skyrmion induced on a ferromagnetic topological insulator (TI) is a real-space manifestation of the chiral spin texture in the momentum space and can be a carrier for information processing by manipulating it in tailored structures. Here, a sandwich structure containing two layers of a self-assembled ferromagnetic septuple-layer TI, Mn(Bi_1-xSb_x)₂Te₄ (MnBST), separated by quintuple layers of TI, (Bi_1-xSb_x)₂Te₃ (BST), is fabricated and skyrmions are observed through the topological Hall effect in an intrinsic magnetic topological insulator for the first time. The thickness of BST spacer layer is crucial in controlling the coupling between the gapped topological surface states in the two MnBST layers to stabilize the skyrmion formation. The homogeneous, highly ordered arrangement of the Mn atoms in the septuple-layer MnBST leads to a strong exchange interaction therein, which makes the skyrmions "soft magnetic". This would open an avenue toward a topologically robust rewritable magnetic memory.

Infinite-layer/perovskite oxide heterostructure-induced high-spin states in SrCuO2/SrRuO3 bilayer films

Heterostructures composed of dissimilar oxides with different properties offer opportunities to develop emergent devices with desired functionalities. A key feature of oxide heterostructures is interface electronics and orbital reconstructions. Here, we combined infinite-layered SrCuO₂ and perovskite SrRuO₃ into heterostructures. A rare high spin state as large as 3.0 μ_B f.u^-1 and an increase in Curie temperature by 12 K are achieved in an ultrathin SrRuO₃ film capped by a SrCuO₂ layer. Atomic-scale lattice imaging shows the uniform CuO₂-plane-to-RuO₅-pyramid connection at the interface, where the regularly arranged RuO₅ pyramids were elongated along the out-of-plane direction. As revealed by theoretical calculations and spectral analysis, these features finally result in an abnormally high spin state of the interfacial Ru ions with highly polarized e_g orbitals. The present work demonstrates that oxygen coordination engineering at the infinite-layer/perovskite oxide interface is a promising approach towards advanced oxide electronics.

Coupling Charge and Topological Reconstructions at Polar Oxide Interfaces

In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion symmetry across the heterointerfaces. A notable example is the interface between polar and nonpolar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way for the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wave functions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO_{3}, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and LaAlO_{3}, a polar wide-band-gap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO_{2}/SrO interface configuration, leading to excess charge being pinned near the LaAlO_{3}/SrRuO_{3} interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction drives a reorganization of the topological charges in the band structure, thereby modifying the momentum-space Berry curvature in SrRuO_{3}. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.

Defect-Engineered Dzyaloshinskii-Moriya Interaction and Electric-Field-Switchable Topological Spin Texture in SrRuO3

In situ electrical control of the Dzyaloshinskii-Moriya interaction (DMI) is one of the central but challenging goals toward skyrmion-based device applications. An atomic design of defective interfaces in spin-orbit-coupled transition-metal oxides can be an appealing strategy to achieve this goal. In this work, by utilizing the distinct formation energies and diffusion barriers of oxygen vacancies at SrRuO₃ /SrTiO₃ (001), a sharp interface is constructed between oxygen-deficient and stoichiometric SrRuO₃ . This interfacial inversion-symmetry breaking leads to a sizable DMI, which can induce skyrmionic magnetic bubbles and the topological Hall effect in a more than 10 unit-cell-thick SrRuO₃ . This topological spin texture can be reversibly manipulated through the migration of oxygen vacancies under electric gating. In particular, the topological Hall signal can be deterministically switched ON and OFF. This result implies that the defect-engineered topological spin textures may offer an alternate perspective for future skyrmion-based memristor and synaptic devices.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in the field.

Tailoring Dzyaloshinskii-Moriya interaction in a transition metal dichalcogenide by dual-intercalation

Dzyaloshinskii-Moriya interaction (DMI) is vital to form various chiral spin textures, novel behaviors of magnons and permits their potential applications in energy-efficient spintronic devices. Here, we realize a sizable bulk DMI in a transition metal dichalcogenide (TMD) 2H-TaS₂ by intercalating Fe atoms, which form the chiral supercells with broken spatial inversion symmetry and also act as the source of magnetic orderings. Using a newly developed protonic gate technology, gate-controlled protons intercalation could further change the carrier density and intensely tune DMI via the Ruderman-Kittel-Kasuya-Yosida mechanism. The resultant giant topological Hall resistivity [Formula: see text] of [Formula: see text] at [Formula: see text] (about [Formula: see text] larger than the zero-bias value) is larger than most known chiral magnets. Theoretical analysis indicates that such a large topological Hall effect originates from the two-dimensional Bloch-type chiral spin textures stabilized by DMI, while the large anomalous Hall effect comes from the gapped Dirac nodal lines by spin-orbit interaction. Dual-intercalation in 2H-TaS₂ provides a model system to reveal the nature of DMI in the large family of TMDs and a promising way of gate tuning of DMI, which further enables an electrical control of the chiral spin textures and related electromagnetic phenomena.

Real-space observation of ferroelectrically induced magnetic spin crystal in SrRuO3

Unusual features in the Hall Resistivity of thin film systems are frequently associated with whirling spin textures such as Skyrmions. A host of recent investigations of Hall Hysteresis loops in SrRuO₃ heterostructures have provided conflicting evidence for different causes for such features. We have constructed an SrRuO₃-PbTiO₃ (Ferromagnetic – Ferroelectric) bilayer that exhibits features in the Hall Hysteresis previously attributed to a Topological Hall Effect, and Skyrmions. Here we show field dependent Magnetic Force Microscopy measurements throughout the key fields where the ‘THE’ presents, revealing the emergence to two periodic, chiral spin textures. The zero-field cycloidal phase, which then transforms into a ‘double-q’ incommensurate spin crystal appears over the appearance of the ‘Topological-like’ Hall effect region, and develop into a ferromagnetic switching regime as the sample reaches saturation, and the ‘Topological-like’ response diminishes. Scanning Tunnelling Electron Microscopy and Density Functional Theory is used to observe and analyse surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system.

There is an ongoing debate in the origin of unusual bumps in the resistive Hall measurements in SrRuO3 systems. Here, the authors analyze surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system, revealing a magnetic spin crystal emergent across the unusual bumps.

Berry Phase Engineering in SrRuO3/SrIrO3/SrTiO3 Superlattices Induced by Band Structure Reconstruction

The Berry phase, which reveals the intimate geometrical structure underlying quantum mechanics, plays a central role in the anomalous Hall effect. In this work, we observed a sign change of Berry curvatures at the interface between the ferromagnet SrRuO₃ (SRO) layer and the SrIrO₃ (SIO) layer with strong spin-orbit coupling. The negative Berry curvature at the interface, induced by the strongly spin-orbit-coupled Ir 5d bands near the Fermi level, makes the SRO/SIO interface different from the SRO layer that has a positive Berry curvature. These opposite Berry curvatures led to two anomalous Hall effect (AHE) channels with opposite signs at the SRO/SIO interface and in the SRO layer, respectively, resulting in a hump-like feature in the Hall resistivity loop. This observation offers a straightforward explanation of the hump-like feature that is usually associated with the chiral magnetic structure or magnetic skyrmions. Hence, this study provides evidence to oppose the widely accepted claim that magnetic skyrmions induce the hump-like feature.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Electric field induced reversal of spin polarization, magnetic anisotropy and tailored Dzyaloshinskii-Moriya interaction in underoxidized SrRuO3/SrTiO3 heterostructures

Electric field tailored magnetic properties of the perovskite-type oxide heterostructures are important in spintronic devices with low energy consumption and small size. Here, the electric field modulated magnetic properties of underoxidized SrRuO3 (SRO)/SrTiO3 (STO) heterostructures are investigated using first-principles calculations. The spin polarization of underoxidized SRO/STO heterostructures turns from negative to positive as the electric field changes from -0.2 to 0.2 V nm-1. The underoxidized SRO/STO heterostructure with 7 SRO atomic layers turns from perpendicular magnetic anisotropy to in-plane magnetic anisotropy as the electric field turns from -0.2 to 0.2 V nm-1, which can be attributed to the in-plane dx2-y2 and out-of-plane dxz, dyz orbitals. The Dzyaloshinskii-Moriya interaction of underoxidized SRO/STO heterostructures can also be effectively tailored using an electric field. These results indicate that the use of electric field is an effective method to modulate magnetic properties of perovskite-type oxide heterostructures, which is beneficial for the development of the high-performance spintronic devices.

Recent Progress on Topological Structures in Ferroic Thin Films and Heterostructures

Topological spin/polarization structures in ferroic materials continue to draw great attention as a result of their fascinating physical behaviors and promising applications in the field of high-density nonvolatile memories as well as future energy-efficient nanoelectronic and spintronic devices. Such developments have been made, in part, based on recent advances in theoretical calculations, the synthesis of high-quality thin films, and the characterization of their emergent phenomena and exotic phases. Herein, progress over the last decade in the study of topological structures in ferroic thin films and heterostructures is explored, including the observation of topological structures and control of their structures and emergent physical phenomena through epitaxial strain, layer thickness, electric, magnetic fields, etc. First, the evolution of topological spin structures (e.g., magnetic skyrmions) and associated functionalities (e.g., topological Hall effect) in magnetic thin films and heterostructures is discussed. Then, the exotic polar topologies (e.g., domain walls, closure domains, polar vortices, bubble domains, and polar skyrmions) and their emergent physical properties in ferroelectric oxide films and heterostructures are explored. Finally, a brief overview and prospectus of how the field may evolve in the coming years is provided.

Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

Berry curvature connects to exotic electronic phases hence it provides important insights to understand quantum materials. Here, the authors report sign change of the anomalous Hall effect resulted from Berry curvature change at the interface of a topological insulator/magnetic topological insulator heterostructure.

Detection of the Chiral Spin Structure in Ferromagnetic SrRuO3 Thin Film

SrRuO₃ (SRO) thin films and their heterostructure have attracted much attention because of the recently demonstrated fascinating properties, such as topological Hall effect and skyrmions. Critical to the understanding of those SRO properties is the study of the spin configuration. Here, we conduct resonant soft X-ray scattering (RSXS) at the oxygen K edge to investigate the spin configuration of a four-unit-cell SRO film that was grown epitaxially on a single-crystal SrTiO₃. The RSXS signal under a magnetic field (∼0.4 tesla) clearly shows a magnetic dichroism pattern around the specular reflection. Model calculations on the RSXS signal demonstrate that the magnetic dichroism pattern originates from a Néel-type chiral spin structure in this SRO thin film. We believe that the observed spin structure of the SRO system is a critical piece of information for understanding its intriguing magnetic and transport properties.

Strain engineering of the magnetic multipole moments and anomalous Hall effect in pyrochlore iridate thin films

The recent observation of the anomalous Hall effect (AHE) without notable magnetization in antiferromagnets has suggested that ferromagnetic ordering is not a necessary condition. Thus, recent theoretical studies have proposed that higher-rank magnetic multipoles formed by clusters of spins (cluster multipoles) can generate the AHE without magnetization. Despite such an intriguing proposal, controlling the unconventional AHE by inducing these cluster multipoles has not been investigated. Here, we demonstrate that strain can manipulate the hidden Berry curvature effect by inducing the higher-rank cluster multipoles in spin-orbit-coupled antiferromagnets. Observing the large AHE on fully strained antiferromagnetic Nd₂Ir₂O₇ thin films, we prove that strain-induced cluster T ₁-octupoles are the only source of observed AHE. Our results provide a previously unidentified pathway for generating the unconventional AHE via strain-induced magnetic structures and establish a platform for exploring undiscovered topological phenomena via strain in correlated materials.

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

Ferroelectrically tunable magnetism in BiFeO3/BaTiO3 heterostructure revealed by the first-principles calculations

The perovskite oxide interface has attracted extensive attention as a platform for achieving strong coupling between ferroelectricity and magnetism. In this work, robust control of magnetoelectric (ME) coupling in the BiFeO3/BaTiO3 (BFO/BTO) heterostructure (HS) was revealed by using the first-principles calculation. Switching of the ferroelectric polarization of BTO induce large ME effect with significant changes on the magnetic ordering and easy magnetization axis, making up for the weak ME coupling effect of single-phase multiferroic BFO. In addition, the Dzyaloshinskii-Moriya interaction (DMI) and the exchange coupling constants J for the BFO part of the HSs are simultaneously manipulated by the ferroelectric polarization, especially the DMI at the interface is significantly enhanced, which is three or four times larger than that of the individual BFO bulk. This work paves the way for designing new nanomagnetic devices based on the substantial interfacial ME effect.

Steering of the Skyrmion Hall Angle by Gate Voltages

Magnetic skyrmions can be driven by an applied spin-polarized electron current that exerts a spin-transfer torque on the localized spins constituting the skyrmion. However, the longitudinal dynamics is plagued by the skyrmion Hall effect, which causes the skyrmions to acquire a transverse velocity component. We show how to use spin-orbit interaction to control the skyrmion Hall angle and how the interplay of spin-transfer and spin-orbit torques can lead to a complete suppression of the transverse motion. Since the spin-orbit torques can be controlled all electronically by a gate voltage, the skyrmion motion can be steered all electronically on a broad racetrack at high speed and conceptually new writing and gating operations can be realized.

Controllable Thickness Inhomogeneity and Berry Curvature Engineering of Anomalous Hall Effect in SrRuO3 Ultrathin Films

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for understanding exotic topological properties. A prominent example is Hall anomalies observed in SrRuO₃ films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the evolution of AHE with controllable inhomogeneities in SrRuO₃ film thickness (t_SRO). By exploiting the step-flow growth of SrRuO₃ films, we induced a microscopically ordered stripe pattern with one-unit-cell differences in t_SRO. The associated spatial distribution of momentum-space Berry curvatures enables a two-channel AHE with hump-like Hall anomalies, which can be continuously engineered according to non-integer t_SRO. We further microscopically characterized the stripe-like ferromagnetic domains and two-step magnetic switching behavior in the inhomogeneous SrRuO₃ film. These unique features can be utilized to identify the two-channel AHE model and understand its microscopic origin.

Electronic Inhomogeneity Influence on the Anomalous Hall Resistivity Loops of SrRuO3 Epitaxially Interfaced with 5d Perovskites

SrRuO₃, a 4d ferromagnet with multiple Weyl nodes at the Fermi level, offers a rich playground to design epitaxial heterostructures and superlattices with fascinating magnetic and magnetotransport properties. Interfacing ultrathin SrRuO₃ layers with large spin-orbit coupling 5d transition-metal oxides, such as SrIrO₃, results in pronounced peaklike anomalies in the magnetic field dependence of the Hall resistivity. Such anomalies have been attributed either to the formation of Néel-type skyrmions or to modifications of the Berry curvature of the topologically nontrivial conduction bands near the Fermi level of SrRuO₃. Here, epitaxial multilayers based on SrRuO₃ interfaced with 5d perovskite oxides, such as SrIrO₃ and SrHfO₃, were studied. This work focuses on the magnetotransport properties of the multilayers, aiming to unravel the role played by the interfaces with 5d perovskites in the peaklike anomalies of the Hall resistance loops of SrRuO₃ layers. Interfacing with large band gap insulating SrHfO₃ layers did not influence the anomalous Hall resistance loops, while interfacing with the nominally paramagnetic semimetal SrIrO₃ resulted in pronounced peaklike anomalies, which have been lately attributed to a topological Hall effect contribution as a result of skyrmions. This interpretation is, however, under strong debate and lately alternative causes, such as inhomogeneity of the thickness and the electronic properties of the SrRuO₃ layers, have been considered. Aligned with these latter proposals, our findings reveal the central role played in the anomalies of the Hall resistivity loops by electronic inhomogeneity of SrRuO₃ layers due to the interfacing with semimetallic 5d⁵ SrIrO₃.

Polar coupling enabled nonlinear optical filtering at MoS2/ferroelectric heterointerfaces

Complex oxide heterointerfaces and van der Waals heterostructures present two versatile but intrinsically different platforms for exploring emergent quantum phenomena and designing new functionalities. The rich opportunity offered by the synergy between these two classes of materials, however, is yet to be charted. Here, we report an unconventional nonlinear optical filtering effect resulting from the interfacial polar alignment between monolayer MoS₂ and a neighboring ferroelectric oxide thin film. The second harmonic generation response at the heterointerface is either substantially enhanced or almost entirely quenched by an underlying ferroelectric domain wall depending on its chirality, and can be further tailored by the polar domains. Unlike the extensively studied coupling mechanisms driven by charge, spin, and lattice, the interfacial tailoring effect is solely mediated by the polar symmetry, as well explained via our density functional theory calculations, pointing to a new material strategy for the functional design of nanoscale reconfigurable optical applications.

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the reinterpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

Interfacial Control of Ferromagnetism in Ultrathin SrRuO3 Films Sandwiched between Ferroelectric BaTiO3 Layers

Interfaces between materials provide an intellectually rich arena for fundamental scientific discovery and device design. However, the frustration of magnetization and conductivity of perovskite oxide films under reduced dimensionality is detrimental to their device performance, preventing their active low-dimensional application. Herein, by inserting the ultrathin 4d ferromagnetic SrRuO₃ layer between ferroelectric BaTiO₃ layers to form a sandwich heterostructure, we observe enhanced physical properties in ultrathin SrRuO₃ films, including longitudinal conductivity, Curie temperature, and saturated magnetic moment. Especially, the saturated magnetization can be enhanced to ∼3.12 μ_B/Ru in ultrathin BaTiO₃/SrRuO₃/BaTiO₃ trilayers, which is beyond the theoretical limit of bulk value (2 μ_B/Ru). This observation is attributed to the synergistic ferroelectric proximity effect (SFPE) at upper and lower BaTiO₃/SrRuO₃ heterointerfaces, as revealed by the high-resolution lattice structure analysis. This SFPE in dual-ferroelectric interface cooperatively induces ferroelectric-like lattice distortions in RuO₆ oxygen octahedra and subsequent spin-state crossover in SrRuO₃, which in turn accounts for the observed enhanced magnetization. Besides the fundamental significance of interface-induced spin-lattice coupling, our findings also provide a viable route to the electrical control of magnetic ordering, taking a step toward low-power applications in all-oxide spintronics.

Atomic-Scale Metal-Insulator Transition in SrRuO3 Ultrathin Films Triggered by Surface Termination Conversion

The metal-insulator transition (MIT) in transition-metal-oxide is fertile ground for exploring intriguing physics and potential device applications. Here, an atomic-scale MIT triggered by surface termination conversion in SrRuO₃ ultrathin films is reported. Uniform and effective termination engineering at the SrRuO₃ (001) surface can be realized via a self-limiting water-leaching process. As the surface termination converts from SrO to RuO₂ , a highly insulating and nonferromagnetic phase emerges within the topmost SrRuO₃ monolayer. Such a spatially confined MIT is corroborated by systematic characterizations on electrical transport, magnetism, and scanning tunneling spectroscopy. Density functional theory calculations and X-ray linear dichroism further suggest that the surface termination conversion breaks the local octahedral symmetry of the crystal field. The resultant modulation in 4d orbital occupancy stabilizes a nonferromagnetic insulating surface state. This work introduces a new paradigm to stimulate and tune exotic functionalities of oxide heterostructures with atomic precision.

Site dilution and charge disorder effect on physical properties in SrRu1-x Ga x O3

Here, we report an evolution of structural, magnetic and transport behavior in doped SrRu_1-x Ga _x O₃ (x [Formula: see text] 0.2). The nonmagnetic dopant Ga³⁺ (3d ¹⁰) not only acts for magnetic site dilution in SrRuO₃ but also modifies the Ru charge state and electronic density. Our studies show that Ga³⁺ substitution does not affect the original orthorhombic- Pbnm structure of SrRuO₃ which is due to its matching ionic radii with Ru⁴⁺ . However, Ga³⁺ has a substantial effect on the magnetic behavior of SrRuO₃ where it decreases both magnetic moment as well as magnetic transition temperature [Formula: see text]. Further, this dilution induces Griffiths phase behavior across [Formula: see text] and cluster-glass behavior at low temperature with higher concentration of doping. The magnetic critical exponent [Formula: see text] increases with x due to this site dilution effect. The Ga³⁺ induces an insulating state in SrRuO₃ with x  >  0.05. The charge transport in paramagnetic as well as in insulating state of samples can be well described with Mott's modified variable-range-hopping model. The metallic charge transport just below [Formula: see text] in SrRuO₃ obeys Fermi liquid behavior which breaks down at low temperature. We further find a correlation between field dependent magnetoresistance and magnetization through power-law behavior over the series.

Reversible manipulation of the magnetic state in SrRuO3 through electric-field controlled proton evolution

Ionic substitution forms an essential pathway to manipulate the structural phase, carrier density and crystalline symmetry of materials via ion-electron-lattice coupling, leading to a rich spectrum of electronic states in strongly correlated systems. Using the ferromagnetic metal SrRuO3 as a model system, we demonstrate an efficient and reversible control of both structural and electronic phase transformations through the electric-field controlled proton evolution with ionic liquid gating. The insertion of protons results in a large structural expansion and increased carrier density, leading to an exotic ferromagnetic to paramagnetic phase transition. Importantly, we reveal a novel protonated compound of HSrRuO3 with paramagnetic metallic as ground state. We observe a topological Hall effect at the boundary of the phase transition due to the proton concentration gradient across the film-depth. We envision that electric-field controlled protonation opens up a pathway to explore novel electronic states and material functionalities in protonated material systems.

Robustness of the electronic structure and charge transfer in topological insulator Bi2Te2Se and Bi2Se2Te thin films under an external electric field

The electronic structure and charge transfer of Bi₂Te₂Se and Bi₂Se₂Te thin films are robust to an external electrical field.

Moisture-Responsive Graphene Actuators Prepared by Two-Beam Laser Interference of Graphene Oxide Paper

Here, we reported an ingenious fabrication of moisture responsive graphene-based actuator via unilateral two-beam laser interference (TBLI) treatment of graphene oxide (GO) papers. TBLI technique has been recognized as a representative photoreduction and patterning strategy for hierarchical structuring of GO. The GO paper can be reduced and cut into grating-like periodic reduced graphene oxide (RGO) microstructures due to laser ablation effect. However, the lower light transmittance of the thick GO paper and the corresponding thermal relaxation phenomenon make it impossible to trigger complete reduction, leading to the formation of the anisotropic GO/reduced GO (RGO) bilayer structure. Interestingly, the RGO side that feature lower OCGs and higher roughness shows strong water adsorption due to the formation of micronanostructures. Due to the different water adsorption capacities of the two sides, a flower moisture-responsive actuator has been fabricated, which exhibits “opening” and “closing” behavior under different humidity conditions.

Interface-driven chiral magnetism and current-driven domain walls in insulating magnetic garnets

Magnetic oxides exhibit rich fundamental physics^1-4 and technologically desirable properties for spin-based memory, logic and signal transmission^5-7. Recently, spin-orbit-induced spin transport phenomena have been realized in insulating magnetic oxides by using proximate heavy metal layers such as platinum^8-10. In their metallic ferromagnet counterparts, such interfaces also give rise to a Dzyaloshinskii-Moriya interaction^11-13 that can stabilize homochiral domain walls and skyrmions with efficient current-driven dynamics. However, chiral magnetism in centrosymmetric oxides has not yet been observed. Here we discover chiral magnetism that allows for pure spin-current-driven domain wall motion in the most ubiquitous class of magnetic oxides, ferrimagnetic iron garnets. We show that epitaxial rare-earth iron garnet films with perpendicular magnetic anisotropy exhibit homochiral Néel domain walls that can be propelled faster than 800 m s^-1 by spin current from an adjacent platinum layer. We find that, despite the relatively small interfacial Dzyaloshinskii-Moriya interaction, very high velocities can be attained due to the antiferromagnetic spin dynamics associated with ferrimagnetic order.

Observation of Nanoscale Skyrmions in SrIrO3/SrRuO3 Bilayers

Skyrmion imaging and electrical detection via topological Hall (TH) effect are two primary techniques for probing magnetic skyrmions, which hold promise for next-generation magnetic storage. However, these two kinds of complementary techniques have rarely been employed to investigate the same samples. We report the observation of nanoscale skyrmions in SrIrO₃/SrRuO₃ (SIO/SRO) bilayers in a wide temperature range from 10 to 100 K. The SIO/SRO bilayers exhibit a remarkable TH effect, which is up to 200% larger than the anomalous Hall (AH) effect at 5 K, and zero-field TH effect at 90 K. Using variable-temperature, high-field magnetic force microscopy (MFM), we imaged skyrmions as small as 10 nm, which emerge in the same field ranges as the TH effect. These results reveal a rich space for skyrmion exploration and tunability in oxide heterostructures.

Emergence of Topological Hall Effect in a SrRuO3 Single Layer

Topological Hall effect (THE), appearing as bumps and/or dips in the Hall resistance curves, is considered as a hallmark of the skyrmion spin texture originated from the inversion symmetry breaking and spin-orbit interaction. Recently, Néel-type skyrmion is proposed based on the observed THE in 5d transition metal oxides heterostructures such as SrRuO₃ /SrIrO₃ bilayers, where the interfacial Dzyaloshinskii-Moriya interaction (DMI), due to the strong spin-orbit coupling (SOC) in SrIrO₃ and the broken inversion symmetry at the interface, is believed to play a significant role. Here the emergence of THE in SrRuO₃ single layers with thickness ranging from 3 to 6 nm is experimentally demonstrated. It is found that the oxygen octahedron rotation in SrRuO₃ also has a significant effect on the observed THE. Furthermore, the THE may be continuously tuned by an applied electrical field. It is proposed that the large SOC of Ru ions together with the broken inversion symmetry, mainly from the interface, produce the DMI that is responsible for the observed THE. The emergence of the gate-tunable DMI in SrRuO₃ single layer may stimulate further investigations of new spin-orbit physics in strong SOC oxides.

Ferroelectrically tunable magnetic skyrmions in ultrathin oxide heterostructures

Magnetic skyrmions are topologically protected whirling spin texture. Their nanoscale dimensions, topologically protected stability and solitonic nature, together are promising for future spintronics applications. To translate these compelling features into practical spintronic devices, a key challenge lies in achieving effective control of skyrmion properties, such as size, density and thermodynamic stability. Here, we report the discovery of ferroelectrically tunable skyrmions in ultrathin BaTiO₃/SrRuO₃ bilayer heterostructures. The ferroelectric proximity effect at the BaTiO₃/SrRuO₃ heterointerface triggers a sizeable Dzyaloshinskii-Moriya interaction, thus stabilizing robust skyrmions with diameters less than a hundred nanometres. Moreover, by manipulating the ferroelectric polarization of the BaTiO₃ layer, we achieve local, switchable and nonvolatile control of both skyrmion density and thermodynamic stability. This ferroelectrically tunable skyrmion system can simultaneously enhance the integratability and addressability of skyrmion-based functional devices.

Strongly correlated oxides for energy harvesting

We review recent advances in strongly correlated oxides as thermoelectric materials in pursuit of energy harvesting. We discuss two topics: one is the enhancement of the ordinary thermoelectric properties by controlling orbital degrees of freedom and orbital fluctuation not only in bulk but also at the interface of correlated oxides. The other topic is the use of new phenomena driven by spin-orbit coupling (SOC) of materials. In 5d electron oxides, we show some SOC-related transport phenomena, which potentially contribute to energy harvesting. We outline the current status and a future perspective of oxides as thermoelectric materials.

Asymmetric and Symmetric Exchange in a Generalized 2D Rashba Ferromagnet

Dzyaloshinskii-Moriya interaction (DMI) is investigated in a 2D ferromagnet (FM) with spin-orbit interaction of Rashba type at finite temperatures. The FM is described in the continuum limit by an effective s-d model with arbitrary dependence of spin-orbit coupling (SOC) and kinetic energy of itinerant electrons on the absolute value of momentum. In the limit of weak SOC, we derive a general expression for the DMI constant D from a microscopic analysis of the electronic grand potential. We compare D with the exchange stiffness A and show that, to the leading order in small SOC strength α_{R}, the conventional relation D=(4mα_{R}/ℏ)A, in general, does not hold beyond the Bychkov-Rashba model. Moreover, in this model, both A and D vanish at zero temperature in the metal regime (i.e., when two spin sub-bands are partly occupied). For nonparabolic bands or nonlinear Rashba coupling, these coefficients are finite and acquire a nontrivial dependence on the chemical potential that demonstrates the possibility to control the size and chirality of magnetic textures by adjusting a gate voltage.