Proximity induced high-temperature magnetic order in topological insulator--ferrimagnetic insulator heterostructure

Topological Quantum Well States in Pb/Sb Thin-Film Heterostructures

Composite topological heterostructures, wherein topologically protected states are electronically tuned due to their proximity to other matter, are key avenues for exploring emergent physical phenomena. Particularly, pairing a topological material with a superconductor such as Pb is a promising means for generating a topological superconducting phase with exotic Majorana quasiparticles, but oft-neglected is the emergence of bulklike spin-polarized states that are quite relevant to applications. Using high-resolution photoemission spectroscopy and first-principles calculations, we report the emergence of bulk-like spin-polarized topological quantum well states with long coherence lengths in Pb films grown on the topological semimetal Sb. The results establish Pb/Sb heterostructures as topological superconductor candidates and advance the current understanding of topological coupling effects required for realizing emergent physics and for designing advanced spintronic device architectures.

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films

The anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator. However, the origin of its intriguing AHE behaviors remains elusive. Here, we demonstrate the Berry curvature-dominated intrinsic AHE in wafer-scale MnBi2Te4 films. By applying back-gate voltages, we observe an ambipolar conduction and n-p transition in ∼7-layer MnBi2Te4, where a quadratic relation between the AHE resistance and longitudinal resistance suggests its intrinsic AHE nature. In particular, for ∼3-layer MnBi2Te4, the AHE sign can be tuned from pristine negative to positive. First-principles calculations unveil that such an AHE reversal originated from the competing Berry curvature between oppositely polarized spin-minority-dominated surface states and spin-majority-dominated inner bands. Our results shed light on the underlying physical mechanism of the intrinsic AHE and provide new perspectives for the unconventional sign-tunable AHE.

Proximity induced band gap opening in topological-magnetic heterostructure (Ni80Fe20/p-TlBiSe2/p-Si) under ambient condition

The broken time reversal symmetry states may result in the opening of a band gap in TlBiSe2 leading to several interesting phenomena which are potentially relevant for spintronic applications. In this work, the quantum interference and magnetic proximity effects have been studied in Ni80Fe20/p-TlBiSe2/p-Si (Magnetic/TI) heterostructure using physical vapor deposition technique. Raman analysis shows the symmetry breaking with the appearance of A21u mode. The electrical characteristics are investigated under dark and illumination conditions in the absence as well as in the presence of a magnetic field. The outcomes of the examined device reveal excellent photo response in both forward and reverse bias regions. Interestingly, under a magnetic field, the device shows a reduction in electrical conductivity at ambient conditions due to the crossover of weak localization and separation of weak antilocalization, which are experimentally confirmed by magnetoresistance measurement. Further, the photo response has also been assessed by the transient absorption spectroscopy through analysis of charge transfer and carrier relaxation mechanisms. Our results can be beneficial for quantum computation and further study of topological insulator/ferromagnet heterostructure and topological material based spintronic devices due to high spin orbit coupling along with dissipationless conduction channels at the surface states.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Spin transfer torques due to the bulk states of topological insulators

Spin torques at topological insulator (TI)/ferromagnet interfaces have received considerable attention in recent years with a view towards achieving full electrical manipulation of magnetic degrees of freedom. The most important question in this field concerns the relative contributions of bulk and surface states to the spin torque, a matter that remains incompletely understood. Whereas the surface state contribution has been extensively studied, the contribution due to the bulk states has received comparatively little attention. Here we study spin torques due to TI bulk states and show that: (i) there is no spin-orbit torque due to the bulk states on a homogeneous magnetisation, in contrast to the surface states, which give rise to a spin-orbit torque via the well-known Edelstein effect. (ii) The bulk states give rise to a spin transfer torque (STT) due to the inhomogeneity of the magnetisation in the vicinity of the interface. This spin transfer torque, which has not been considered in TIs in the past, is somewhat unconventional since it arises from the interplay of the bulk TI spin-orbit coupling and the gradient of the monotonically decaying magnetisation inside the TI. Whereas we consider an idealised model in which the magnetisation gradient is small and the spin transfer torque is correspondingly small, we argue that in real samples the spin transfer torque should be sizable and may provide the dominant contribution due to the bulk states. We show that an experimental smoking gun for identifying the bulk states is the fact that the field-like component of the spin transfer torque generates a spin density with the same size but opposite sign for in-plane and out-of-plane magnetisations. This distinguishes them from the surface states, which are expected to give a spin density of a similar size and the same sign for both an in-plane and out-of-plane magnetisations.

Intrinsic Magnetic (EuIn)As Nanowire Shells with a Unique Crystal Structure

In the pursuit of magneto-electronic systems nonstoichiometric magnetic elements commonly introduce disorder and enhance magnetic scattering. We demonstrate the growth of (EuIn)As shells, with a unique crystal structure comprised of a dense net of Eu inversion planes, over InAs and InAs_1-xSb_x core nanowires. This is imaged with atomic and elemental resolution which reveal a prismatic configuration of the Eu planes. The results are supported by molecular dynamics simulations. Local magnetic and susceptibility mappings show magnetic response in all nanowires, while a subset bearing a DC signal points to ferromagnetic order. These provide a mechanism for enhancing Zeeman responses, operational at zero applied magnetic field. Such properties suggest that the obtained structures can serve as a preferred platform for time-reversal symmetry broken one-dimensional states including intrinsic topological superconductivity.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

Two-dimensional antiferromagnetic nodal-line semimetal and quantum anomalous Hall state in the van der Waals heterostructure germanene/Mn2S2

Materials with interactions between the topology and magnetism are triggering increasing interest. We constructed a two-dimensional (2D) van der Waals heterostructure germanene/Mn₂S₂, where the germanene is a quantum spin Hall insulator and Mn₂S₂provides antiferromagnetic (AFM) interactions. In this structure, a 2D AFM nodal-line semimetal (NLSM) phase is expected without the spin-orbit coupling (SOC), which is of a high density of states around the Fermi level. The band touching rings originate from the intersection between different spin components ofporbitals of germanene. This result provides a possible 2D realization of NLSMs, which are usually realized in three-dimensional systems. When the SOC is present, a quantum anomalous Hall (QAH) state emerges with the annihilation of the band-touching rings. The nontrivial topology is determined by calculating the Chern number and Wannier charge centers. This provides an alternative platform to realize QAH states. These results could also provide the possibility of further understanding the topological states in NLSM and electronic applications.

Gate-Tunable Anomalous Hall Effect in Stacked van der Waals Ferromagnetic Insulator-Topological Insulator Heterostructures

The search of novel topological states, such as the quantum anomalous Hall insulator and chiral Majorana fermions, has motivated different schemes to introduce magnetism into topological insulators. A promising scheme is using the magnetic proximity effect (MPE), where a ferromagnetic insulator magnetizes the topological insulator. Most of these heterostructures are synthesized by growth techniques which prevent mixing many of the available ferromagnetic and topological insulators due to difference in growth conditions. Here, we demonstrate that MPE can be obtained in heterostructures stacked via the dry transfer of flakes of van der Waals ferromagnetic and topological insulators (Cr₂Ge₂Te₆/BiSbTeSe₂), as evidenced in the observation of an anomalous Hall effect (AHE). Furthermore, devices made from these heterostructures allow modulation of the AHE when controlling the carrier density via electrostatic gating. These results show that simple mechanical transfer of magnetic van der Waals materials provides another possible avenue to magnetize topological insulators by MPE.

Gate-Tunable Anomalous Hall Effect in a 3D Topological Insulator/2D Magnet van der Waals Heterostructure

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a three-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe₂ and the magnet Cr₂Ge₂Te₆, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet.

Anomalous transverse resistance in the topological superconductor β-Bi2Pd

A supercurrent flowing in a superconductor meets no resistance. Yet an electric field may still be established within the superconductor in the presence of dissipative processes, such as vortex motion. Here we report the observation of a transverse voltage drop in superconducting β-Bi2Pd thin films. Unlike the Hall effect in general or in other superconductors, the sign of the observed transverse voltage does not depend on the external magnetic field. Instead, it is dictated by the broken inversion symmetry on the film interfaces. This anomalous transverse voltage, or transverse resistance, is indicative of a chirality that likely resonates with the topological surface states reported in β-Bi2Pd.

Ultrafast optical control of surface and bulk magnetism in magnetic topological insulator/antiferromagnet heterostructure

Optical control of the magnetic properties in topological insulator systems is an important step in applying these materials in ultrafast optoelectronic and spintronic schemes. In this work, we report the experimental observation of photo-induced magnetization dynamics in the magnetically doped topological insulator (MTI)/antiferromagnet (AFM) heterostructure composed of Cr-(Bi,Sb)₂Te₃/CrSb. Through proximity coupling to the AFM layer, the MTI displays a dramatically enhanced magnetism, with robust perpendicular magnetic anisotropy. When subjected to intense laser irradiation, both surface and bulk magnetism of the MTI are weakened by laser-induced heating of the lattice, however, at the surface, the deleterious heat effect is compensated by the strengthening of Dirac-hole-mediated exchange coupling as demonstrated by an unconventional pump-fluence-dependent exchange-bias effect. Through theoretical analyses, the sizes of exchange coupling energies are estimated in the MTI/AFM bilayer structure. The fundamentally different mechanisms supporting the surface and bulk magnetic order in MTIs allow a novel and distinctive photo-induced transient magnetic state with antiparallel spin configuration, which broadens the understanding of the magnetization dynamics of MTIs under ultrashort and intense optical excitation.

Proximity-Induced Magnetism in a Topological Insulator/Half-Metallic Ferromagnetic Thin Film Heterostructure

Topological insulator (TI) Bi2Se3 thin films were prepared on half-metallic ferromagnetic La0.7Sr0.3MnO3 thin film by magnetron sputtering, forming a TI/FM heterostructure. The conductivity of Bi2Se3was modified by La0.7Sr0.3MnO3 at high- and low-temperature regions via different mechanisms, which could be explained by the short-range interactions and long-range interaction between ferromagnetic insulator and Bi2Se3 due to the proximity effect. Magnetic and transport measurements prove that the ferromagnetic phase and extra magnetic moment are induced in Bi2Se3 films. The weak anti-localized (WAL) effect was suppressed in Bi2Se3 films, accounting for the magnetism of La0.7Sr0.3MnO3 layers. This work clarifies the special behavior in Bi2Se3/La0.7Sr0.3MnO3 heterojunctions, which provides an effective way to study the magnetic proximity effect of the ferromagnetic phase in topological insulators.

Understanding Signatures of Emergent Magnetism in Topological Insulator/Ferrite Bilayers

Magnetic insulator-topological insulator heterostructures have been studied in search of chiral edge states via proximity induced magnetism in the topological insulator, but these states have been elusive. We identified MgAl_{0.5}Fe_{1.5}O_{4}/Bi_{2}Se_{3} bilayers for a possible magnetic proximity effect. Electrical transport and polarized neutron reflectometry suggest a proximity effect, but structural data indicate a disordered interface as the origin of the magnetic response. Our results provide a strategy via correlation of microstructure with magnetic data to confirm a magnetic proximity effect.

Progress and prospects in magnetic topological materials

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications, from information storage and control to dissipationless spin and charge transport. Here we review the theoretical and experimental progress achieved in the field of magnetic topological materials, beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline recent theoretical progress that has resulted in the tabulation of, for the first time, all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter, and we survey future perspectives.

Enormous Berry-Curvature-Based Anomalous Hall Effect in Topological Insulator (Bi,Sb)2Te3 on Ferrimagnetic Europium Iron Garnet beyond 400 K

To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, the approach of magnetic proximity effect (MPE) was adopted to break the time-reversal symmetry in the topological insulator (Bi_0.3Sb_0.7)₂Te₃ (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate large anomalous Hall resistance (R_AHE) exceeding 8 Ω (ρ_AHE of 3.2 μΩ·cm) at 300 K and sustaining to 400 K in 35 BST/EuIG samples, surpassing the past record of 0.28 Ω (ρ_AHE of 0.14 μΩ·cm) at 300 K. The large R_AHE is attributed to an atomically abrupt, Fe-rich interface between BST and EuIG. Importantly, the gate dependence of the AHE loops shows no sign change with varying chemical potential. This observation is supported by our first-principles calculations via applying a gradient Zeeman field plus a contact potential on BST. Our calculations further demonstrate that the AHE in this heterostructure is attributed to the intrinsic Berry curvature. Furthermore, for gate-biased 4 nm BST on EuIG, a pronounced topological Hall effect-like (THE-like) feature coexisting with AHE is observed at the negative top-gate voltage up to 15 K. Interface tuning with theoretical calculations has realized topologically distinct phenomena in tailored magnetic TI-based heterostructures.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Quantum anomalous Hall effect in Cr2Ge2Te6/Bi2Se3/Cr2Ge2Te6heterostructures

Currently, quantum anomalous Hall (QAH) effect can only be observed at very low temperatures, which severely hinders its utilization from spintronics to quantum computation. Finding or predicting new systems supporting QAH effect at high temperatures remains essential and challenging. This work presents first-principles studies on the proximity effect between Bi₂Se₃slabs and Cr₂Ge₂Te₆(CGT) layers, reporting that Chern insulators are available in CGT/Bi₂Se₃/CGT heterostructures. If the sandwiched Bi₂Se₃slab is 4 quintuple layers (QLs) or thicker, the Chern insulating state is robust against the interfacial stacking manner. If the Bi₂Se₃slab is only 2 or 3 QLs, the CrBi- and CrH-aligned heterostructures are also Chern insulators, while the CrSe-aligned ones are trivial. The Chern insulators support the Hall conductivityσ_xy=e²/hand have energy gaps ranging from 3 to 20 meV, implying QAH effect at higher temperatures. An effective model Hamiltonian is introduced to understand the topological phase of the heterostructures.

Epitaxial growth of Bi(110) and Bi2Se3thin films on a ferromagnetic insulator substrate of Cr2Ge2Te6

When a topological insulator (TI) is brought to the proximity of a ferromagnetic insulator (FMI), the breaking of the time-reversal symmetry may give rise to quantum anomalous Hall effect (QAHE). The physical properties of such TI-FMI systems are greatly affected by the interfacial structures of the components. Here, we report the growth and structural properties of Bi(110) and Bi₂Se₃thin films on a FMI of Cr₂Ge₂Te₆(CGT) substrate by scanning tunneling microscopy. We observed various defects and impurities on the CGT surfaces, which serve as the preferential sites for initial nucleation and epitaxial growth of Bi(110) thin films. The exposure of the as-grown Bi(110) thin films to Se vapor leads to the formation of polycrystalline Bi₂Se₃thin films with randomly distributed holes. The structure and composition of the as-prepared Bi₂Se₃thin films were further confirmed by Raman spectroscopy and x-ray photoelectron spectroscopy. Our work shows that the quality of the CGT crystals is vital for the growth of high-quality TIs on CGT substrates for QAHE.

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.

Spacer-Layer-Tunable Magnetism and High-Field Topological Hall Effect in Topological Insulator Heterostructures

Controlling magnetic order in magnetic topological insulators (MTIs) is a key to developing spintronic applications with MTIs and is commonly achieved by changing the magnetic doping concentration, which inevitably affects the spin-orbit coupling strength and the topological properties. Here, we demonstrate tunable magnetic properties in topological heterostructures over a wide range, from a ferromagnetic phase with a Curie temperature of around 100 K all the way to a paramagnetic phase, while keeping the overall chemical composition the same, by controlling the thickness of nonmagnetic spacer layers between two atomically thin magnetic layers. This work showcases that spacer-layer control is a powerful tool to manipulate magneto-topological functionalities in MTI heterostructures. Furthermore, the interaction between the MTI and the Cr₂O₃ buffer layers also leads to a robust topological Hall effect surviving up to a record-high 6 T of magnetic field, shedding light on the critical role of interfacial layers in thin-film topological materials.

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This Letter reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2-3 K and an AHE at T = 80-300 K. Over T = 3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii-Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

Termination switching of antiferromagnetic proximity effect in topological insulator

This work reports the ferromagnetism of topological insulator, (Bi,Sb)2Te3 (BST), with a Curie temperature of approximately 120 K induced by magnetic proximity effect (MPE) of an antiferromagnetic CrSe. The MPE was shown to be highly dependent on the stacking order of the heterostructure, as well as the interface symmetry: Growing CrSe on top of BST results in induced ferromagnetism, while growing BST on CrSe yielded no evidence of an MPE. Cr-termination in the former case leads to double-exchange interactions between Cr3+ surface states and Cr2+ bulk states. This Cr3+-Cr2+ exchange stabilizes the ferromagnetic order localized at the interface and magnetically polarizes the BST Sb band. In contrast, Se-termination at the CrSe/BST interface yields no detectable MPE. These results directly confirm the MPE in BST films and provide critical insights into the sensitivity of the surface state.

Exchange Bias in Magnetic Topological Insulator Superlattices

Magnetic doping and proximity coupling can open a band gap in a topological insulator (TI) and give rise to dissipationless quantum conduction phenomena. Here, by combining these two approaches, we demonstrate a novel TI superlattice structure that is alternately doped with transition and rare earth elements. An unexpected exchange bias effect is unambiguously confirmed in the superlattice with a large exchange bias field using magneto-transport and magneto-optical techniques. Further, the Curie temperature of the Cr-doped layers in the superlattice is found to increase by 60 K compared to a Cr-doped single-layer film. This result is supported by density-functional-theory calculations, which indicate the presence of antiferromagnetic ordering in Dy:Bi2Te3 induced by proximity coupling to Cr:Sb2Te3 at the interface. This work provides a new pathway to realizing the quantum anomalous Hall effect at elevated temperatures and axion insulator state at zero magnetic field by interface engineering in TI heterostructures.

High-Temperature Anomalous Hall Effect in a Transition Metal Dichalcogenide Ferromagnetic Insulator Heterostructure

Integration of transition metal dichalcogenides (TMDs) on ferromagnetic materials (FM) may yield fascinating physics and promise for electronics and spintronic applications. In this work, high-temperature anomalous Hall effect (AHE) in the TMD ZrTe₂ thin film using a heterostructure approach by depositing it on a ferrimagnetic insulator YIG (Y₃Fe₅O₁₂, yttrium iron garnet) is demonstrated. In this heterostructure, significant anomalous Hall effect can be observed at temperatures up to at least 400 K, which is a record high temperature for the observation of AHE in TMDs, and the large R_AHE is more than 1 order of magnitude larger than those previously reported values in topological insulators or TMD-based heterostructures. A complicated interface with additional ZrO₂ and amorphous YIG layers is actually observed between ZrTe₂ and YIG. The magnetization of interfacial reaction-induced ZrO₂ and YIG is believed to play a crucial role in the induced high-temperature AHE in the ZrTe₂. These results present a promising system for the spintronic device applications, and it may shed light on the designing approach to introduce magnetism to TMDs at room temperature.

Two-dimensional ferromagnetic superlattices

Mechanically exfoliated two-dimensional ferromagnetic materials (2D FMs) possess long-range ferromagnetic order and topologically nontrivial skyrmions in few layers. However, because of the dimensionality effect, such few-layer systems usually exhibit much lower Curie temperature (T C) compared to their bulk counterparts. It is therefore of great interest to explore effective approaches to enhance their T C, particularly in wafer-scale for practical applications. Here, we report an interfacial proximity-induced high-T C 2D FM Fe3GeTe2 (FGT) via A-type antiferromagnetic material CrSb (CS) which strongly couples to FGT. A superlattice structure of (FGT/CS)n, where n stands for the period of FGT/CS heterostructure, has been successfully produced with sharp interfaces by molecular-beam epitaxy on 2-inch wafers. By performing elemental specific X-ray magnetic circular dichroism (XMCD) measurements, we have unequivocally discovered that T C of 4-layer Fe3GeTe2 can be significantly enhanced from 140 K to 230 K because of the interfacial ferromagnetic coupling. Meanwhile, an inverse proximity effect occurs in the FGT/CS interface, driving the interfacial antiferromagnetic CrSb into a ferrimagnetic state as evidenced by double-switching behavior in hysteresis loops and the XMCD spectra. Density functional theory calculations show that the Fe-Te/Cr-Sb interface is strongly FM coupled and doping of the spin-polarized electrons by the interfacial Cr layer gives rise to the T C enhancement of the Fe3GeTe2 films, in accordance with our XMCD measurements. Strikingly, by introducing rich Fe in a 4-layer FGT/CS superlattice, T C can be further enhanced to near room temperature. Our results provide a feasible approach for enhancing the magnetic order of few-layer 2D FMs in wafer-scale and render opportunities for realizing realistic ultra-thin spintronic devices.

Tailoring the Hybrid Anomalous Hall Response in Engineered Magnetic Topological Insulator Heterostructures

Engineering the anomalous Hall effect (AHE) is the key to manipulate the magnetic orders in the emerging magnetic topological insulators (MTIs). In this letter, we synthesize the epitaxial Bi₂Te₃/MnTe magnetic heterostructures and observe pronounced AHE signals from both layers combined together. The evolution of the resulting hybrid AHE intensity with the top Bi₂Te₃ layer thickness manifests the presence of an intrinsic ferromagnetic phase induced by the topological surface states at the heterolayer interface. More importantly, by doping the Bi₂Te₃ layer with Sb, we are able to manipulate the sign of the Berry phase-associated AHE component. Our results demonstrate the unparalleled advantages of MTI heterostructures over magnetically doped TI counterparts in which the tunability of the AHE response can be greatly enhanced. This in turn unveils a new avenue for MTI heterostructure-based multifunctional applications.

Ferromagnetic resonance studies of strain tuned Bi:YIG films

Bismuth-doped Yttrium iron garnet (Bi:YIG) thin films known for large magneto-optical activity with low losses still need to get probed for its magnetization dynamics. We demonstrate a controlled tuning of magnetocrystalline anisotropy in Bi-doped Y₃Fe₅O₁₂ (Bi:YIG) films of high crystalline quality using growth induced epitaxial strain on [1 1 1]-oriented Gd₃Ga₅O₁₂ (GGG) substrate. We optimize a growth protocol to get thick highly-strained epitaxial films showing large magneto-crystalline anisotropy, compare to thin films prepared using a different protocol. Ferromagnetic resonance measurements establish a linear dependence of the out-of-plane uniaxial anisotropy on the strain induced rhombohedral distortion of Bi:YIG lattice. Interestingly, the enhancement in the magnetoelastic constant due to an optimum substitution of Bi³⁺ ions with strong spin orbit coupling does not strongly affect the precessional damping (∼[Formula: see text]). Large magneto-optical activity, reasonably low damping, large magnetocrystalline anisotropy and large magnetoelastic coupling in Bi:YIG are the properties that may help Bi:YIG emerge as a possible material for photo-magnonics and other spintronics applications.

Tuning the magnetotransport behavior of topological insulator with a transition-metal oxide layer

The interaction between topological insulator (TI) and its adjacent magnetic layer serves as a basis for exploring the device application of TI. Here we investigate the modulation of the magnetotransport behavior of Bi₂Te₃ TI with a transition-metal oxide layer NiO. It is found that the weak-antilocalization effect is absent at low magnetic fields and the magnetoresistance ratio decreases monotonically with increasing the NiO growth temperature from 300 to 473 K, indicating the suppression of the topological surface states of Bi₂Te₃. Such behaviors are attributed to the decomposition of NiO and the concomitant formation of magnetic impurities at the Bi₂Te₃/NiO interface. Differently, the weak-antilocalization shows no significant weakening with the growth of Cr₂O₃ top layer, due to its better chemical stability. Our observation would be significant for the material selection for the device integration of TI.

Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes

Magnetic topological insulators (MTIs) offer a combination of topologically nontrivial characteristics and magnetic order and show promise in terms of potentially interesting physical phenomena such as the quantum anomalous Hall (QAH) effect and topological axion insulating states. However, the understanding of their properties and potential applications have been limited due to a lack of suitable candidates for MTIs. Here, we grow two-dimensional single crystals of Mn(SbxBi(1-x))2Te4 bulk and exfoliate them into thin flakes in order to search for intrinsic MTIs. We perform angle-resolved photoemission spectroscopy, low-temperature transport measurements, and first-principles calculations to investigate the band structure, transport properties, and magnetism of this family of materials, as well as the evolution of their topological properties. We find that there exists an optimized MTI zone in the Mn(SbxBi(1-x))2Te4 phase diagram, which could possibly host a high-temperature QAH phase, offering a promising avenue for new device applications.

Magnetization switching using topological surface states

Topological surface states (TSSs) in a topological insulator are expected to be able to produce a spin-orbit torque that can switch a neighboring ferromagnet. This effect may be absent if the ferromagnet is conductive because it can completely suppress the TSSs, but it should be present if the ferromagnet is insulating. This study reports TSS-induced switching in a bilayer consisting of a topological insulator Bi₂Se₃ and an insulating ferromagnet BaFe₁₂O₁₉. A charge current in Bi₂Se₃ can switch the magnetization in BaFe₁₂O₁₉ up and down. When the magnetization is switched by a field, a current in Bi₂Se₃ can reduce the switching field by ~4000 Oe. The switching efficiency at 3 K is 300 times higher than at room temperature; it is ~30 times higher than in Pt/BaFe₁₂O₁₉. These strong effects originate from the presence of more pronounced TSSs at low temperatures due to enhanced surface conductivity and reduced bulk conductivity.

Record High-Proximity-Induced Anomalous Hall Effect in (BixSb1-x)2Te3 Thin Film Grown on CrGeTe3 Substrate

Quantum anomalous Hall effect (QAHE) can only be realized at extremely low temperatures in magnetically doped topological insulators (TIs) due to limitations inherent with the doping process. In an effort to boost the quantization temperature of QAHE, the magnetic proximity effect in magnetic insulator/TI heterostructures has been extensively investigated. However, the observed anomalous Hall resistance has never been more than several ohms, presumably owing to the interfacial disorders caused by the structural and chemical mismatch. Here, we show that, by growing (Bi_xSb_1-x)₂Te₃ (BST) thin films on structurally and chemically well-matched, ferromagnetic-insulating CrGeTe₃ (CGT) substrates, the proximity-induced anomalous Hall resistance can be enhanced by more than an order of magnitude. This sheds light on the importance of structural and chemical matches for magnetic insulator/TI proximity systems.

Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of the ferromagnetic insulator Cr_{2}Ge_{2}Te_{6} and topological insulator (Bi,Sb)_{2}Te_{3}. Despite small magnetization in the (Bi,Sb)_{2}Te_{3} layer, the anomalous Hall conductivity reaches a large value of 0.2e^{2}/h in accord with a ferromagnetic response of the Cr_{2}Ge_{2}Te_{6}. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr_{2}Ge_{2}Te_{6} layer is effective and strong enough to open the sizable exchange gap in the surface state.

Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator

Inducing magnetic orders in a topological insulator (TI) to break its time reversal symmetry has been predicted to reveal many exotic topological quantum phenomena. The manipulation of magnetic orders in a TI layer can play a key role in harnessing these quantum phenomena toward technological applications. Here we fabricated a thin magnetic TI film on an antiferromagnetic (AFM) insulator Cr₂O₃ layer and found that the magnetic moments of the magnetic TI layer and the surface spins of the Cr₂O₃ layers favor interfacial AFM coupling. Field cooling studies show a crossover from negative to positive exchange bias clarifying the competition between the interfacial AFM coupling energy and the Zeeman energy in the AFM insulator layer. The interfacial exchange coupling also enhances the Curie temperature of the magnetic TI layer. The unique interfacial AFM alignment in magnetic TI on AFM insulator heterostructures opens a new route toward manipulating the interplay between topological states and magnetic orders in spin-engineered heterostructures, facilitating the exploration of proof-of-concept TI-based spintronic and electronic devices with multifunctionality and low power consumption.

Axion Insulator State in a Ferromagnet/Topological Insulator/Antiferromagnet Heterostructure

We propose the use of ferromagnetic insulator MnBi₂Se₄/Bi₂Se₃/antiferromagnetic insulator Mn₂Bi₂Se₅ heterostructures for the realization of the axion insulator state. Importantly, the axion insulator state in such heterostructures only depends on the magnetization of the ferromagnetic insulator and, hence, can be observed in a wide range of external magnetic fields. Using density functional calculations and model Hamiltonian simulations, we find that the top and bottom surfaces have opposite half-quantum Hall conductances, [Formula: see text] and [Formula: see text], with a sizable global spin gap of 5.1 meV opened for the topological surface states of Bi₂Se₃. Our work provides a new strategy for the search of axion insulators by using van der Waals antiferromagnetic insulators along with three-dimensional topological insulators.

New Universal Type of Interface in the Magnetic Insulator/Topological Insulator Heterostructures

Magnetic proximity effect at the interface between magnetic and topological insulators (MIs and TIs) is considered to have great potential in spintronics as, in principle, it allows realizing the quantum anomalous Hall and topological magneto-electric effects (QAHE and TME). Although an out-of-plane magnetization induced in a TI by the proximity effect was successfully probed in experiments, first-principles calculations reveal that a strong electrostatic potential mismatch at abrupt MI/TI interfaces creates harmful trivial states rendering both the QAHE and TME unfeasible in practice. Here on the basis of recent progress in formation of planar self-assembled single layer MI/TI heterostructure (T. Hirahara et al. Nano Lett. 2017 , 17 , 3493 - 3500 ), we propose a conceptually new type of the MI/TI interfaces by means of density functional theory calculations. By considering MnSe/Bi₂Se₃, MnTe/Bi₂Te₃, and EuS/Bi₂Se₃ we demonstrate that, instead of a sharp MI/TI interface clearly separating the two subsystems, it is energetically far more favorable to form a built-in interface via insertion of the MI film inside the TI's surface quintuple layer (e.g., Se-Bi-Se-[MnSe]-Bi-Se) where it forms a bulk-like MI structure. This results in a smooth MI-to-TI connection that yields the interface electronic structure essentially free of trivial states. Our findings open a new direction in studies of the MI/TI interfaces and restore their potential for the QAHE and TME observation.

Topological Transitions Induced by Antiferromagnetism in a Thin-Film Topological Insulator

Magnetism in topological insulators (TIs) opens a topologically nontrivial exchange band gap, providing an exciting platform for manipulating the topological order through an external magnetic field. Here, we show that the surface of an antiferromagnetic thin film can magnetize the top and the bottom TI surface states through interfacial couplings. During the magnetization reversal, intermediate spin configurations are ascribed from unsynchronized magnetic switchings. This unsynchronized switching develops antisymmetric magnetoresistance spikes during magnetization reversals, which might originate from a series of topological transitions. With the high Néel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists up to ∼90  K.

Proximity-induced magnetism and an anomalous Hall effect in Bi2Se3/LaCoO3: a topological insulator/ferromagnetic insulator thin film heterostructure

Inducing magnetism in a topological insulator (TI) by exchange coupling with a ferromagnetic insulator (FMI) will break the time-reversal symmetry of topological surface states, offering possibilities to realize several predicted novel magneto-electric effects. Seeking suitable FMI materials is crucial for the coupling of heterojunctions, and yet is challenging as well and only a few kinds have been explored. In this report, we introduce epitaxial LaCoO3 thin films on a SrTiO3 substrate, which is an insulating ferromagnet with a Curie temperature of TC ∼ 85 K, to be combined with TIs for proximity coupling. Thin films of the prototype topological insulator, Bi2Se3, are successfully grown onto the (001) surface of LaCoO3/SrTiO3, forming a high-quality TI/FMI heterostructure with a sharp interface. The magnetic and transport measurements manifest the emergence of a ferromagnetic phase in Bi2Se3 films, with additional induced moments and a suppressed weak antilocalization effect, while preserving the carrier mobility of the intrinsic Bi2Se3 films at the same time. Moreover, a signal of an anomalous Hall effect is observed and persists up to temperatures above 100 K, paving the way towards spintronic device applications.

Proximity-Induced Magnetic Order in a Transferred Topological Insulator Thin Film on a Magnetic Insulator

Breaking the time reversal symmetry (TRS) in a topological insulator (TI) by introducing a magnetic order gives rise to exotic quantum phenomena. One of the promising routes to inducing a magnetic order in a TI is utilizing magnetic proximity effect between a TI and a strong magnetic insulator (MI). In this article, we demonstrate a TI/MI heterostructure prepared through transferring a molecular beam epitaxy (MBE)-grown Bi₂Se₃ film onto a yttrium iron garnet (YIG) substrate via wet transfer. The transferred Bi₂Se₃ exhibits excellent quality over a large scale. Moreover, through wet transfer we are able to engineer the interface and perform a comparative study to probe the proximity coupling between Bi₂Se₃ and YIG under different interface conditions. A detailed investigation of both the anomalous Hall effect and quantum corrections to the conductivity in magnetotransport measurements reveals an induced magnetic order as well as TRS breaking in the transferred Bi₂Se₃ film on YIG. In contrast, a thin layer of AlO _x at the interface obstructs the proximity coupling and preserves the TRS, indicating the critical role of the interface in mediating magnetic proximity effect.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Relativistic quantum chaos-An emergent interdisciplinary field

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Strongly exchange-coupled and surface-state-modulated magnetization dynamics in Bi2Se3/yttrium iron garnet heterostructures

Harnessing the spin–momentum locking of topological surface states in conjunction with magnetic materials is the first step to realize novel topological insulator-based devices. Here, we report strong interfacial coupling in Bi₂Se₃/yttrium iron garnet (YIG) bilayers manifested as large interfacial in-plane magnetic anisotropy (IMA) and enhancement of damping probed by ferromagnetic resonance. The interfacial IMA and damping enhancement reaches a maximum when the Bi₂Se₃ film approaches its two-dimensional limit, indicating that topological surface states play an important role in the magnetization dynamics of YIG. Temperature-dependent ferromagnetic resonance of Bi₂Se₃/YIG reveals signatures of the magnetic proximity effect of T_C as high as 180 K, an emerging low-temperature perpendicular magnetic anisotropy competing the high-temperature IMA, and an increasing exchange effective field of YIG steadily increasing toward low temperature. Our study sheds light on the effects of topological insulators on magnetization dynamics, essential for the development of topological insulator-based spintronic devices.

Understanding the effects of topological insulators on magnetization dynamics of adjacent magnetic materials is essential for novel spintronic devices. Here, Fanchiang et al. report thickness dependence of interfacial in-plane magnetic anisotropy and damping enhancement in Bi₂Se₃/yttrium iron garnet (YIG) bilayers, indicating an important role of topological surface states in the magnetization dynamics of YIG.

Interface-Induced Enhancement of Ferromagnetism in Insulating LaMnO3 Ultrathin Films

Engineering ferromagnetism, by modulating its magnitude or anisotropy, is an important topic in the field of magnetism and spintronics. Among different types of magnetic materials, ferromagnetic insulators, in which magnetic moment unusually coexists with localized electrons, are of particular interest. Here, we report a remarkable interfacial enhancement of the ferromagnetism by adding one unit-cell LaAlO₃ adjacent to an insulating LaMnO₃ ultrathin film. The enhancement of ferromagnetism is explained in terms of charge transfer at the interface, as evidenced by X-ray absorption spectroscopy and ab initio calculations. This study demonstrates an effective and dramatic approach to modulate the functionality of ferromagnetic insulators, contributing to the arsenal of engineering techniques for future spintronics.

Understanding the Giant Enhancement of Exchange Interaction in Bi_{2}Se_{3}-EuS Heterostructures

A recent experiment indicated that a ferromagnetic EuS film in contact with a topological insulator Bi_{2}Se_{3} might show a largely enhanced Curie temperature and perpendicular magnetic anisotropy [F. Katmis et al., Nature (London) 533, 513 (2016).NATUAS0028-083610.1038/nature17635]. Through systematic density functional calculations, we demonstrate that in addition to the factor that Bi_{2}Se_{3} has a strong spin orbit coupling, the topological surface states are crucial to make these unusual behaviors robust as they hybridize with EuS states and extend rather far into the magnetic layers. The magnetic moments of Eu atoms are nevertheless not much enhanced, unlike what was reported in the experiment. Our results and model analyses provide useful insights for how these quantities are linked, and pave a way for the control of properties of magnetic films via contact with topological insulators.

Above 400-K robust perpendicular ferromagnetic phase in a topological insulator

The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TIs) exhibits many fascinating physical properties for potential applications in nanoelectronics and spintronics. However, in transition metal-doped TIs, the only experimentally demonstrated QAHE system to date, the QAHE is lost at practically relevant temperatures. This constraint is imposed by the relatively low Curie temperature (T_c) and inherent spin disorder associated with the random magnetic dopants. We demonstrate drastically enhanced T_c by exchange coupling TIs to Tm₃Fe₅O₁₂, a high-T_c magnetic insulator with perpendicular magnetic anisotropy. Signatures showing that the TI surface states acquire robust ferromagnetism are revealed by distinct squared anomalous Hall hysteresis loops at 400 K. Point-contact Andreev reflection spectroscopy confirms that the TI surface is spin-polarized. The greatly enhanced T_c, absence of spin disorder, and perpendicular anisotropy are all essential to the occurrence of the QAHE at high temperatures.

Proximity Effect induced transport Properties between MBE grown (Bi1-xSbx)2Se3 Topological Insulators and Magnetic Insulator CoFe2O4

In this study, we investigate the proximity effect in topological insulator (TI) and magnetic insulator bilayer system. (Bi_1−xSb_x)₂Se₃/CoFe₂O₄ (CFO) heterostructure was fabricated using molecular beam epitaxy and pulsed laser deposition system respectively. As revealed from the magnetoresistance measurement, the weak anti-localization (WAL) is strongly suppressed by proximity effect in (Bi_1−xSb_x)₂Se₃/CFO interface. Modified Hikama-Larkin-Nagaoka equation was used to fit the WAL results so that the size of surface state gap can be extracted successfully. The temperature-dependent resistance of the heterostructures at small and large perpendicular magnetic fields were also measured and analyzed. The results indicate that the surface band gap can be induced in TI and continuously enlarged up to 9 T, indicating the gradual alignment of the magnetic moment in CFO under perpendicular magnetic field. The approaches and results accommodated in this work show that CFO can effectively magnetize (Bi_1−xSb_x)₂Se₃ and the heterostructures are promising for TI-based spintronic device applications.

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehoglike “spin” texture in momentum space. Here, we apply the previously formulated low-energy model for Bi₂Se₃, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e²/2h. The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Interface electronic structure at the topological insulator-ferrimagnetic insulator junction

An interface electron state at the junction between a three-dimensional topological insulator film, Bi₂Se₃, and a ferrimagnetic insulator film, Y₃Fe₅O₁₂ (YIG), was investigated by measurements of angle-resolved photoelectron spectroscopy and x-ray absorption magnetic circular dichroism. The surface state of the Bi₂Se₃ film was directly observed and localized 3d spin states of the Fe³⁺ in the YIG film were confirmed. The proximity effect is likely described in terms of the exchange interaction between the localized Fe 3d electrons in the YIG film and delocalized electrons of the surface and bulk states in the Bi₂Se₃ film.

Rational Design of Two-Dimensional Metallic and Semiconducting Spintronic Materials Based on Ordered Double-Transition-Metal MXenes

Two-dimensional (2D) materials that display robust ferromagnetism have been pursued intensively for nanoscale spintronic applications, but suitable candidates have not been identified. Here we present theoretical predictions on the design of ordered double-transition-metal MXene structures to achieve such a goal. On the basis of the analysis of electron filling in transition-metal cations and first-principles simulations, we demonstrate robust ferromagnetism in Ti₂MnC₂T_x monolayers regardless of the surface terminations (T = O, OH, and F), as well as in Hf₂MnC₂O₂ and Hf₂VC₂O₂ monolayers. The high magnetic moments (3-4 μB/unit cell) and high Curie temperatures (495-1133 K) of these MXenes are superior to those of existing 2D ferromagnetic materials. Furthermore, semimetal-to-semiconductor and ferromagnetic-to-antiferromagnetic phase transitions are predicted to occur in these materials in the presence of small or moderate tensile in-plane strains (0-3%), which can be externally applied mechanically or internally induced by the choice of transition metals.