Magnetic Topological Insulators Research Articles

Intrinsic magnetic topological materials

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.

Creation of chiral interface channels for quantized transport in magnetic topological insulator multilayer heterostructures

One-dimensional chiral interface channels can be created at the boundary of two quantum anomalous Hall (QAH) insulators with different Chern numbers. Such a QAH junction may function as a chiral edge current distributer at zero magnetic field, but its realization remains challenging. Here, by employing an in-situ mechanical mask, we use molecular beam epitaxy to synthesize QAH insulator junctions, in which two QAH insulators with different Chern numbers are connected along a one-dimensional junction. For the junction between Chern numbers of 1 and −1, we observe quantized transport and demonstrate the appearance of the two parallel propagating chiral interface channels along the magnetic domain wall at zero magnetic field. For the junction between Chern numbers of 1 and 2, our quantized transport shows that a single chiral interface channel appears at the interface. Our work lays the foundation for the development of QAH insulator-based electronic and spintronic devices and topological chiral networks.

Exchange bias in the van der Waals heterostructure MnBi2Te4/Cr2Ge2Te6

The exchange bias effect, namely the horizontal shift in the magnetic hysteretic loop, is known as a fundamentally and technologically important property of magnetic systems. Though the exchange bias effect has been widely observed in normal magnetic heterostructure, it is desirable to raise such pinning coupling in topology-based multilayer structure. Furthermore, the exchange bias effect was theoretically proposed to be able to further open the surface magnetization gap in the recently discovered intrinsic magnetic topological insulator $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$. Such an exchange interaction can be ensured and programmed in the heterojunction, or applied to spintronics. Here we report the electrically tunable exchange bias in the van der Waals $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}/{\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ heterostructure. The exchange bias emerges over a critical magnetic field and reaches the maximum value near the band gap. Moreover, the exchange bias is experienced by net ferromagnetic (FM) odd-layers $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ rather than the pure FM insulator ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$. Accompanied by nonlocal signal, an unfamiliar antisymmetric peak endows a domain-related structure within interface of the heterostructure. Such van der Waals heterostructure provides a promising platform to study the novel exchange bias effect and explore the possible application of spintronics or $\mathrm{high}\ensuremath{-}{\mathrm{T}}_{\mathrm{c}}$ quantum anomalous Hall effect.

Van der Waals Engineering of Ultrafast Carrier Dynamics in Magnetic Heterostructures

Heterostructures composed of the intrinsic magnetic topological insulator MnBi2Te4 and its nonmagnetic counterpart Bi2Te3 host distinct surface electronic band structures depending on the stacking order and exposed termination. Here, we probe the ultrafast dynamical response of MnBi2Te4 and MnBi4Te7 following near-infrared optical excitation using time- and angle-resolved photoemission spectroscopy and disentangle surface from bulk dynamics based on density functional theory slab calculations of the surface-projected electronic structure. We gain access to the out-of-equilibrium charge carrier populations of both MnBi2Te4 and Bi2Te3 surface terminations of MnBi4Te7, revealing an instantaneous occupation of states associated with the Bi2Te3 surface layer followed by carrier extraction into the adjacent MnBi2Te4 layers with a laser fluence-tunable delay of up to 350 fs. The ensuing thermal relaxation processes are driven by phonon scattering with significantly slower relaxation times in the magnetic MnBi2Te4 septuple layers. The observed competition between interlayer charge transfer and intralayer phonon scattering demonstrates a method to control ultrafast charge transfer processes in MnBi2Te4-based van der Waals compounds.

Quantum transport phenomena in magnetic topological insulators

In the past decade, magnetic topological insulators have been an important focus in condensed matter physics research. The intricate interplay between the nontrivial band topology and spin, orbit, charge, and dimensionality degrees of freedom can give rise to abundant exotic topological quantum states and topological phase transitions. Measuring the transport properties of magnetic topological insulators is a crucial approach to exploring their exotic properties, which is of significant scientific importance in deepening our understanding of topological quantum states. Simultaneously, it also holds substantial potential applications in the development of novel low-power electronic devices. In this work, experimental progress of transport researches of magnetic topological insulators is reviewed, including quantum anomalous Hall effect and topological quantum phase transitions in magnetically doped topological insulators, the quantum anomalous Hall phase, axion insulator phase and Chern insulator phase in intrinsic antiferromagnetic topological insulator MnBi<sub>2</sub>Te<sub>4</sub>, as well as the helical phase emerged from the Chern insulator in pulsed high magnetic fields. Finally, this work analyzes the future direction of development in magnetic topological insulators, and the transport phenomena that have not been understood in these systems, offering an insight into and perspectives on the potential breakthroughs to be achieved in this area of research.

Novel magnetic topological insulator FeBi2Te4 with controllable topological quantum phase

Topological phase transition processes in FM-z order FeBi2Te4 under pressure are determined and topologically classified.

Strain-tunable magnetism and topological states in layered VBi2Te4.

Similar to the magnetic topological insulator of MnBi2Te4, recent studies have demonstrated that VBi2Te4 is also an ideal candidate to explore many intriguing quantum states. Different from the strong interlayer antiferromagnetic (AFM) coupling in layered MnBi2Te4, based on first-principles calculations, we find that the energy difference between AFM and ferromagnetic (FM) orders in layered VBi2Te4 is much smaller than that of MnBi2Te4. Specifically, it is found that the interlayer FM coupling can be readily achieved by applying strain. Further electronic band structures reveal that the VBi2Te4 bilayer is a time-reversal symmetry broken quantum spin Hall insulator with a spin Chern number of CS = 1, which is essentially different from the QAH state with a Chern number of C = 1 in the MnBi2Te4 bilayer. Most strikingly, the topological states of the magnetic VBi2Te4 bilayer can be well tuned by strain, whose topological phase diagram is mapped out as a function of strain by employing continuum model analyses. All of these results indicate that the layered VBi2Te4 not only enriches the family of magnetic topological materials, but also provides a promising platform to explore more exotic quantum phenomena.

Research progress of intrinsic magnetic topological insulator MnBi<sub>2</sub>Te<sub>4</sub>

The interaction between non-trivial topological states and the magnetic order of intrinsic magnetic topological insulators gives rise to various exotic physical properties, including the quantum anomalous Hall effect and axion insulator. These materials possess great potential applications in low-power topological spintronic devices and topological quantum computation. Since the first intrinsic magnetic topological insulator, MnBi<sub>2</sub>Te<sub>4</sub>, was discovered in 2019, this material system has received significant attention from researchers and sparked a research boom. This paper begins with discussing the fundamental properties of MnBi<sub>2</sub>Te<sub>4</sub> and then turns to important research findings related to this intrinsic magnetic topological insulator. Specifically, it focuses on the quantum anomalous Hall effect, axion insulating state, and Majorana zero energy mode exhibited by the MnBi<sub>2</sub>Te<sub>4</sub> series. Furthermore, this paper highlights other research directions and current challenges associated with this material system. Finally, this paper provides a summary and outlook for future research on MnBi<sub>2</sub>Te<sub>4</sub>, aiming to offer valuable references for researchers in related fields.

Magnetic correlations in the magnetic topological insulator (Cr,Sb)2Te3

Chromium-doped ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ is a magnetic topological insulator (MTI), which belongs to the $(\mathrm{Sb},{\mathrm{Bi})}_{2}(\mathrm{Se},{\mathrm{Te})}_{3}$ family. When doped with the transition metals V, Cr, and Mn this family displays long-range ferromagnetic order above liquid nitrogen temperature and is currently intensely explored for quantum device applications. Despite the large magnetic ordering temperature, the experimental observation of dissipationless electrical transport channels, i.e., the quantum anomalous Hall effect, is limited in these materials to temperatures below $\ensuremath{\approx}2$ K. Inhomogeneities in the MTI have been identified as a major concern, affecting the coupling between the Dirac states and the magnetic dopants. Nevertheless, details on the local magnetic order in these materials are not well understood. Here, we report the study of the magnetic correlations in thin films using a combination of muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$, and magnetic soft x-ray spectroscopy and imaging. $\ensuremath{\mu}\mathrm{SR}$ provides two key quantities for understanding the microscopic magnetic behavior: The magnetic volume fraction, i.e., the percentage of the material that is ferromagnetically ordered, and the relaxation rate, which is sensitive to the magnetic static $(\ensuremath{\approx}\ensuremath{\mu}\mathrm{s})$ and dynamic disorder. By choosing different implantation depths for the muons, one can further discriminate between near-surface and bulk properties. No evidence for a surface enhancement of the magnetic ordering is observed, but, instead, we find evidence of small magnetically ordered clusters in a paramagnetic background, which are coupled. The significant magnetic field shift that is present in all samples indicates a percolation transition that proceeds through the formation and growth of magnetically ordered spin clusters. We further find that fluctuations are present even at low temperatures, and that there appears to be a transition between superparamagnetism and superferromagnetism.

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators.

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Large Exchange Bias Effect and Coverage-Dependent Interfacial Coupling in CrI3/MnBi2Te4 van der Waals Heterostructures

Igniting interface magnetic ordering of magnetic topological insulators by building a van der Waals heterostructure can help to reveal novel quantum states and design functional devices. Here, we observe an interesting exchange bias effect, indicating successful interfacial magnetic coupling, in CrI3/MnBi2Te4 ferromagnetic insulator/antiferromagnetic topological insulator (FMI/AFM-TI) heterostructure devices. The devices originally exhibit a negative exchange bias field, which decays with increasing temperature and is unaffected by the back-gate voltage. When we change the device configuration to be half-covered by CrI3, the exchange bias becomes positive with a very large exchange bias field exceeding 300 mT. Such sensitive manipulation is explained by the competition between the FM and AFM coupling at the interface of CrI3 and MnBi2Te4, pointing to coverage-dependent interfacial magnetic interactions. Our work will facilitate the development of topological and antiferromagnetic devices.

Effect of external fields in high Chern number quantum anomalous Hall insulators

A quantum anomalous Hall state with a high Chern number has so far been realized in multilayer structures consisting of alternating magnetic and undoped topological insulator (TI) layers. However, in previous proposals, the Chern number can only be tuned by varying the doping concentration or the width of the magnetic TI layers. This drawback largely restricts the applications of dissipationless chiral edge currents in electronics since the number of conducting channels remains fixed. In this paper, we propose a way of varying the Chern number at will in these multilayered structures by means of an external electric field applied along the stacking direction. In the presence of an electric field in the stacking direction, the inverted bands of the unbiased structure coalesce and hybridize, generating new inverted bands and collapsing the previously inverted ones. In this way, the number of Chern states can be tuned externally in the sample, without the need for modifying the number and width of the layers or the doping level. We showed that this effect can be uncovered by the variation of the transverse conductance as a function of the electric field at constant injection energy at the Fermi level.

Transport properties of crystallized antiferromagnetic MnBi2Te4 thin films grown by magnetron sputtering

The intrinsic magnetic topological insulator MnBi2Te4 has drawn great attention due to its novel quantum states, among which the most promising one is the quantum anomalous Hall effect. However, MnBi2Te4 is a metastable phase with a narrow temperature range for synthesis, which remains a challenge to grow uniform and high quality MnBi2Te4 sample. Large-area MnBi2Te4 thin films are mainly prepared by molecular beam epitaxy so far. Here, we report a highly versatile method for growing crystallized MnBi2Te4 films on amorphous SiO2/Si substrates by magnetron sputtering at room temperature and post-annealing. High-quality MnBi2Te4 films with a c-axis perpendicular to the substrate and low surface roughness are realized. MnBi2Te4 films have an antiferromagnetic Néel temperature of 21 K, with low carrier concentration (2.5 × 1019 cm−3) and decent mobility (34 cm2 V−1s−1). The films reveal ferromagnetic at ground state and a typical spin-flop transition at 2–3 T. This work provides a pathway toward the fabrication of sputtered-MnBi2Te4 devices for electronic and spintronic applications.

Tailoring the magnetic exchange interaction in MnBi2Te4 superlattices via the intercalation of ferromagnetic layers

The intrinsic magnetic topological insulator MnBi2Te4 (MBT) provides a platform for the creation of exotic quantum phenomena. Novel properties can be created by modification of the MnBi2Te4 framework, but the design of stable magnetic structures remains challenging. Here we report ferromagnet-intercalated MnBi2Te4 superlattices with tunable magnetic exchange interactions. Using molecular beam epitaxy, we intercalate ferromagnetic MnTe layers into MnBi2Te4 to create [(MBT)(MnTe)m]N superlattices and examine their magnetic interaction properties using polarized neutron reflectometry and magnetoresistance measurements. Incorporation of the ferromagnetic spacer tunes the antiferromagnetic interlayer coupling of the MnBi2Te4 layers through the exchange-spring effect at MnBi2Te4/MnTe hetero-interfaces. The MnTe thickness can be used to modulate the relative strengths of the ferromagnetic and antiferromagnetic order, and the superlattice periodicity can tailor the spin configurations of the synthesized multilayers.

The model for non-Abelian field topology for the multilayer fractional quantum anomalous Hall device

From the recent empirical discovery of the quantum anomalous Hall effect (QAHE), the interaction of the particle with spin–orbit coupling (SOC) plays an essential role in the cause of the QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then, the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to the fractional quantum Hall effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to the FQHE, which also includes two terms: the hopping of sublattice and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement the FQHE on the lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This study theoretically predicts the FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.

Mixed Type of the Magnetic Order in Intrinsic Magnetic Topological Insulators Mn(Bi,Sb)2Te4

It is known that Mn(Bi1 –xSbx)2Te4 is an intrinsic magnetic topological insulator, where the Dirac point can be localized at the Fermi level by substituting Bi atoms for Sb atoms to implement the quantum anomalous Hall effect and other unique quantum effects. It has already been shown that Mn(Bi1 – xSbx)2Te4 samples has antiferromagnetic order in a wide range of Sb concentration x = [0, 0.5]. In this paper a mixed type of magnetic ordering is experimentally demonstrated. This implies that there is both a ferromagnetic and an antiferromagnetic order in the system. We revealed the main reproducible magnetic characteristics of this magnetic structure, as well as their dependence on the concentration of Sb atoms.

Quantum anomalous Hall effect in perfectly compensated collinear antiferromagnetic thin films

We show that the quantum anomalous Hall effect almost always occurs in magnetic topological insulator thin films whenever the top and bottom surface layer magnetizations are parallel at some temperature, independent of the interior layer magnetization configuration. Using this criterion, we identify structures that have a quantum anomalous Hall effect even though they have collinear magnetic structures with no net magnetization, and discuss strategies for realizing these interesting magnetic states experimentally.

Topology-insensitive axion mass in magnetic topological insulators

We study the axion in three-dimensional topological insulators with magnetic impurities under finite temperature. We find a stable antiferromagnetic ground state and ferromagnetic metastable state. In both magnetic states, the mass of the axion is found to be up to eV scale and it approaches zero near the phase boundary of the magnetic state. This result applies to both normal and topological insulator phases, i.e., the axion mass is insensitive to the topological states, and it will have a direct impact on the targeted mass range of particle axion dark matter in future experiments.

Axion insulators protected by C2T symmetry, their K -theory invariants, and material realizations

Axion insulators are generally understood as magnetic topological insulators whose Chern-Simons axion coupling term is quantized and equal to $\pi$. Inversion and time reversal, or the composition of either one with a rotation or a translation, are symmetries which protect this invariant. In this work, we focus our attention on the composition of a 2-fold rotation with time reversal, and we show that insulators with this symmetry possess a Z2 invariant arising from Atiyah's real K-theory. We call this invariant the K-theory Kane-Mele invariant due to the similarities it has with the Kane-Mele invariant for systems with time-reversal symmetry. Whenever all Chern numbers vanish, we demonstrate that this invariant is equivalent to the Chern-Simons axion coupling, and in the presence of the inversion symmetry, we show how this invariant could be obtained from the eigenvalues of the inversion operator on its fixed points in momentum space. For the general case of non-trivial Chern numbers, the Chern-Simons axion coupling term incorporates information of the K-theory Kane-Mele invariant as well as information regarding bands with non-trival Chern numbers. An explicit formula in terms of K-theory generators is presented for the Chern-Simons axion coupling term, the relation with the K-theory Kane-Mele invariant is explained, and a formula in terms of eigenvalues of the inversion operator is obtained. Using an effective Hamiltonian model and first-principles calculations, we also show that the occurrence of bulk-band inversion and nontrivial K-theory Kane-Mele invariant index can be observed in axion insulators of the pnictides family. In particular, we demonstrate that NpBi can be classified as an axion insulator due to the detection of additional topological indicators such as the quantum spin Hall effect, gapped surface states, surface quantized anomalous Hall effect, and chiral hinge modes

Crystal structure and Raman-active lattice vibrations of magnetic topological insulators MnBi2Te4·n(Bi2Te3) ( n=0 , 1,...,6)

Further to the structure of the intrinsic magnetic topological insulators $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}n({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})$ with $n<4$, where index $n$ is the number of quintuple Te-Bi-Te-Bi-Te building blocks inserted between the neighboring septuple Te-Bi-Te-Mn-Te-Bi-Te building blocks, the structure of the members with $n=4$, 5, and 6 was studied using x-ray powder diffraction. The unit-cell parameters and atomic positions were obtained. The obtained and available structural data were summarized to show that the crystal structure of all members of $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}n({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})$ follows the cubic close-packing principle, independently of the space group of the given member. Confocal Raman spectroscopy was then applied. Comparative analysis of the number, frequency, symmetry, and broadening of the vibration modes responsible for the lines in the Raman spectra of the systems with $n=1$,\dots{},6, as well as $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\phantom{\rule{0.16em}{0ex}}(n=0)$ and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ ($n=\ensuremath{\infty}$) has shown that lattice dynamics of $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}n({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})$ with $n>0$ overwhelmingly dominates by the cooperative atomic displacements in the quintuple building blocks.