Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators

Ubiquitous Order-Disorder Transition in the Mn Antisite Sublattice of the (MnBi2Te4)(Bi2Te3)n Magnetic Topological Insulators

Magnetic topological insulators (TIs) herald a wealth of applications in spin-based technologies, relying on the novel quantum phenomena provided by their topological properties. Particularly promising is the (MnBi2Te4)(Bi2Te3)n layered family of established intrinsic magnetic TIs that can flexibly realize various magnetic orders and topological states. High tunability of this material platform is enabled by manganese-pnictogen intermixing, whose amounts and distribution patterns are controlled by synthetic conditions. Here, nuclear magnetic resonance and muon spin spectroscopy, sensitive local probe techniques, are employed to scrutinize the impact of the intermixing on the magnetic properties of (MnBi2Te4)(Bi2Te3)n and MnSb2Te4. The measurements not only confirm the opposite alignment between the Mn magnetic moments on native sites and antisites in the ground state of MnSb2Te4, but for the first time directly show the same alignment in (MnBi2Te4)(Bi2Te3)n with n = 0, 1 and 2. Moreover, for all compounds, the static magnetic moment of the Mn antisite sublattice is found to disappear well below the intrinsic magnetic transition temperature, leaving a homogeneous magnetic structure undisturbed by the intermixing. The findings provide a microscopic understanding of the crucial role played by Mn-Bi intermixing in (MnBi2Te4)(Bi2Te3)n and offer pathways to optimizing the magnetic gap in its surface states.

Recent progress of MnBi2Te4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi2Te4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi2Te4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Understanding how the breakdown of the QAHE occurs in MnBi2Te4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi2Te4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi2Te4 thin films.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2Te4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN, though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex) and its spatial fluctuation in the QAH insulator 5-layer MnBi2Te4. Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Tunable Magnetic Domains in Ferrimagnetic MnSb2Te4

Highly tunable properties make Mn(Bi,Sb)2Te4 a rich playground for exploring the interplay between band topology and magnetism: On one end, MnBi2Te4 is an antiferromagnetic topological insulator, while the magnetic structure of MnSb2Te4 (MST) can be tuned between antiferromagnetic and ferrimagnetic. Motivated to control electronic properties through real-space magnetic textures, we use magnetic force microscopy (MFM) to image the domains of ferrimagnetic MST. We find that magnetic field tunes between stripe and bubble domain morphologies, raising the possibility of topological spin textures. Moreover, we combine in situ transport with domain manipulation and imaging to both write MST device properties and directly measure the scaling of the Hall response with the domain area. This work demonstrates measurement of the local anomalous Hall response using MFM and opens the door to reconfigurable domain-based devices in the M(B,S)T family.

Recent progress in MnBi2nTe3n+1 intrinsic magnetic topological insulators: crystal growth, magnetism and chemical disorder

The search for magnetic topological materials has been at the forefront of condensed matter research for their potential to host exotic states such as axion insulators, magnetic Weyl semimetals, Chern insulators, etc. To date, the MnBi2nTe3n+1 family is the only group of materials showcasing van der Waals-layered structures, intrinsic magnetism and non-trivial band topology without trivial bands at the Fermi level. The interplay between magnetism and band topology in this family has led to the proposal of various topological phenomena, including the quantum anomalous Hall effect, quantum spin Hall effect and quantum magnetoelectric effect. Among these, the quantum anomalous Hall effect has been experimentally observed at record-high temperatures, highlighting the unprecedented potential of this family of materials in fundamental science and technological innovation. In this paper, we provide a comprehensive review of the research progress in this intrinsic magnetic topological insulator family, with a focus on single-crystal growth, characterization of chemical disorder, manipulation of magnetism through chemical substitution and external pressure, and important questions that remain to be conclusively answered.

Topological phase transition in the antiferromagnetic topological insulator MnBi[Formula: see text]Te[Formula: see text] from the point of view of axion-like state realization

This work aims to study the conditions of topological phase transition (TPT) between the topological and trivial states in the antiferromagnetic topological insulator (AFM TI) MnBi[Formula: see text]Te[Formula: see text] and propose some theory about the relationship of this TPT with the possibility of axion-like state realization in this material. Using the density functional approach we have analyzed the changes in the electronic and spin structure of topological surface states (TSSs) and the nearest conduction and valence bands (CB and VB) including the changes in the bulk band gap as well as the Dirac point (DP) gap in TSSs under variation of the spin-orbit coupling strength in the region of the TPT for infinite crystal and slab with a surface both. We have shown that in both cases the TPT occurs with inversion of the contributions of the Bi-[Formula: see text] and Te-[Formula: see text] states of different parity at the gap edges related to change in the gap sign. In the case of surface calculations, the Bi-[Formula: see text] and Te-[Formula: see text] states at the edges of the bulk band gap and their inversion at the TPT point are transformed into the TSSs with an energy gap at the DP. In this case the TPT takes place without closing the band gap, i.e. with a "jump" through zero and the formation of the nonzero gap during such a transition. Our calculations show that the TPT point is also characterized by an inversion of the out-of-plane spin polarization [Formula: see text] at the [Formula: see text] point for lower and upper parts of the Dirac cone and a significant spatial redistribution of the TSSs between the surface and the bulk. We suppose that the nonzero Dirac gap can have some relationship with the formation of the axion-like state, which presumably couples nonmagnetic spin-orbit and magnetic contributions at the boundary between the topological and trivial phases for a system with parameters close to the TPT conditions. A practically realized system is proposed - the AFM TI with a stoichiometry close to that of MnBi[Formula: see text]Te[Formula: see text]Se[Formula: see text] with partial (about 50%) substitution of Te atoms for Se atoms in MnBi[Formula: see text]Te[Formula: see text] which can be an experimental platform for the implementation and experimental analysis of the TPT and the corresponding possibility of the axion-like state realization in Condensed Matter. Besides, such system could serve as a good platform for studying the dynamic axion effect, where the axion field fluctuations are maximised when a small external field is applied to the system which state is close to the TPT.

Role of Magnetic Defects in Tuning Ground States of Magnetic Topological Insulators

Magnetic defects play an important, but poorly understood, role in magnetic topological insulators (TIs). For example, topological surface transport and bulk magnetic properties are controlled by magnetic defects in Bi₂ Se₃ -based dilute ferromagnetic (FM) TIs and MnBi₂ Te₄ (MBT)-based antiferromagnetic (AFM) TIs. Despite its nascent ferromagnetism, the inelastic neutron scattering data show that a fraction of the Mn defects in Sb₂ Te₃ form strong AFM dimer singlets within a quintuple block. The AFM superexchange coupling occurs via Mn-Te-Mn linear bonds and is identical to the AFM coupling between antisite defects and the FM Mn layer in MBT, establishing common interactions in the two materials classes. It is also found that the FM correlations in (Sb_1-x Mn_x )₂ Te₃ are likely driven by magnetic defects in adjacent quintuple blocks across the van der Waals gap. In addition to providing answers to long-standing questions about the evolution of FM order in dilute TI, these results also show that the evolution of global magnetic order from AFM to FM in Sb-substituted MBT is controlled by defect engineering of the intrablock and interblock coupling.

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet MnBi_{2}Te_{4}

Many experiments observed a metallic behavior at zero magnetic fields (antiferromagnetic phase, AFM) in MnBi_{2}Te_{4} thin film transport, which coincides with gapless surface states observed by angle-resolved photoemission spectroscopy, while it can become a Chern insulator at field larger than 6 T (ferromagnetic phase, FM). Thus, the zero-field surface magnetism was once speculated to be different from the bulk AFM phase. However, recent magnetic force microscopy refutes this assumption by detecting persistent AFM order on the surface. In this Letter, we propose a mechanism related to surface defects that can rationalize these contradicting observations in different experiments. We find that co-antisites (exchanging Mn and Bi atoms in the surface van der Waals layer) can strongly suppress the magnetic gap down to several meV in the AFM phase without violating the magnetic order but preserve the magnetic gap in the FM phase. The different gap sizes between AFM and FM phases are caused by the exchange interaction cancellation or collaboration of the top two van der Waals layers manifested by defect-induced surface charge redistribution among the top two van der Waals layers. This theory can be validated by the position- and field-dependent gap in future surface spectroscopy measurements. Our work suggests suppressing related defects in samples to realize the quantum anomalous Hall insulator or axion insulator at zero fields.