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

Distinguishing surface and bulk electromagnetism via their dynamics in an intrinsic magnetic topological insulator

The indirect exchange interaction between local magnetic moments via surface electrons has been long predicted to bolster the surface ferromagnetism in magnetic topological insulators (MTIs), which facilitates the quantum anomalous Hall effect. This unconventional effect is critical to determining the operating temperatures of future topotronic devices. However, the experimental confirmation of this mechanism remains elusive, especially in intrinsic MTIs. Here, we combine time-resolved photoemission spectroscopy with time-resolved magneto-optical Kerr effect measurements to elucidate the unique electromagnetism at the surface of an intrinsic MTI MnBi2Te4. Theoretical modeling based on 2D Ruderman-Kittel-Kasuya-Yosida interactions captures the initial quenching of a surface-rooted exchange gap within a factor of two but overestimates the bulk demagnetization by one order of magnitude. This mechanism directly explains the sizable gap in the quasi-2D electronic state and the nonzero residual magnetization in even-layer MnBi2Te4. Furthermore, it leads to efficient light-induced demagnetization comparable to state-of-the-art magnetophotonic crystals, promising an effective manipulation of magnetism and topological orders for future topotronics.

Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

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.

Fabrication-induced even-odd discrepancy of magnetotransport in few-layer MnBi2Te4

The van der Waals antiferromagnetic topological insulator MnBi2Te4 represents a promising platform for exploring the layer-dependent magnetism and topological states of matter. Recently observed discrepancies between magnetic and transport properties have aroused controversies concerning the topological nature of MnBi2Te4 in the ground state. In this article, we demonstrate that fabrication can induce mismatched even-odd layer dependent magnetotransport in few-layer MnBi2Te4. We perform a comprehensive study of the magnetotransport properties in 6- and 7-septuple-layer MnBi2Te4, and reveal that both even- and odd-number-layer device can show zero Hall plateau phenomena in zero magnetic field. Importantly, a statistical survey of the optical contrast in more than 200 MnBi2Te4 flakes reveals that the zero Hall plateau in odd-number-layer devices arises from the reduction of the effective thickness during the fabrication, a factor that was rarely noticed in previous studies of 2D materials. Our finding not only provides an explanation to the controversies regarding the discrepancy of the even-odd layer dependent magnetotransport in MnBi2Te4, but also highlights the critical issues concerning the fabrication and characterization of 2D material devices.

On the topological surface states of the intrinsic magnetic topological insulator Mn-Bi-Te family

We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi2Te4) · (Bi2Te3)n ([Formula: see text]) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the topological Dirac surface state observed by photoemission spectroscopy, even though a large Dirac gap is expected because of surface ferromagnetic order. The dichotomy between experiment and theory concerning this gap behavior is perhaps the most critical and puzzling question in this frontier. We discuss various proposals accounting for the lack of magnetic effect on the topological Dirac surface state, which are mainly categorized into two pictures, magnetic reconfiguration and topological surface state redistribution. Band engineering towards opening a magnetic gap of topological surface states provides great opportunities to realize quantized topological transport and axion electrodynamics at higher temperatures.

ARPES investigation of the electronic structure and its evolution in magnetic topological insulator MnBi2+2nTe4+3n family

In the past 5 years, there has been significant research interest in the intrinsic magnetic topological insulator family compounds MnBi2+2nTe4+3n (where n = 0, 1, 2 …). In particular, exfoliated thin films of MnBi2Te4 have led to numerous experimental breakthroughs, such as the quantum anomalous Hall effect, axion insulator phase and high-Chern number quantum Hall effect without Landau levels. However, despite extensive efforts, the energy gap of the topological surface states due to exchange magnetic coupling, which is a key feature of the characteristic band structure of the system, remains experimentally elusive. The electronic structure measured by using angle-resolved photoemission (ARPES) shows significant deviation from ab initio prediction and scanning tunneling spectroscopy measurements, making it challenging to understand the transport results based on the electronic structure. This paper reviews the measurements of the band structure of MnBi2+2nTe4+3n magnetic topological insulators using ARPES, focusing on the evolution of their electronic structures with temperature, surface and bulk doping and film thickness. The aim of the review is to construct a unified picture of the electronic structure of MnBi2+2nTe4+3n compounds and explore possible control of their topological properties.

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect and nonreciprocal magnetoresistance (longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in films of the doped antiferromagnetic topological insulator MnBi_{2}Te_{4}. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

Antisite-Defects Control of Magnetic Properties in MnSb2Te4

The intrinsic magnetic topological materials Mn(Sb/Bi)2n+2Te3n+4 have attracted extensive attention due to their topological quantum properties. Although, the Mn-Sb/Bi antisite defects have been frequently reported to exert significant influences on both magnetism and band topology, their formation mechanism and the methods to manipulate their distribution and concentration remain elusive. Here, we present MnSb2Te4 as a typical example and demonstrate that Mn-Sb antisite defects and magnetism can be tuned by controlling the crystal growth conditions. The cooling rate is identified as the primary key parameter. Magnetization and chemical analysis demonstrate that a slower cooling rate would lead to a higher Mn concentration, a higher magnetic transition temperature, and a higher saturation moment. Further analysis indicates that the Mn content at the original Mn site (MnMn, 3a site) varies more significantly with the cooling rate than the Mn content at the Sb site (MnSb, 6c site). Based on experimental observations, magnetic phase diagrams regarding MnMn and MnSb concentrations are constructed. With the assistance of first-principles calculations, it is demonstrated that the Mn-Sb mixing states primarily result from the mixing entropy and the growth kinetics. The present findings offer valuable insights into defects engineering for preparation of two-dimensional quantum materials.

Stacking Faults and Topological Properties in MnBi2Te4: Reconciling Gapped and Gapless States

Despite theoretical predictions of a gapped surface state for the magnetic topological insulator MnBi2Te4 (MBT), there has been a series of experimental evidence pointing toward gapless states. Here, we theoretically explore how stacking faults could influence the topological characteristics of MBT. We envisage a scenario that a stacking fault exists at the surface of MBT, causing the uppermost layer to deviate from the ground state and its interlayer separation to be expanded. This stacking fault with modulated interlayer couplings hosts a nearly gapless state within the topmost layer due to charge redistribution as the outermost layer recedes. Furthermore, we find evidence of spin-momentum locking and preservation of weak band inversion in the gapless surface state, suggesting the nontrivial topological surface states in the presence of the stacking fault. Our findings provide a plausible elucidation to the long-standing conundrum of reconciling the observation of gapped and gapless states on MBT surfaces.

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.

Irremovable Mn-Bi Site Mixing in MnBi2Te4

MnBi₂Te₄, an antiferromagnetic topological insulator, was theoretically predicted to have a gapped surface state on its (111) surface. However, a much smaller gapped or even gapless surface state has been observed experimentally, which is thought to be caused by the defects in MnBi₂Te₄. Here, we have theoretically identified the antisite Mn_Bi and Bi_Mn as dominant defects and revealed their evolution during the phase transition from MnTe/Bi₂Te₃ to MnBi₂Te₄. We found that the complete elimination of Mn_Bi and Bi_Mn defects in MnBi₂Te₄ by simple annealing is almost impossible due to the high migration barrier in kinetics. Moreover, the gap of the Dirac point-related bands in a MnBi₂Te₄ monolayer would be eliminated with an increasing concentration of Mn_Bi and Bi_Mn defects, which could explain the experimentally unobserved large-gap surface state in MnBi₂Te₄. Our results provide an insight into the theoretical understanding of the quality and the experimentally measured topological properties of the synthesized MnBi₂Te₄.