Half-Magnetic Topological Insulator with Magnetization-Induced Dirac Gap at a Selected Surface

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Half-Magnetic Topological Insulator with Magnetization-Induced Dirac Gap at a Selected Surface

Ruie Lu, Hongyi Sun, Shiv Kumar, Yuan Wang, Mingqiang Gu, Meng Zeng, Yu-Jie Hao, Jiayu Li, Jifeng Shao, Xiao-Ming Ma, Zhanyang Hao, Ke Zhang, Wumiti Mansuer, Jiawei Mei, Yue Zhao, Cai Liu, Ke Deng, Wen Huang, Bing Shen, Kenya Shimada, Eike F. Schwier, Chang Liu, Qihang Liu, and Chaoyu Chen

Phys. Rev. X 11, 011039 – Published 25 February 2021; Erratum Phys. Rev. X 11, 029902 (2021)

Abstract

Topological magnets are a new family of quantum materials providing great potential to realize emergent phenomena, such as the quantum anomalous Hall effect and the axion-insulator state. Here, we present our discovery that the stoichiometric ferromagnet ${MnBi}_{8} {Te}_{13}$ with natural heterostructure ${MnBi}_{2} {Te}_{4} / ({Bi}_{2} {Te}_{3})_{3}$ is an unprecedented “half-magnetic topological insulator,” with the magnetization existing at the ${MnBi}_{2} {Te}_{4}$ surface but not at the opposite surface terminated by triple ${Bi}_{2} {Te}_{3}$ layers. Our angle-resolved photoemission spectroscopy measurements unveil a massive Dirac gap at the ${MnBi}_{2} {Te}_{4}$ surface and a gapless Dirac cone on the other side. Remarkably, the Dirac gap (about 28 meV) at the ${MnBi}_{2} {Te}_{4}$ surface decreases monotonically with increasing temperature and closes right at the Curie temperature, thereby representing the first smoking-gun spectroscopic evidence of a magnetization-induced topological surface gap among all known magnetic topological materials. We further demonstrate theoretically that the half-magnetic topological insulator is desirable to realize the surface anomalous Hall effect, which serves as direct proof of the general concept of axion electrodynamics in condensed matter systems.

Received 9 September 2020
Revised 17 November 2020
Accepted 13 January 2021

DOI:https://doi.org/10.1103/PhysRevX.11.011039

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Topological insulators Topological materials

Condensed Matter, Materials & Applied Physics

Erratum

Erratum: Half-Magnetic Topological Insulator with Magnetization-Induced Dirac Gap at a Selected Surface [Phys. Rev. X 11, 011039 (2021)]

Ruie Lu, Hongyi Sun, Shiv Kumar, Yuan Wang, Mingqiang Gu, Meng Zeng, Yu-Jie Hao, Jiayu Li, Jifeng Shao, Xiao-Ming Ma, Zhanyang Hao, Ke Zhang, Wumiti Mansuer, Jiawei Mei, Yue Zhao, Cai Liu, Ke Deng, Wen Huang, Bing Shen, Kenya Shimada, Eike F. Schwier, Chang Liu, Qihang Liu, and Chaoyu Chen

Phys. Rev. X 11, 029902 (2021)

Authors & Affiliations

Ruie Lu ^1,*, Hongyi Sun ^1,*, Shiv Kumar ^2,*, Yuan Wang ^1,*, Mingqiang Gu¹, Meng Zeng ¹, Yu-Jie Hao ¹, Jiayu Li ¹, Jifeng Shao¹, Xiao-Ming Ma ¹, Zhanyang Hao ¹, Ke Zhang², Wumiti Mansuer², Jiawei Mei¹, Yue Zhao ¹, Cai Liu ¹, Ke Deng ¹, Wen Huang ¹, Bing Shen ³, Kenya Shimada ², Eike F. Schwier ^2,†, Chang Liu ^1,‡, Qihang Liu ^1,4,§, and Chaoyu Chen ^1,‖

¹Shenzhen Institute for Quantum Science and Engineering (SIQSE) and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
²Hiroshima Synchrotron Radiation Centre, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-0046, Japan
³School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
⁴Guangdong Provincial Key Laboratory for Computational Science and Material Design, Southern University of Science and Technology, Shenzhen 518055, China

^*These authors contributed equally to this work.
^†Corresponding author. Eike.schwier@physik.uni-wuerzburg.de
^‡Corresponding author. liuc@sustech.edu.cn
^§Corresponding author. liuqh@sustech.edu.cn
^‖Corresponding author. chency@sustech.edu.cn

Popular Summary

Topological insulators (TIs) support the flow of electric currents only on their surfaces but not in their interiors. Ordered magnetic elements generally destroy the surface conductivity of the TIs, making them insulating throughout. However, such magnetic TIs are promised to host two exotic quantum phenomena: the quantum anomalous Hall effect and the axion insulating state. Partially because of the lack of suitable materials, thus far it is not clear if the latter case can be observed. In this work, we find experimentally that an intrinsic ferromagnetic TI can be an ideal platform for exploring the key signature of axion dynamics.

Specifically, we find that these materials are excellent for studying and manipulating exotic half-quantized surface conductance, in which the electrical conductance at the surface takes on a very particular set of discrete values. Using angle-resolved photoemission, we reveal that the conducting surfaces of a specific ferromagnetic TI become insulating at low temperatures but return to normal TI behavior at exactly the transition temperature where its ferromagnetism is killed. This phenomenon happens only at its magnetic layer but not at its nonmagnetic layers. We further demonstrate theoretically that this system can be termed a “half-magnetic topological insulator,” possessing a half-quantized surface anomalous transverse (or Hall) conductivity.

Our result calls for direct measurements of such half-quantized Hall currents in this system, which would be a direct proof of the general concept of axion electrodynamics in condensed matter systems.

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Issue

Vol. 11, Iss. 1 — January - March 2021

Subject Areas

Condensed Matter Physics

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Figure 1
Ferromagnetism and anomalous Hall effect in ${MnBi}_{8} {Te}_{13}$ single crystals. (a) Schematic crystal structure with one unit of -SL-QL-QL-QL- sequences. (b) Single-crystal x-ray diffraction result taken at 300 K. (c) Zero-field-cooled (ZFC, dashed line) and field-cooled (FC, solid line) magnetic susceptibility ( $χ$ ) vs temperature ( $T$ ) for magnetic field $H = 100 Oe$ parallel to the $a b$ plane (blue) and the $c$ axis (red), respectively. The inset shows the Curie-Weiss fitting for a temperature range of 150 K–300 K. (d) Zero-field in-plane resistivity ( $ρ_{xx}$ ) vs $T$ . The inset shows the results up to 300 K. (e) Field-dependent magnetization hysteresis at $2 K$ for $H / / a b$ (blue) and $H / / c$ (red). (f) Field-dependent anomalous Hall resistivity ( $ρ_{x y}^{A}$ ) at $2 K$ for $H / / c$ . (g) Field-dependent transverse resistivity change ( $M R = [ρ_{x x} (H) / ρ_{x x} (0)] - 1$ ) at $2 K$ for $H / / c$ .
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Figure 2
Temperature evolution of the TSS Dirac cone gap at the S and QQQ termination of ${MnBi}_{8} {Te}_{13}$ . (a)–(d) ARPES results for the S termination. (a) Schematic structural stacking configuration of the S termination. (b) DFT band structure calculated for the FM state, with the surface-only states (dark violet to black) being superposed on the bulk states (yellow, orange, and light violet). (c) Band structure along $\bar{M} - \bar{Γ} - \bar{M}$ measured at 7 K (FM state). (d) Band structure along $\bar{M} - \bar{Γ} - \bar{M}$ measured at 20 K (PM state). Data in panels (c) and (d) are shown in the form of the ARPES original spectra (top panel) and the 2D curvature spectra [46] (bottom panel). (e)–(h) Same as panels (a)–(d) but for the QQQ termination. Clearly, entering the FM state opens a gap at the TSS Dirac cone for the S termination, while no such gap is observed for the QQQ termination.
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Figure 3
Temperature dependence of the TSS gap in the S termination of ${MnBi}_{8} {Te}_{13}$ . (a) Enlarged ARPES spectrum of the S termination measured at 15 K (PM phase). (b) Two-dimensional curvature plot for the spectrum in panel (a). (c) Energy distribution curve (EDC) at $\bar{Γ}$ (integrated over a $\pm 0.001 Å^{- 1}$ momentum window) and its fitting with multiple Lorentzian peaks. (d)–(f) Same plots as those in panels (a)–(c) but for data measured at 7 K (FM phase). (g) EDC fitting analysis at various temperatures, showing a clear gap opening for $T \leq 10.0 K$ . The EDCs for each temperature are extracted from the corresponding spectra shown in Fig. S6 integrated over a $\pm 0.001 Å^{- 1}$ momentum $k_{∥}$ window. Furthermore, the spectra for each temperature are extracted from the corresponding map shown in Fig. S5 integrated over a $\pm 0.002 Å^{- 1}$ momentum ( $k_{y}$ ) window. (h) TSS Dirac cone gap size (blue triangles) evolution with temperature and its fitting (red solid line) using a power-law curve. The error bar of the gap size is defined as $e = \sqrt{w_{1}^{2} + w_{2}^{2}}$ , where $w_{1}$ and $w_{2}$ represent the half width at half maximum for peaks $E_{1}$ and $E_{2}$ , respectively. We note that the EDC fitting in panel (g) yields the standard deviation of the peak positions much smaller (less than 1 meV) than the error bars shown in panel (h).
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Figure 4
Half-quantized surface AHC at the S termination. (a,b) Integrated, layer-projected, anomalous Hall conductance for the slabs with 16 and 17 vdW layers, respectively. The 16-layer slab is not symmetric, containing four unit cells as a half-magnetic topological insulator, while the 17-layer slab is symmetric with a global band gap and nontrivial Chern number, as shown in the insets. (c) Schematic plot for the nonlocal transport measurement with a hexagonal six-contact-probing setup. (d) Spectral functions at three spots denoted in panel (c), showing chiral hinge states at the S termination that manifest the half-QAH effect.
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