Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{2}{\mathrm{Te}}_{4}$

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Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$

Seng Huat Lee, David Graf, Lujin Min, Yanglin Zhu, Hemian Yi, Samuel Ciocys, Yuanxi Wang, Eun Sang Choi, Rabindra Basnet, Arash Fereidouni, Aaron Wegner, Yi-Fan Zhao, Katrina Verlinde, Jingyang He, Ronald Redwing, V. Gopalan, Hugh O. H. Churchill, Alessandra Lanzara, Nitin Samarth, Cui-Zu Chang, Jin Hu, and Z. Q. Mao

Phys. Rev. X 11, 031032 – Published 10 August 2021

Abstract

The discovery of Weyl semimetals (WSMs) has fueled tremendous interest in condensed matter physics. The realization of WSMs requires the breaking of either inversion symmetry (IS) or time-reversal symmetry (TRS). WSMs can be categorized into type-I and type-II WSMs, which are characterized by untilted and strongly tilted Weyl cones, respectively. Type-I WSMs with breaking of either IS or TRS and type-II WSMs with solely broken IS have been realized experimentally, but a TRS-breaking type-II WSM still remains elusive. In this article, we report transport evidence for a TRS-breaking type-II WSM observed in the intrinsic antiferromagnetic topological insulator $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ under magnetic fields. This state is manifested by the electronic structure transition caused by the spin-flop transition. The transition results in an intrinsic anomalous Hall effect and negative $c$ -axis longitudinal magnetoresistance attributable to the chiral anomaly in the ferromagnetic phases of lightly hole-doped samples. Our results establish a promising platform for exploring the underlying physics of the long-sought, ideal TRS-breaking type-II WSM.

Received 21 June 2020
Revised 25 April 2021
Accepted 8 June 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031032

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)

Anomalous Hall effect Magnetotransport Topological insulators Topological materials Topological phase transition

Antiferromagnets Single crystal materials Weyl semimetal

Angle-resolved photoemission spectroscopy Crystal growth DC susceptibility measurements Energy spectroscopy for chemical analysis Hall bar Magnetization measurements Resistivity measurements Shubnikov-de Haas effect X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Seng Huat Lee ^1,2, David Graf ^3,*, Lujin Min ^2,4, Yanglin Zhu ^1,2, Hemian Yi², Samuel Ciocys⁵, Yuanxi Wang^1,2, Eun Sang Choi³, Rabindra Basnet⁶, Arash Fereidouni⁶, Aaron Wegner ⁶, Yi-Fan Zhao², Katrina Verlinde⁴, Jingyang He^2,4, Ronald Redwing^1,4, V. Gopalan⁴, Hugh O. H. Churchill⁶, Alessandra Lanzara⁵, Nitin Samarth^1,2, Cui-Zu Chang², Jin Hu^6,†, and Z. Q. Mao ^1,2,4,‡

¹2D Crystal Consortium, Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
²Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
³National High Magnetic Field Lab, Tallahassee, Florida 32310, USA
⁴Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
⁵Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
⁶Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA

^*graf@magnet.fsu.edu
^†jinhu@uark.edu
^‡zim1@psu.edu

Popular Summary

Weyl semimetals are materials where the valence and conduction bands cross in single points, known as Weyl nodes. The discovery of Weyl semimetals has fueled tremendous interest in condensed-matter physics because they provide not only model platforms for studying concepts in high-energy physics but also a means of realizing technologically relevant exotic quantum states. Although Weyl semimetals have been demonstrated in several nonmagnetic and magnetic materials, one challenge in the current study of Weyl fermion physics is the lack of “ideal” Weyl semimetals. This article reports experimental evidence for the simplest ideal Weyl state, induced by magnetic fields in the antiferromagnetic topological insulator $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ .

In an ideal Weyl semimetal, all the Weyl nodes are at the same energy level without interference from any other energy bands, and if the location of one pair of nodes in reciprocal space (the Fourier transform of real space) is known, the location of others can be found through symmetry operations. While ideal Weyl states have been long pursued, they have been realized only in bosonic systems such as photonic crystals.

We achieve such a Weyl state by tuning the Sb:Bi ratio. When the system is tuned to a state with a small hole concentration, we find the magnetic-field-induced transition from an antiferromagnetic state to a ferromagnetic one causes an electronic structure transition, which leads to transport properties characteristic of a Weyl state: an intrinsic anomalous Hall effect caused by effective magnetic fields in momentum space as well as negative magnetoresistance induced by parallel electric and magnetic fields.

These results establish an ideal model system for further understanding of Weyl fermion physics.

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Vol. 11, Iss. 3 — July - September 2021

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Figure 1
Magnetic and transport properties of $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ . Magnetic field dependence of Hall resistivity $ρ_{y x}$ at various temperatures and magnetization $M$ at 2 K for $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ with (a) $x = 0$ and 0.22, (b)–(d) 0.26, (e) 0.39, and (f) 0.79. All these measurements are conducted with the currents applied along the ab plane and the magnetic fields perpendicular to the plane. The rose, blue, and orange regions refer to the AFM, CAFM, and FM phase regions, respectively, determined by magnetization [blue curves in (a)–(f)]. The heavily (a),(f) and moderately (e) doped samples exhibit linear magnetic field dependence for $ρ_{y x}$ or almost linear $ρ_{y x}$ background, while the lightly doped samples S3A, S3B, and S3C show nonlinear field dependence in $ρ_{y x}$ (b)–(d). The S3A, S3B, and S3C samples used in this study are taken from the same growth batch but display either electronlike (b) or holelike (c),(d) transport behavior in $ρ_{y x} (H)$ owing to inevitable chemical inhomogeneity as discussed in the text. (g) Temperature dependences of the Hall resistivity slope $d ρ_{y x} / d (μ_{o} H)$ at 1 and 10 T for the lightly hole-doped (S3B, S3C), heavily electron-doped (S2A), and heavily hole-doped (S5A) samples. (h) Temperature dependence of Hall resistivity $ρ_{y x}$ at 20 T for the lightly hole-doped (S3B and S3C), heavily electron-doped (S2A), and heavily hole-doped (S5A) samples. (i) The transverse in-plane magnetoresistivity for lightly hole-doped (S3B and S3C), heavily electron-doped (S1A), and heavily hole-doped samples (S5A). The downward and upward arrows refer to the two magnetic transitions upon increasing the magnetic field along the $c$ axis, i.e., the AFM-to-CAFM transition at $H_{c 1}$ and the CAFM-to-FM transition at $H_{c 2}$ .
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Figure 2
Band structures of $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ . (a) ARPES spectra measured on (i) sample S3D using the photon energy of 21.218 eV and (ii),(iii) sample S3E using the photon energy of 81 eV. Spectra in (ii) and (iii) are measured on two different spots of sample S3E. All the spectra in (a) are measured below $T_{N} = 25 K$ along the $Γ - K$ direction [see (b)]. (b) ARPES constant energy maps at spot 2, acquired by integrating over $- 300$ to $- 260 meV$ (left) and $- 40$ to 0 meV (right). A pointlike Fermi surface centered at Γ can be seen on the $k_{x} - k_{y}$ plane.
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Figure 3
Composition dependence of carrier density $n$ and transport mobility $μ_{H}$ of $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ . For heavily and moderately doped samples showing linear or almost linear $ρ_{y x}$ (Fig. 1 and Supplemental Material, Fig. S1 [48]), $n$ is obtained from the linear slope of $ρ_{y x} (H)$ at $T = 2 K$ for the FM phase (purple diamond) and 75 K for the PM phase (red triangle). The black and blue circles represent transport mobility $μ_{H} [= R_{H} / ρ_{x x} (0)]$ for the FM and PM phases, respectively. For lightly hole-doped samples (from the $x = 0.26$ batch) with nonlinear $ρ_{y x} (H)$ , $n$ (empty orange triangle) and $μ_{H}$ (empty blue circle) are extracted from the two-band model fit (see Supplemental Material, Sec. S2 [48]), and only the data of dominant bands are presented here. The magenta bar represents the maximal statistical error of the measured Sb content by EDX.
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Figure 4
Anomalous Hall effect in $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ . (a) Field dependence of anomalous Hall conductivity $σ_{x y}^{AH}$ for samples S1A, S3A, S4A, and S5A at 2 and 0.7 K. $σ_{x y}^{AH}$ is derived using $σ_{x y}^{AH} = ρ_{y x}^{AH} / [ρ_{x x}^{2} + ρ_{y x}^{2}]$ , where $ρ_{y x}^{AH}$ is the anomalous Hall resistivity, obtained after subtracting the normal Hall contribution $(ρ_{y x}^{N} = R_{H} H)$ (see Sec. 3). (b) Field dependence of $σ_{x y}^{2 K} - σ_{x y}^{24 K}$ for S3B, S3C, and S5A. $σ_{x y}^{2 K}$ and $σ_{x y}^{24 K}$ are extracted using $σ_{x y} = ρ_{y x} / (ρ_{x x}^{2} + ρ_{y x}^{2})$ at 2 and 24 K, respectively. (c) The maximal anomalous Hall angle $Θ_{x y}^{AH} = σ_{x y}^{AH} / σ_{x x}$ in the FM phase as a function of the carrier density, obtained from the field dependence of $Θ_{x y}^{AH}$ shown in Supplemental Material, Fig. S3 [48]. All data points are obtained at 2 K, except for S4A (0.7 K, red circle). (d) Temperature dependence of longitudinal resistivity $ρ_{x x}$ for S3B at various fields (applied along the $c$ axis).
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Figure 5
Magnetoresistivity and SdH oscillations in $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$ . (a),(b) The $c$ -axis magnetoresistivity $MR = [ρ_{z z} (H) - ρ_{z z} (0)] / ρ_{z z} (0)$ under various field orientations for (a) the lightly (S3F) and (b) heavily hole-doped (S5B) samples. The schematic in (b) illustrates the experimental setup for the $c$ -axis MR angular dependence measurements. (c) FFT spectra of $- d^{2} ρ_{x x} / d {(μ_{o} H)}^{2}$ for various moderately and lightly electron- and hole-doped samples [see Supplemental Material, Fig. S5(a) [48], for the SdH oscillations]. (d),(g) In-plane transverse MR of samples (d) S3A and (g) S4A at various temperatures. (e),(h) The second derivative of the in-plane resistivity $ρ_{x x} (H)$ with respect to field $H$ (perpendicular to the plane) for samples (e) S3A and (h) S4A as a function of the inverse of the field at various temperatures. (f),(i) FFT spectra of the second derivative of $ρ_{x x} (H)$ for samples (f) S3A and (i) S4A at various temperatures. The insets in both (f) and (i) show the oscillation frequency ( $f_{osc}$ ) as a function of the temperature for samples S3A and S4A, respectively. The error bar shown in the insets in (f) and (i) is defined as the difference of the oscillation frequencies obtained from the FFT spectra of $- d^{2} ρ_{x x} / d {(μ_{o} H)}^{2}$ and $Δ ρ_{x x} (H)$ [the oscillatory component of $ρ_{x x} (H)$ ], respectively. All the measurements shown in (c), (d), and (g) are conducted with the currents applied along the ab plane and the magnetic fields perpendicular to the plane.
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Physical Review X

Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator Mn(Bi1−xSbx)2Te4

Phys. Rev. X 11, 031032 – Published 10 August 2021

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Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator $Mn {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{4}$