Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet ${MnBi}_{2} {Te}_{4}$

Hengxin Tan and Binghai Yan

Phys. Rev. Lett. 130, 126702 – Published 24 March 2023

Abstract

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.

Received 27 July 2022
Accepted 3 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.126702

Physics Subject Headings (PhySH)

Defects First-principles calculations Quantum anomalous Hall effect Topological materials

Magnetic systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hengxin Tan and Binghai Yan

Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel

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Vol. 130, Iss. 12 — 24 March 2023

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Figure 1
Cation co-antisite configurations in the surface SL. sNN: nearest-neighboring ${Mn}_{Bi}$ and ${Bi}_{Mn}$ on the surface side; sNNN: next nearest-neighboring ${Mn}_{Bi}$ and ${Bi}_{Mn}$ on the surface side; bNN: nearest-neighboring ${Mn}_{Bi}$ and ${Bi}_{Mn}$ on the bulk side; bNNN: next nearest-neighboring ${Mn}_{Bi}$ and ${Bi}_{Mn}$ on the bulk side. For simplicity, only the surface SL is shown where the bold dashed line indicates the surface. The orange vector in each panel connects the antisites ${Mn}_{Bi}$ and ${Bi}_{Mn}$ .
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Figure 2
Band structures of the different co-antisites as shown in Fig. 1. Upper panels: band structures under $A$ -type AFM. Lower panels: band structures under FM. For better comparison, the band structures of the perfect surface are also shown (titled perfect). The color red stands for the surface SL weight to the bands while the color gray stands for the weight from the rest of the slab. Here we still employ the $− M − Γ − M$ $k$ path of the hexagonal Brillouin zone of the perfect surface, though the surfaces with antisites may no longer have the hexagonal Brillouin zone. The band structures along the $− K − Γ − K$ line of the hexagonal Brillouin zone share similar band characters [65]. Band gaps are found in Table 1.
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Figure 3
Charge distribution of the top surface valence band (SVB) and bottom surface conduction band (SCB) at the $Γ$ point of the perfect surface (a) and surface with sNNN co-antisites (b) (see the configuration in Fig. 1). Corresponding band structures under AFM and FM are shown in Fig. 2. The left part of each panel shows the charge distribution in the lattice (isosurface of $3.4 \times 10^{- 4} e / Å^{3}$ ), and the right part shows the corresponding planar average along the out-of-plane direction [68]. The red vectors indicate the magnetic configuration in each SL. Only three SL layers are shown for simplicity, where the top dashed line of each panel indicates the surface. Compared to the perfect surface, the charge density of the sNNN surface is distributed closer to the vdW gap (the centroid of charge density is moved 1–2 Å toward the vdW gap).
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Figure 4
Schematics for the relationship between surface charge distribution and magnetic gap under AFM (a) and FM (b). The red vectors represent the magnetic configuration. For a perfect surface where surface states (blue curves) are mainly distributed in the surface SL (gray rectangles), the topological surface states (blue linear crossing lines) under both AFM and FM open a magnetic gap. For a defective surface where surface states (orange curves) are pushed down toward the second SL, the magnetic gap is diminished heavily under AFM while not changing under FM (orange crossing lines).
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Physical Review Letters

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet MnBi2Te4

Hengxin Tan and Binghai Yan

Phys. Rev. Lett. 130, 126702 – Published 24 March 2023

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Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet ${MnBi}_{2} {Te}_{4}$