Ferromagnetic Weyl semimetal phase in a tetragonal structure

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Ferromagnetic Weyl semimetal phase in a tetragonal structure

Y. J. Jin, R. Wang, Z. J. Chen, J. Z. Zhao, Y. J. Zhao, and H. Xu

Phys. Rev. B 96, 201102(R) – Published 2 November 2017

Abstract

Magnetic topological semimetals have drawn significant interest since they can combine band topology with intrinsic magnetic order. Here, we propose that ideal Weyl semimetal features can coexist with a ferromagnetic (FM) ground state in a class of compounds with centrosymmetric tetragonal structures. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetry protected band structures from a node-line type to a Weyl one in the presence of spin-orbital coupling. The FM node-line semimetal phase is protected by mirror symmetry with the reflection-invariant plane perpendicular to the magnetic order. Within mirror symmetry breaking due to magnetization along other directions, the gapless node-line loop will degenerate to only one pair of Weyl points protected by rotational symmetry along the magnetic axis, which is largely separated in momentum space. Such a FM Weyl semimetal phase offers a nice platform with a minimum number of Weyl points in a condensed matter system. These findings provide several realistic candidates for the investigation of topological semimetals with time-reversal symmetry breaking, especially demonstrating the use of system symmetry as a powerful recipe for discovering FM Weyl semimetals with attractive features.

Received 11 June 2017
Revised 31 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.201102

Physics Subject Headings (PhySH)

Electronic structure Ferromagnetism

Weyl semimetal

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. J. Jin¹, R. Wang^1,2, Z. J. Chen^1,3, J. Z. Zhao^1,4, Y. J. Zhao³, and H. Xu^1,*

¹Department of Physics, South University of Science and Technology of China, Shenzhen 518055, People's Republic of China
²Institute for Structure and Function & Department of Physics, Chongqing University, Chongqing 400044, People's Republic of China
³Department of Physics, South China University of Technology, Guangzhou 510640, People's Republic of China
⁴Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China

^*xuh@sustc.edu.cn

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Issue

Vol. 96, Iss. 20 — 15 November 2017

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Images

Figure 1
Crystal structure and Brillouin zone (BZ). (a) Side and (b) top views of the crystal structure of $β − V_{2} {OPO}_{4}$ with space group $I 4_{1} a m d$ (No. 141). V, P, and O atoms are represented by blue, green, and red spheres, respectively. (c) The body-centered-tetragonal (bct) BZ and the corresponding (001) surface BZ. The high-symmetry points are indicated. Two Weyl points with opposite chirality are symmetrically located at the $Γ − X$ axis as red ( $C = + 1$ ) and black ( $C = - 1$ ) dots, with magnetization along the [110] direction.
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Figure 2
(a) The band structure of $β − V_{2} {OPO}_{4}$ along high-symmetry lines without spin-orbital coupling (SOC). The majority and minority spin bands are denoted by the solid (black) and dashed (red) lines, respectively. (b) Band structure with SOC. The upper right inset represents the bands in the $Γ − Σ$ direction with a [001] magnetization direction, and each band corresponds to either of the mirror eigenvalues $i$ and $- i$ . The lower left and right panels respectively denote the bands in the $Γ − X$ and $Γ − Σ$ directions with a [110] magnetization direction. The two crossing bands in $Γ − X$ respectively belong to the two irreducible representations $Γ_{3}$ and $Γ_{4}$ of $C_{2}^{110}$ .
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Figure 3
(a) $β − V_{2} {OPO}_{4}$ with the magnetization direction along the [001] axis, and a variation of the Berry phase along the high-symmetry lines in a $k_{z} = 0$ plane. (b) With the magnetization direction along the [110] axis, the evolution of the average position of Wannier centers obtained by the Wilson-loop method applied on a sphere that encloses a Weyl point. The average Wannier center shifts downwards from south to north, indicating a negative chirality $W^{-}$ . The average Wannier center shifts upwards from south to north, indicating a positive chirality $W^{+}$ . (c) The distribution of Berry curvature for the $k_{z} = 0$ plane. The red and black regions denote the Weyl points with negative and positive chirality, respectively.
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Figure 4
Surface states and Fermi surfaces of $β − V_{2} {OPO}_{4}$ with magnetization along the [110] direction. (a) The energy bands projected on the (001) surface. In the left of (a), the upper and lower panels show magnified views of the regions near the $\bar{X}$ and $\bar{Y}$ points, respectively. (b) The corresponding Fermi surface for the (001) surface. The projected Fermi surface is calculated with a chemical potential at 60 meV above the Fermi level. (c) The spectral function with only a surface contribution of (b). The yellow and black dots in (b) and (c) denote the Weyl points with positive and negative chirality projected on the (001) surface, respectively.
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