Discovery of Weyl Nodal Lines in a Single-Layer Ferromagnet

Baojie Feng, Run-Wu Zhang, Ya Feng, Botao Fu, Shilong Wu, Koji Miyamoto, Shaolong He, Lan Chen, Kehui Wu, Kenya Shimada, Taichi Okuda, and Yugui Yao

Phys. Rev. Lett. 123, 116401 – Published 12 September 2019

Abstract

Two-dimensional (2D) materials have attracted great attention and spurred rapid development in both fundamental research and device applications. The search for exotic physical properties, such as magnetic and topological order, in 2D materials could enable the realization of novel quantum devices and is therefore at the forefront of materials science. Here, we report the discovery of twofold degenerate Weyl nodal lines in a 2D ferromagnetic material, a single-layer gadolinium-silver compound, based on combined angle-resolved photoemission spectroscopy measurements and theoretical calculations. These Weyl nodal lines are symmetry protected and thus robust against external perturbations. The coexistence of magnetic and topological order in a 2D material is likely to inform ongoing efforts study the rich physics in 2D topological ferromagnets.

Received 23 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.116401

Physics Subject Headings (PhySH)

Ferromagnetism First-principles calculations Topological materials

Monolayer films Node-line semimetals

Angle-resolved photoemission spectroscopy Molecular beam epitaxy Molecular dynamics X-ray photoelectron spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Baojie Feng ^1,2,3,*, Run-Wu Zhang⁴, Ya Feng^5,2, Botao Fu⁶, Shilong Wu⁷, Koji Miyamoto², Shaolong He⁵, Lan Chen^1,3, Kehui Wu^1,3, Kenya Shimada², Taichi Okuda², and Yugui Yao^4,†

¹Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Hiroshima Synchrotron Radiation Center, Hiroshima University, 2-313 Kagamiyama, Higashi-Hiroshima 739-0046, Japan
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing 100081, China
⁵Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
⁶College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China
⁷Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan

^*bjfeng@iphy.ac.cn
^†ygyao@bit.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 123, Iss. 11 — 13 September 2019

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
First-principles calculation results for freestanding ${GdAg}_{2}$ . (a) Optimized structure of single-layer ${GdAg}_{2}$ . Large pink and small grey balls represent Gd and Ag atoms, respectively. (b) Spin-resolved band structures of single-layer ${GdAg}_{2}$ without spin-orbit coupling (SOC) effects. Red and blue lines represent spin up and spin down, respectively. The black circles indicate the gapless band crossing points. The plus and minus signs indicate the $M_{z}$ parity of each band, which are also valid when the SOC is considered. (c) Orbital-projected band structures of single-layer ${GdAg}_{2}$ without SOC. (d) Band structures of single-layer ${GdAg}_{2}$ after shifting the Gd atoms by 0.2 Å in the out-of-plane direction. (e) Momentum distribution of the band crossing points without SOC. The crossing points form four nodal lines: NL1, NL2, NL3, and NL4. (f) and (g) Calculated band structures with SOC. The magnetization direction is out of plane in (f) and in plane in (g). The gapless and gapped band crossing points are indicated by black and red circles, respectively.
Reuse & Permissions
Figure 2
Low-energy electron diffraction (LEED) and photoemission measurements of single-layer ${GdAg}_{2}$ on Ag(111). (a) A LEED pattern of single-layer ${GdAg}_{2}$ on Ag(111) measured with a beam energy of 50 eV. The $1 \times 1$ spots of Ag(111) and ${GdAg}_{2}$ are indicated by blue and red arrows, respectively. (b) Angle-integrated photoemission spectra of single-layer ${GdAg}_{2}$ on Ag(111), which include both on (red) and off (blue) resonance of the Gd $4 f$ levels. The spectra were acquired with photon energies of 145.2 eV (red) and 35 eV (blue). (c) Second-derivative ARPES intensity images along the $Γ − M$ direction acquired with photon energies of 16, 20, and 23 eV. Black dashed lines are a visual guide to trace the band dispersions.
Reuse & Permissions
Figure 3
ARPES measurements of the electronic structure of single-layer ${GdAg}_{2}$ on Ag(111). (a)–(b) ARPES intensity images along various momentum cuts from $Γ − K$ to $Γ − M$ . The corresponding momentum paths in the Brillouin zone are shown in the inset. The photon energy is 21 eV and the polarization is $p$ . (f)–(j) Corresponding second-derivative images with respect to the momentum to enhance the contrast of the bands.
Reuse & Permissions
Figure 4
Orbital-projected band structures of single-layer ${GdAg}_{2}$ on Ag(111). The Gd atoms sit on the (a) fcc and (b) hcp sites of the underlying Ag(111) substrates. Contributions from the Ag $s$ , Ag $p$ , and Gd $d$ orbitals are shown in green, blue, and red, respectively. The yellow shaded circles highlight the position of NL3.
Reuse & Permissions

Physical Review Letters