Diamond Annual Review 2019/20

30 31 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 1 9 / 2 0 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 1 9 / 2 0 ab initio calculations for thismaterial 4 , there are three pairs ofWeyl points within each bulk Brillouin zone (BZ) connected by the SFAs (Fig. 1c).The temperature- dependent transport (Fig. 1d) and magnetisation measurements (Fig. 1d, inset) clearly illustrate that an FM transition occurs at a critical temperature T C = 175 K with a hysteresis loop. According to the calculations, the SFAs in Co 3 Sn 2 S 2 are located around the K’ of the BZ (Fig. 2a (i)), formed by a line segment that connects one pair of Weyl points with opposite chirality in each BZ. These line segments from three Figure 3: (a) Schematic of the measurement k y -k z plane (vertical yellow plane) in 3b. Weyl points are also illustrated; (b) Photoemission intensity plot along the k y -k z plane (yellow plane in 3a) near Fermi level. Overlaid red contours are calculated bulk FSs; (c) 3D ARPES spectra intensity plot measured with 115 eV photon energy, showing both the FS (top surface) and the band dispersions (side surfaces). The grey plane indicates the location of the band dispersion cut in 3d. (d) Band dispersion showing linear Weyl dispersion, in agreement with the calculations (red curves overlaid). a c d Structures and Surfaces Group Beamline I05 Discovery of theWeyl fermion in a ferromagnetic crystal Related publication: Liu D. F., Liang A. J., Liu E. K., Xu Q. N., LiY.W., Chen C., Pei D., ShiW. J., Mo S. K., Dudin P., KimT., Cacho C., Li G., SunY.,Yang L. X., Liu Z. K., Parkin S. S. P., Felser C. & ChenY. L. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365 , 1282 (2019). DOI: 10.1126/ science.aav2873 Publication keywords: MagneticWeyl semimetal;Weyl fermion; Fermi-arcs; Angle-Resolved Photoemission Spectroscopy (ARPES) C ondensed matter systems, such as crystalline solids, can serve as a platform for the study of phenomena in other fields of physics, including high energy physics. In some ways, a crystal can be viewed as a ‘mini-universe’. An international team of researchers were intrigued by the search for a massless chiral particle – theWeyl fermion – in a magnetic compound. The existence of theWeyl fermion was initially proposed in 1929, but never proven. In 2011, there was a prediction that a magnetic crystal can host Weyl fermions, and the unique electronic structures in a crystal with Weyl fermions could give rise to many intriguing physical phenomena. The research team used the Angle-Resolved PhotoEmission Spectroscopy (ARPES) beamline (I05) to investigate the electronic structures of the crystal. They successfully found both the bulkWeyl fermions and the unique surface Fermi-arcs that connect them. The exoticWeyl fermions in this compound havemany interesting and useful properties. Their enormous electronmobilitymeans that they could be used for fast electronic devices. A large magnetoresistance makes them a candidate for large density magnetic storage devices. With spin-polarised surface electrons, this compound could be used in spintronics devices, and the bulk-surface electron correlation could be useful for unique optoelectronic applications. Weyl semimetals (WSMs) represent a novel type of topological matter that hosts emergent Weyl fermions in the bulk of a crystal and associated surface electrons that form an exotic unclosed surface Fermi surface (called the surface Fermi-arcs, or SFAs).The unique electronic structures in theWSM can give rise to many intriguing physical phenomena such as chiral magnetic effects, unusually large anomalous Hall effect and quantum anomalous Hall effect 1 . In solids, WSMs can exist in crystals that break the time-reversal symmetry (TRS) or inversion symmetry (IS), or both.TheTRS-broken (i.e. magnetic)WSMs were first proposed in 2011 2 and have many preferred properties over the IS-breakingWSMs 3 . However, despite the many candidates predicted over the years, experimental confirmation that they exist had remained elusive. In this work, Angle-Resolved PhotoEmission Spectroscopy (ARPES) was used to systematically study the electronic structures of a Kagomé crystal Co 3 Sn 2 S 2 and directly observe the characteristic Weyl fermions and the associated SFAs, thus confirming the existence of magneticWSMs 3 . The crystal structure of Co 3 Sn 2 S 2 is composed of stacked ...-Sn-[S-(Co 3 -Sn)-S]-... layers (Fig. 1a). In each Sn-[S-(Co 3 -Sn)-S] layer group, the central Co layer forms a two-dimensional Kagomé lattice with an Sn atom at the centre of the hexagon; S atoms are located alternately above and below the triangles formed by the Co atoms, with the adjacent Sn-[S-(Co 3 -Sn)-S] layer groups linked by layer-sharing Sn atoms. The TRS-breaking WSM phase in Co 3 Sn 2 S 2 (Fig. 1b) is caused by the joint effects of crystal field, ferromagnetism (FM), and spin-orbital coupling (SOC). The crystal field first mixes the valence band (VB) and conduction band (CB) to form four-fold degenerate nodal lines (Fig. 1b (ii), black curve); subsequently, the degeneracy of the nodal line is lifted (Fig. 1b (iii), green curve) by the FM transition that breaks the TRS; finally, SOC splits the doubly degenerate nodal line in Fig. 1b (iii) into a pair of Weyl points with opposite chirality (Fig. 1b (iv)). According to adjacent BZs can form a triangle-shaped surface Fermi surface (FS) piece. This unusual surface FS topology was indeed observed experimentally (Fig. 2a (ii)-(iii)), where the unchanged shape of these line-segment FS pieces from different photon energies indicates their surface origin (Fig. 2a (ii)-(iii)). Notably, each line-segment FS piece merges into the bulk FS pockets near the M’ point of the BZ (Fig. 2a (i)), in excellent agreement with the calculations. In addition to the FS topology, the dispersions of the topological surface states (TSSs) that result in the SFAs from different photon energies are also in good agreement with calculations (Fig. 2b, c). With the SFAs identified, a search was undertaken for the characteristic bulk Weyl fermion dispersion. For this purpose, broad range (50 to 150 eV) photon energy dependent ARPES measurements were performed to precisely identify the k z momentum locations of the Weyl points (Fig. 3b). The bulk bands with strong k z dispersion can be seen in the k y –k z spectra intensity map (Fig. 3b), agreeing well with the calculations (overlaid in red in Fig. 3b). The agreement between experiments and calculations (Fig. 3b), allows the identification of the bulk Weyl points in Co 3 Sn 2 S 2 , which lie at k z = ±0.086 Å −1 planes (Fig. 3a) and can be accessed by using 115 eV photons (corresponding to k z = −0.086 Å −1 in Fig. 3a). To precisely locate the in-plane momentum loci of the Weyl points, k x -k y FS mapping (Fig. 3c) of the band structures across the surface BZ were performed first, then with a focus on band dispersions that cut through theWeyl point (see the cutting plane in Fig. 3c). Indeed, point-like FSs (the Weyl points) were observed as illustrated in Fig. 3c. The band dispersions in Fig. 3d also show the linear crossing of the bands at the Weyl point, in good agreement with the calculations. The observation of the distinctive SFAs and bulk Weyl points with linear dispersions, together with the overall agreement of the measurements with theoretical calculations, establishes Co 3 Sn 2 S 2 as a magneticWSM.This finding extends the possibilities for the exploration of other exotic phenomena associated with TRS-breaking WSMs (such as the unusually large anomalous Hall conductivity and quantum anomalous Hall effects at the 2D limit) and potential applications. References: 1. Armitage N. P. et al. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90 , 015001 (2018). DOI:10.1103/RevModPhys.90.015001 2. Wan X. et al . Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83 , 205101 (2011). DOI:10.1103/PhysRevB.83.205101 3. Liu D. F. et al. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365 , 1282 (2019). DOI:10.1126/science.aav2873 4. Xu Q. et al. Topological surface Fermi arcs in the magnetic Weyl semimetal Co 3 Sn 2 S 2 . Phys. Rev. B 97 , 235416 (2018). DOI:10.1103/PhysRevB.97.235416 Funding acknowledgement: This work was supported by the Shanghai Municipal Science and Technology Major Project (grant no. 2018SHZDZX02), the Alexander von Humboldt Foundation, the National Natural Science Foundation of China (grant nos. 11774190, 11634009, 11674229, and 11974394), the National Key R&D Program of China (grant nos. 2017YFA0305400 and 2017YFA0206303), the Tsinghua University Initiative Scientific Research Program, and the Wurzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147, no. 39085490). Corresponding author: Prof Yulin Chen, University of Oxford, yulin.chen@physics.ox.ac.uk Figure 1: (a) Crystal structure of Co 3 Sn 2 S 2 ; (b) Mechanism for the magnetic WSM phase in Co 3 Sn 2 S 2 ; (c) Schematic of the bulk and surface Brillouin zones along the (001) surface of Co 3 Sn 2 S 2 , with the Weyl points marked and connected by SFAs (yellow line segments); (d) Temperature dependences of longitudinal electric resistivity. Inset: Hystersis loop of the magnetisation (external magnetic field is along the z axis) measured at T= 2 K, showing a typical ferromagnetic behaviour. a b c d Figure 2: (a) Comparison of (i) the calculated FS from both bulk and surface states and (ii)-(iv) the experimental FSs under different photon energies. The magenta and green dots in (i) represent the Weyl points with opposite chirality and the SFAs are indicated by red arrows; (b) Comparison of the dispersion from (i) calculated TSS along the high Γ-K’-Γ direction and (ii)-(iv) the experimental TSSs; (c) 3D intensity plot of the experimental band structure near the K’ point. a b c b