Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co 2 MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in our samples. Our experimental results suggest a rich interplay of strongly correlated electrons and topology in this quantum magnet.The discovery of topological phases of matter has led to a new paradigm in physics, 30 which not only explores the analogs of particles relevant for high energy physics, but also 31 offers new perspectives and pathways for the application of quantum materials [1][2][3][4][5][6][7][8][9][10]. To 32 date, most topological phases have been discovered in non-magnetic materials [6][7][8], which 33 severely limits their magnetic field tunability and electronic/magnetic functionality. Iden-34 tifying and understanding electronic topology in magnetic materials will not only provide 35 indispensable information to make their existing magnetic properties more robust, but also 36 has the potential to lead to the discovery of novel magnetic response that can be used to ex-37 plore future spintronics technology. Recently, several magnets were found to exhibit a large 38 anomalous Hall response in transport, which has been linked to a large Berry curvature in 39 their electronic structures [11][12][13][14][15]. However, it is largely unclear in experiment whether the 40 Berry curvature originates from a topological band structure, such as Dirac/Weyl point or 41 line nodes, due to the lack of spectroscopic investigation. In particular, there is no direct vi-42 sualization of a topological magnetic phase demonstrating a bulk-boundary correspondence 43 with associated anomalous transport. 44Here we use angle-resolved photoemission spectroscopy (ARPES), ab initio calculation 45 and transport to explore the electronic topological phase of the ferromagnet Co 2 MnGa [10]. 46In our ARPES spectra we discover a line node in the bulk of the sample. Taken together with 47 our ab initio calculations, we conclude that we observe Weyl lines protected by crystalline 48 mirror symmetry and requiring magnetic order. In ARPES we further observe drumhead 49 surface states connecting the bulk Weyl lines, revealing a bulk-boundary correspondence in a 50 magnet. Combining our ARPES and ab initio calculation results with transport, we further 51 find that Berry curvature concentrated by the Weyl lines accounts for the giant intrinsic 52 anomal...
Magnetic topological phases of quantum matter are an emerging frontier in physics and material science [1][2][3][4]. Along these lines, several kagome magnets [5][6][7][8][9] have appeared as the most promising platforms. However, the magnetic nature of these materials in the presence of topological state remains an unsolved issue [5][6][7][8][9]. Here, we explore magnetic correlations in the kagome magnet Co 3 Sn 2 S 2 . Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an outof-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a nonmagnetic state. Strikingly, the reduction of the anomalous Hall conductivity above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature field via external tuning of magnetic order. Our study shows that Co 3 Sn 2 S 2 is a rare example where the magnetic competition drives the thermodynamic evolution * Electronic address: zurab.guguchia@psi.ch of the Berry curvature field, thus tuning its topological state.The kagome lattice is a two-dimensional pattern of corner-sharing triangles. With this unusual symmetry and the associated geometrical frustration, the kagome lattice can host peculiar states including flat bands [8], Dirac fermions [5,6] and spin liquid phases [7,10]. In particular, magnetic kagome materials offer a fertile ground to study emergent behaviors resulting from the interplay between unconventional magnetism and band topology. Recently, transition-metal based kagome magnets [5][6][7][8][9][10][11][12][13] are emerging as outstanding candidates for such studies, as they feature both large Berry curvature fields and unusual magnetic tunability. In this family, the kagome magnet Co 3 Sn 2 S 2 is found to exhibit both a large anomalous Hall effect and anomalous Hall angle, and is identified as a promising Weyl semimetal candidate [9,11,14,15]. However, despite knowing the magnetic ground state is ferromagnetic below T C = 177 K [16] with spins aligned along the c-axis [9, 11, 17] (see Figs. 1 a and b) there is no report of its magnetic tunability or phase diagram, and its interplay with the topological band structure. Here we use high-resolution µSR to systematically characterize the phase diagram, uncovering another intriguing in-plane antiferromagnetic phase. The magnetic competition between these two phases is further found to be highly tunable via applying either pressure [18][19][20][21] or magnetic field. Combined with first principles calculations, we discover that the tunable magnetic correlation plays a key role in determining the giant anomalous Hall transp...
Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...
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