There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator-a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes. DOI: 10.1103/PhysRevLett.115.147201 PACS numbers: 75.30.Ds When quantum particles are confined to move in reduced dimensions, such as in planes, unexpectedly rich physics can emerge as a result of the geometry and interactions. The quantum Hall effect is a famous example, which results from placing a two-dimensional (2D) gas of electrons or quasiparticles in a large magnetic field [1]. Pioneering theoretical work by Haldane showed that some systems may inherently possess topological bands that allow them to exhibit quantum Hall physics without applied magnetic fields [2]. The discovery of materials in which strong spin-orbit coupling leads to topological bands, such as topological insulators, has led to a flurry of activity in condensed matter physics research [3,4]. Recently, theoretical studies have focused on 2D topological band structures that include flat bands due to the possibility of achieving fractional quantum hall physics in the absence of magnetic fields [5]. Flat bands (bands that are dispersionless in energy) hold unique interest because the interaction energy between particles may dominate the kinetic energy, leading to novel correlated electron states. A number of theoretical models for the fractional quantum Hall effect have been proposed based on flat topological bands [6][7][8]; however, these invariably require tuning of parameters, which is difficult to control in real materials.Topological band structures are not unique to systems with electronlike quasiparticles. It has been demonstrated that topological photon modes can be realized in experimental systems [9][10][11]. Possible realizations of topological bosonic systems that include flat bands have been proposed using dipolar molecules trapped in an optical lattice [12], and using photonic lattices [13] based on the interaction between photons and arrays of superconducting circuits [14], although experimental confirmation has yet to be demonstrated. In this Letter, we show that topological bands exist for another class of quasiparticles: magnons in an insulating ferromagnet. Our material serves as the first realization of an effectively 2D topological magnon insulator [15], an electrically insulating state in which the spin degre...

At low temperatures, the thermal conductivity of spin excitations in a magnetic insulator can exceed that of phonons. However, because they are charge neutral, the spin waves are not expected to display a thermal Hall effect. However, in the kagome lattice, theory predicts that the Berry curvature leads to a thermal Hall conductivity κ xy . Here we report observation of a large κ xy in the kagome magnet Cu(1-3, bdc) which orders magnetically at 1.8 K. The observed κ xy undergoes a remarkable sign reversal with changes in temperature or magnetic field, associated with sign alternation of the Chern flux between magnon bands. The close correlation between κ xy and κ xx firmly precludes a phonon origin for the thermal Hall effect.

The quantum mechanical (Berry) phase of the electronic wavefunction plays a critical role in the anomalous 1,2 and spin Hall e ects 3,4 , including their quantized limits 5-7 . While progress has been made in understanding these e ects in ferromagnets 8 , less is known in antiferromagnetic systems. Here we present a study of antiferromagnet GdPtBi, whose electronic structure is similar to that of the topologically non-trivial HgTe (refs 9-11), and where the Gd ions o er the possibility to tune the Berry phase via control of the spin texture. We show that this system supports an anomalous Hall angle Θ AH > 0.1, comparable to the largest observed in bulk ferromagnets 12 and significantly larger than in other antiferromagnets 13 . Neutron scattering measurements and electronic structure calculations suggest that this e ect originates from avoided crossing or Weyl points that develop near the Fermi level due to a breaking of combined timereversal and lattice symmetries. Berry phase e ects associated with such symmetry breaking have recently been explored in kagome networks 14-17 ; our results extend this to half-Heusler systems with non-trivial band topology. The magnetic textures indicated here may also provide pathways towards realizing the topological insulating and semimetallic states 9-11,18,19 predicted in this material class.The ordinary Hall effect is due to the Lorentz force bending of charge carriers perpendicular to a magnetic field. In systems where time-reversal symmetry (TRS) is spontaneously broken, it typically can be overwhelmed by a different class of mechanisms for transverse velocity. In such systems, there are contributions to transverse velocity from both extrinsic effects due to spindependent scattering 13 and intrinsic effects related to real space 20,21 and momentum space 2 Berry phase mechanisms. The former is relevant in systems with non-coplanar spin textures with finite scalar spin chirality χ ijk = S i · (S j × S k ), where S n are spins, while the latter generically occurs in TRS-broken systems originating from the spin-orbit-interaction-induced Berry curvature of the filled bands. The anomalous Hall effect (AHE) due to magnetic texture is most often associated with finite χ ijk and tends to exhibit relatively small anomalous Hall angles Θ AH 0.01 (such as SrFeO 3 (ref. 22) or Pr 2 Ir 2 O 7 (ref. 23)), while intrinsic band-structure-based effects are common in ferromagnetic systems and can be significantly larger 13 . Recent theoretical work has suggested that effects that rely on both magnetic texture and strong spin-orbit coupling may exist in noncollinear antiferromagnets that lead to significant Hall responses 14 . Single-crystal studies of Mn 3 Sn and Mn 3 Ge have been shown to support Θ AH 0.02 and 0.05, respectively, originating from its inverse triangular spin structure and electronic structure 16,17 .Here we study single crystals of GdPtBi, a member of the family RPtBi (R is a rare earth element) known to exhibit antiferromagnetic ordering 24 . As shown in Fig. 1a, this syste...