Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogues of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example, in which Weyl points can be manipulated in situ in the laboratory by applied fields. We discuss their appearance specifically in the breathing pyrochlore lattice, and give some general discussion of conditions to find Weyl magnons, and how they may be probed experimentally. Our work may inspire a re-examination of the magnetic excitations in many magnetically ordered systems.

We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl semimetal", in which one Weyl node is of type-I while the other is of type-II. For the hybrid Weyl semimetal, we further demonstrate the bulk Fermi surfaces and the topologically protected surface states, analyze the unique Landau level structure and quantum oscillation, and discuss the conditions for possible material realization.Introduction.-Since the theoretical and experimental discovery of topological insulator 1,2 , the study of topological states of matter has become one of the major topics in condensed matter physics. Apart from the triumphs of systems with full energy gaps, the concept and discovery of Weyl semimetals (WSMs) have stimulated intensive activities in understanding the band topology for gapless systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . A WSM, in the original setting, has linear conic band crossings at the Fermi energy 5 . These band crossing points, i.e., the "Weyl nodes", behave like sources and sinks of the Berry curvature in the momentum space and are topologically protected. Based on the bulk-boundary correspondence, the surface state of a WSM takes the form of Fermi arc that connects a pair of Weyl points with opposite chiralities 5 .

Motivated by the experiments on the rare-earth double perovskites, we propose a generalized Kitaev-Heisenberg model to describe the generic interaction between the spin-orbit-entangled Kramers doublets of the rare-earth moments. We carry out a systematic analysis of the mean-field phase diagram of this new model. In the phase diagram, there exist large regions with a continuous U (1) or O(3) degeneracy. Since no symmetry of the model protects such a continuous degeneracy, we predict that the quantum fluctuation lifts the continuous degeneracy and favors various magnetic orders in the phase diagram. From this order by quantum disorder mechanism, we further predict that the magnetic excitations of the resulting ordered phases are characterized by nearly gapless pseudo-Goldstone modes. We find that there exist Weyl magnon excitations for certain magnetic orders. We expect our prediction to inspire further study of Kitaev physics, the order by quantum disorder phenomenon and topological spin wave modes in the rare-earth magnets and the systems alike.

We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first-and second-neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are responsible for the frustrated criticality from the quantum paramagnet to the ordered phases. This work illustrates the effects of magnetic frustration on both magnetic orderings and the magnetic excitations. We discuss the experimental relevance to various Ni-based honeycomb lattice magnets.