Elusive Dirac magnons: experiment meets theory

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons in a two-dimensional CrI3 crystal and in a three-dimensional Heisenberg magnet Cu3TeO6. I will describe the results of an inelastic neutron scattering investigation on a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. I will argue that the magnon dispersion relation is well described by a simple magnetic Hamiltonian with strong easy-plane exchange anisotropy. Importantly, a magnon Dirac cone is found along the edge of the 3D Brillouin zone. However, the simplistic model does not capture the entire picture, therefore I will explain some required modifications. Lastly, I will present a perturbative formulation which allows generating an effective two-band bosonic model, similar to graphene, to analyze band touchings in bosonic Hamiltonians. Our results establish CoTiO3 as a model material to study interacting Dirac bosons in a 3D quantum XY magnet, but pose some yet to be resolved intriguing questions. 

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