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 above an Ising-like ferromagnetic ground state in a twodimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI3, and in a 3D Heisenberg magnet Cu3TeO6. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO3 features ferromagnetic layers of Co 2+ , stacked antiferromagnetically along the c-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO3 as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electron in solids described by a Dirac equation. In particular, the fruitful analogy between fundamental massless Weyl-Dirac fermions in Nature and electrons in graphene or topological semimetals has allowed physicists to simulate theories of particle physics using tabletop experiments [1][2][3][4][5][6]. Remarkably, the concept of Dirac particles is not limited to electrons or other fermionic quasiparticles, prompting a search for analogues in photonic crystals [7,8], acoustic metamaterials [9], and quantum magnets [10][11][12][13]. In particular, Dirac magnons, or more broadly defined topological magnons [14][15][16][17][18][19], have attracted much attention as platforms to investigate the effect of inter-particle interaction or external perturbations on Dirac bosons, and are proposed to be of potential interest in spintronic applications.In contrast to light and sound, the symmetry broken states and emergent bosonic excitations of quantum magnets depend crucially on dimensionality and spin symmetry, which provides a fertile playground for examining the physics of topological bosons. To date, gapped topological magnons in Ising-like ferromagnets have been reported in a kagome lattice material Cu(1,3bdc) [16] and in a layered honeycomb magnet CrI 3 [17]. On the other hand, magnons exhibiting symmetry protected band crossings have been found only in a single material, a three-dimensional (3D) Heisenberg antiferromagnet Cu 3 TeO 6 [18,20]. It is thus desirable to explore new test-beds with distinct spin symmetries to expand our understanding of the physics of Dirac magnons.In this paper, we present a new model 3D quantum XY magnet realizing gapless Dirac magnons, CoTiO 3 , which has a simple ilmenite crystal structure. The magnetic lattice of Co 2+ ions in CoTiO 3 is a stacked honeycomb lattice, exactly the same as in ABC stacked graphene. Below T N ≈ 38 K, this mate...

We report resonant inelastic X-ray scattering (RIXS) measurements on ordered double perovskite samples containing Re 5+ and Ir 5+ with 5d 2 and 5d 4 electronic configurations respectively. In particular, the observed RIXS spectra of Ba2YReO6 and Sr2MIrO6 (M=Y, Gd) show sharp intra-t2g transitions, which can be quantitatively understood using a minimal 'atomic' Hamiltonian incorporating spin-orbit coupling (λ) and Hund's coupling (JH ). Our analysis yields λ = 0.38(2)eV with JH = 0.26(2)eV for Re 5+ , and λ = 0.42(2)eV with JH = 0.25(4)eV for Ir 5+ . Our results provide the first sharp estimates for the Hund's coupling in 5d oxides, and suggest that it should be treated on equal footing with spin-orbit interaction in multi-orbital 5d transition metal compounds.

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t2g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses "single-particle" and "multi-particle" excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated 5d oxides. We present new higher resolution RIXS data at the Re-L3 edge in Ba2YReO6 which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba2MReO6 (with M=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t2g-eg interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d 3 systems, the exchange is one or two orders of magnitude weaker in the d 2 and d 4 materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the sitelocalized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the MO6 cluster. This suggests a possible role for intracluster excitons in Ba2YIrO6 which may lead to a weak breakdown of the atomic J eff = 0 picture and to small magnetic moments. arXiv:1804.02006v2 [cond-mat.str-el]

Quantum spin liquids have been drawing much attention in recent years as a platform to develop future quantum technologies, such as topological quantum computing. In particular, Kitaev’s honeycomb model has provided a blueprint to realize a quantum spin liquid that has Majorana fermions as its elementary excitation. While numerous theoretical studies have shown intriguing properties of quantum spin liquids, an experimental realization remains elusive. The recent observation of the quantized thermal Hall effect in α-RuCl3 has brought us tantalizingly close to an experimental realization of Kitaev quantum spin liquids. However, various groups report conflicting results, indicating that the Kitaev quantum spin liquid phase might be very fragile and its properties strongly depend on the sample. Here, we present a short overview of the rise of α-RuCl3 as a prime candidate material for realizing Kitaev quantum spin liquids. There are already many excellent review papers on this topic, so the emphasis will be on the materials aspect, comparing different crystal growth methods and crystal morphologies. We also discuss current research attempts to find other candidate materials to realize Kitaev quantum spin liquids, mostly focused on 3d transition-metal compounds, such as transition-metal halides and layered cobalt compounds.

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