Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO3

Abstract

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...

Dirac Hamiltonians for bosonic spectra

“…(ii) The three-dimensional magnet CoTiO 3 is composed of stacked honeycomb layers [43]. The spins order ferromagnetically within each layer and antiferromagnetically in the interlayer direction.…”

“…Neutron scattering measurements show that the spin wave spectrum has Dirac-like cones. The spectrum has been fit to X X Z-type models with varying anisotropy strengths [43]. One of the models that has been discussed has XY couplings between nearest and next-nearest neighbors.…”

Kitaev Spin Liquid in 3d Transition Metal Compounds

“…Analyzing the magnetic susceptibility data [20] including all spin-orbit levels [26], we obtain a positive trigonal field Δ ≃ 38 meV and λ ≃ 28 meV; these values are typical for Co 2þ ions in an octahedral environment (see, e.g., Ref. [54]). With Δ=λ ≃ 1.36, we evaluateS ¼ 1=2 doublet g factors g ab ≃ 4.6 and g c ≃ 3, from which a saturated moment of 2.3μ B , consistent with the magnetization data [20], follows.…”

“…Honeycomb lattice cobaltates.-A number of such compounds are known: A 3 Co 2 SbO 6 (A ¼ Na; Ag; Li) [18][19][20]43,44], Na 2 Co 2 TeO 6 [18,[45][46][47], BaCo 2 ðXO 4 Þ 2 (X ¼ As, P) [48][49][50][51], CoTiO 3 [52][53][54], CoPS 3 [55,56]. They are quasi-two-dimensional magnets; within the ab planes, zigzag or FM order is most common.…”

“…Traditionally, experimental data in Co 2þ compounds is analyzed in terms of an effectiveS ¼ 1=2 models of XXZ type [48,50,54,[57][58][59]. AsS ¼ 1=2 magnons (∼10 meV) are well separated from higher lying spin-orbit excitations (∼30 meV), the pseudospin picture itself is well justified; however, a conventional XXZ model neglects the bonddirectional nature of pseudospinS ¼ 1=2 interactions.…”