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 two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI$_3$, and in a 3D Heisenberg magnet Cu$_3$TeO$_6$. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO$_3$, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO$_3$ 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 CoTiO$_3$ as a model pseudospin-$1/2$ material to study interacting Dirac bosons in a 3D quantum XY magnet.
Highlights
The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electrons in solids described by the Dirac equation
We have carried out inelastic neutron scattering on quantum antiferromagnet CoTiO3 with an ilmenite structure
The magnetic excitations in CoTiO3 are well described using a simple model with dominant XY interactions
Summary
The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electrons in solids described by the Dirac equation. Co2þ is a spin S 1⁄4 3=2 ion, resulting in a large magnetic signal, our analysis of the observed low-energy crystal field levels provides evidence for strong, easy-plane, single-ion anisotropy leading to a pseudospin. In contrast with earlier examples of Ising-like and Heisenberg magnets, a simple model with dominant nearest-neighbor XY ferromagnetic (FM) exchange and antiferromagnetic interlayer second-neighbor exchange provides a good description of the magnon dispersion in CoTiO3. The magnetic properties of CoTiO3 are determined by the Co2þ ions that reside in slightly buckled honeycomb layers; see Fig. 1(b). To elucidate the magnetic ground state of each Co2þ ion, we measure the crystal field excitations using high-energy inelastic neutron. We find that λ 1⁄4 28ð1Þ meV and Δtrig 1⁄4 45ð6Þ meV provide a good description of the observed crystal field transitions For the fitted values of (λ, Δtrig), the ratio between g factors parallel (gk) and perpendicular (g⊥) to the honeycomb plane is gk=g⊥ ≈ 1.6 for the pseudospin, leading to a large anisotropy proportional to ðgk=g⊥Þ2 in the magnetic susceptibility, qualitatively consistent with the experiment in Ref. [36]
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