Fig. 1: Magnons in CoTiO₃.

a Spin lattice structure of the buckled honeycomb of Co²⁺ ions in the AFM phase. The spins are ordered ferromagnetically (antiferromagnetically) between intralayer (interlayer) spins coupled by the exchange interaction J₁ (J₂). The colored arrows indicate the direction of magnetic moments aligned in the ab plane. b Calculated magnon dispersion (color solid lines) along the lines of Γ-K-M-Γ in the Brillouin zone. The green and purple dots are experimental data from our Raman measurements and INS from ref. ¹⁶, respectively. c Magnon density of states (DOS) calculated from the magnon dispersion. d Schematics of magnon dispersion that highlights a linear dispersion at the K point and saddle-points at M₁ (red dot) and M₂ (blue dot) points. The hexagon denotes the zone boundary labeled with high symmetry points. e, f Schematic of magnon precession for M₁ and M₂ modes involving two adjacent honeycomb lattices in the ab plane. Atoms in the top (bottom) layer are represented by dark (light) green balls and the arrows describe the phases of the precession. Three atoms (with both blue and red cones) in the two layers overlap in this top view along the c-axis.