Fig. 1. Phase competition in RuCl₃ revealed by Ru L₃ edge RIXS, and the scattering geometry.

a Schematic of classical and quantum energy landscapes in the vicinity of the zigzag ground state. The zigzag order is stabilized by quantum effects, and only slightly lower in energy than the competing metastable ferromagnetic (FM) state. b The pseudospin-1/2 moments (gray arrows) show the zigzag-type magnetic order pattern on the honeycomb lattice of α-RuCl₃. The gray-shaded RuCl₆ octahedra share the edges on the three distinct x, y, and z-type bonds, represented by the red, green, and blue lines, respectively. a, b, and c represent the crystallographic lattice vectors. The incident x-ray photons with momentum k are linearly π-polarized and the polarization of the scattered photons with momentum ${\mathit{k}}^{\prime }$ is not analyzed. The scattering angle is fixed at 90^∘ and the in-plane momentum transfer q is changed by rotating the sample angle θ. The azimuthal angle ϕ is used to change the measurement path. c Local moment direction in the RuCl₆ octahedron. The directions from the central Ru atom to the adjacent Cl atoms denoted by x, y, and z define the local x, y, and z coordinate axes. The magnetic moment lies within the ac plane and points 35^∘ from the a axis^68,53. d q = (H, 0) and (H, H) paths investigated in the RIXS experiment. The dotted hexagon indicates the first Brillouin zone (BZ).