Fig. 1: Determination of exchange interactions in YbCl₃ from high-field neutron scattering data.

a The structure of a honeycomb layer in YbCl₃. In-plane first-neighbor (J₁), second-neighbor (J₂), and third-neighbor (J₃) Heisenberg interactions are indicated. b Energy of the spin-wave dispersion in the monoclinic (HK0) plane of YbCl₃ at zero field. Solid black lines indicate the Brillouin zone boundary. Solid red circles are Γ points, white squares, and open circles are K and M points used in the integration of data shown later, and blue dotted lines represent the path displayed in c–n. The dashed gray lines indicate the paths through reciprocal space discussed in “Quantum effects below the saturation field”. c–e and i–k Inelastic neutron scattering intensity of YbCl₃ as a function of energy transfer and wave-vector transfer for magnetic fields (μ₀H) of 8 T and 6 T, respectively, with μ₀H∥b. Data were acquired at T = 0.08 K with the CNCS instrument. A time-independent background subtraction and non-magnetic background subtraction as described in the Methods and Supplementary Note 4²² were subtracted from the data. Data in c–e and i–k were integrated over the L axis as described in the text and integrated over the orthogonal direction in the honeycomb lattice plane by ±0.05 reciprocal lattice units. Linear spin-wave theory calculations with a single first-neighbor Heisenberg interaction, J₁ = 0.344(6) meV, for μ₀H = 8 T (f–h) and μ₀H = 6 T (l–n) shown over the range of the acquired data and using partial transparency in the kinematically inaccessible regions. Red dashed lines in c–e and i–k are the refined dispersions for the honeycomb lattice Heisenberg model described in the text. As described in the text, data for energy transfers below the horizontal dashed white line were not included in fits, and the residual scattering visible there is due to unsubtracted background. High-symmetry points are indicated along the top horizontal axis.