Fig. 2

Spinons in a magnetic field. a The magnetic field dependence of the static magnetization at k_BT < Δ_S [red, right axis, H||(110)] shows several discontinuous jumps (blue and green dashes), corresponding to transitions among different 3D ordered phases that are more clear in dM/dμ₀H (black, left axis)^23,25. These phases correspond to different ways that magnetic moments arrange into registry minimizing the energy of magnetic dipole interactions between the Yb moments. b When a magnetic field is applied along the chain direction, the chemical potential μ = −gμ_BHS^z (yellow) is lowered, emptying part of the hole band when |μ| > |Δ_S|. μ crosses the hole dispersion at four points in the Brillouin zone (black arrows), defining the Fermi wavevector k_F. c Two AFM ordered, 1D spin chains (top). If two spins on one chain are interchanged, two domain walls are formed between the original domain (green) and a new one (blue). The new domain frustrates the interchain interaction, represented by the red interchain bonds. This frustration creates a linear potential confining low energy spinons to bound states (bottom). d–f The magnetic excitation spectrum and its dispersion along the q_L direction in reciprocal space measured at T = 0.1 K and μ₀H = 1.0 T (d), 1.5 T (e), and 1.7 T (f), summed over −1 ≤ q_HH ≤ 1 rlu. The dispersions for the extremal combinations of particles and holes are shown (black lines) (See Supplementary Note 2). The spinon bound states are manifest from the enhanced low energy spectral weight around 1 ± 2k_F (black arrows). g–i The spinon spectrum computed using tDMRG calculations for the XXZ model Eq. (1) on a 96-site chain with Δ = 2.6 at equivalent chain magnetizations as (d–f), shown on the same color scale. The dispersions for the extremal combinations of particles and holes are also shown as black lines