Fig. 3

Spinon confinement of YbAlO₃ in zero field. Inelastic neutron scattering spectra with background corrected measured at 1 K (a) and 0.05 K (b), compared to DMRG calculation with B_st/J = 0 (c), and B_st/J = 0.27 (d). The DMRG calculation is performed on a 64-site periodic chain with bond dimension M = 400 states at T = 0, with intrachain interaction J = 0.21 meV. In d, the elastic peak at L = 1 has been removed by hand. e Temperature evolution of the energy-dependent neutron scattering spectrum integrated in window H = [−0.1, 0.1] r.l.u., K = [−0.1, 0.1] r.l.u., L = [0.9, 1.1] r.l.u. A gapless continuum is observed at high temperatures, whereas a gap of about 0.3 meV (red circles) opens just at T_N, due to the appearance of the staggered field. f Temperature dependence of the elastic (001) magnetic peak intensity (black circles) and inelastic neutron spectrum (black diamonds) integrated in the window H = [−0.1, 0.1] r.l.u., K = [−0.1, 0.1] r.l.u., L = [0, 2.0] r.l.u., and E = [0.1, 0.6] meV. The elastic and inelastic scatterings correspond to the statically ordered and fluctuating magnetic moments, respectively. The red circles are the temperature-dependent entropy (S). The solid lines are a guide to the eyes, and the vertical red dashed line indicates the spinon confinement–deconfinement transition at T_N