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The Ising chain realizes the fundamental paradigm of spin fractionalization,where locally flipping a spin creates two domain walls (spinons) that canseparate apart at no energy cost. In a quasi-one-dimensional system, themean-field effects of the weak three-dimensional couplings confine the spinonsinto a Zeeman ladder of two-spinon bound states. Here, we experimentally tunethe confinement potential between spinons in the quasi-one-dimensional Isingferromagnet CoNb2O6 by means of an applied magnetic field with a largecomponent along the Ising direction. Using high-resolution single crystalinelastic neutron scattering, we directly observe how the spectrum evolves fromthe limit of very weak confinement at low field (with many closely-spaced boundstates with energies scaling as the field strength to the power 2/3) to verystrong confinement at high field (where it consists of a magnon and adispersive two-magnon bound state, with a linear field dependence). Atintermediate fields, we explore how the higher-order bound states disappearfrom the spectrum as they move to higher energies and overlap with thetwo-particle continuum. By performing a global fit to the observed spectrum inzero field and high field applied along two orthogonal directions, combinedwith a quantitative parameterization of the interchain couplings, we propose arefined single chain and interchain Hamiltonian that quantitatively reproducesall observed dispersions and their field dependence.

physical review. b./physical review. b

Tuning the confinement potential between spinons in the Ising chain  CoNb2O6 using longitudinal fields and quantitative determination of the  microscopic Hamiltonian