Inelastic-neutron-scattering study of the spin dynamics in the Haldane-gap system Ni(${\mathrm{C}}_2$${\mathrm{H}}_8$${\mathrm{N}}_2$${)}_2$${\mathrm{NO}}_2$${\mathrm{ClO}}_4$

We have investigated the spin dynamics of the nearly ideal one-dimensional S=1 antiferromagnet Ni(${\mathrm{C}}_2$ ${\mathrm{H}}_8$ ${\mathrm{N}}_2$ ${)}_2$ ${\mathrm{NO}}_2$ ${\mathrm{ClO}}_4$ (NENP) by inelastic neutron scattering. The measurements have been performed as a function of both the wave vector (in the vicinity of the antiferromagnetic point q=π) and the magnetic field, for field configurations parallel (up to 5 T) or perpendicular to the chain axis (up to 10 T). Our experimental results at low temperature are in good quantitative agreement with most theoretical predictions (both analytical and numerical) established for the spin-1 Haldane-gap system in presence of finite orthorhombic anisotropy: nonmagnetic singlet ground state, three gaps in the excitation spectrum corresponding to the excited triplet (${\mathrm{\Delta }}_{\mathit{y}}^0$≊1.05 meV, ${\mathrm{\Delta }}_{\mathit{x}}^0$≊1.23 meV, ${\mathrm{\Delta }}_{\mathit{z}}^0$≊2.5 meV), finite correlation lengths at T=0 (${\xi }_{\mathit{x}\mathit{y}}$/d≊8,${\xi }_{\mathit{z}}$/d≊4) and unconventional field dependencies. The evolution with field of the various modes and their respective polarization have been determined experimentally and are compared to recent field-theory treatments of the S=1 anisotropic antiferromagnetic chain together with numerical calculations on finite-size systems. We present results concerning the field dependencies of the correlation lengths, both in field parallel and perpendicular to the chain axis, which are not fully understood from the existing theories.