Haldane-gap excitations in the low-$H_c$ one-dimensional quantum antiferromagnet $\mathrm{Ni}\left({\mathrm{C}}_5{\mathrm{D}}_{14}{\mathrm{N}}_2{)}_2{\mathrm{N}}_3\right({\mathrm{PF}}_6)$

Inelastic neutron scattering on deuterated single-crystal samples is used to study Haldane-gap excitations in the new $S=1\mathrm{}$ one-dimensional quantum antiferromagnet $\mathrm{Ni}\left({\mathrm{C}}_5{\mathrm{D}}_{14}{\mathrm{N}}_2{)}_2{\mathrm{N}}_3\right({\mathrm{PF}}_6),$ that was recently recognized as an ideal model system for high-field studies. The Haldane gap energies ${\Delta }_x=0.42\mathrm{}\left(3\right)\mathrm{}\hspace{0.5em}\mathrm{meV},$ ${\Delta }_y=0.52\mathrm{}\left(6\right)\mathrm{}\hspace{0.5em}\mathrm{meV},$ and ${\Delta }_z=1.9\mathrm{}\left(1\right)\mathrm{}\hspace{0.5em}\mathrm{meV},$ for excitations polarized along the a, b, and c crystallographic axes, respectively, are measured. The dispersion relation is studied for momentum transfers both along and perpendicular to the chains’ direction. The in-chain exchange constant $J=2.8\mathrm{}\hspace{0.5em}\mathrm{meV}$ is found to be much larger than interchain coupling, $J_y=1.8\mathrm{}\left(4\right)\mathrm{}\times {10}^{-3}\hspace{0.5em}\mathrm{meV}$ and $J_x=4\mathrm{}\left(3\right)\mathrm{}\times {10}^{-4}\hspace{0.5em}\mathrm{meV},$ along the b and a axes, respectively. The results are discussed in the context of future experiments in high magnetic fields.