Polarized-neutron study of longitudinal Haldane-gap excitations in Nd${}_2$BaNiO${}_5$

Polarized and unpolarized inelastic neutron scattering is used to study Haldane-gap excitations in the mixed-spin linear-chain antiferromagnet Nd2BaNiO5. The longitudinal mode, polarized along the direction of ordered moments, is observed for the first time. The model of isolated Haldane chains in a static staggered exchange field, that is known to work very well for static properties and transverse spin excitations in R2BaNiO5 compounds, fails to explain new results for the longitudinal spin gap.