problem is that we have neglected the spin on the intervening oxygen. The third is that Eq. 1 describes the ground state for a single FM bond, implying that neutron scattering should be elastic, not inelastic as seen experimentally.The first difficulty has a simple resolution. At finite hole densities, the polarization clouds overlap and the isolated impurity model is inadequate. A crude model, which considers the overlaps, simply truncates the polarization clouds at neighboring impurity sites. Because FM impurity bonds are randomly distributed, the inversion symmetry characterizing isolated impurities is broken, thus allowing intensity at q ϭ . Because we know the impurity density, x, from neutron activation analysis, the only parameters in such a description are the extent of the polarization cloud,
Ϫ1, which we adjusted to optimize the fit to our data. As shown by the red lines in Fig. 4, the model provides a good account of the data with Ϫ1 ϭ 8.1 Ϯ 0.2, 7.3 Ϯ 0.2, and 7.2 Ϯ 0.5 for x ϭ 0.04, 0.095, and 0.14 respectively. These values are close to the exponential decay length of 6.03 calculated for the AFM spin polarization at the end of an S ϭ 1 chain (25).The modeling described so far does not include the spins of the holes responsible for the effective FM couplings between Ni 2ϩ ions. The holes reside in oxygen orbitals of Y 2Ϫx Ca x BaNiO 5 (5) but are almost certainly not confined to single, isolated oxygens. We consequently generalized Eq. 1 to take into account the hole spins, with-for the sake of definiteness-the same net amplitude as either of the Ni 2ϩ spins next to the FM bond and distributed (with exponential decay) over ᐉ lattice sites centered on the FM bond. As long as ᐉ exceeds the modest value of 2, comparable to the localization length deduced from transport data (5), the pronounced asymmetry about that occurs when ᐉ ϭ 0 is relieved sufficiently to produce fits indistinguishable from those in Fig. 4.How do we account for the inelasticity of the incommensurate signal? One approach is to view the chain as consisting not of the original S ϭ 1 degrees of freedom but of the composite spin degrees of freedom induced around holes. The latter interact through overlapping AFM polarization clouds and hole wave functions, to produce effective couplings of random sign because the impurity spacing can be even or odd multiples of the Ni-Ni separation. With weak interchain coupling, the ground state is likely to be a spin glass, as deduced from other experiments (10) on Y 2Ϫx Ca x BaNiO 5 . The "incommensurate" nature of the excitations continues to follow from the structure factor of the spin part of the hole wave functions.In summary, we have measured the magnetic fluctuations in single crystals of a doped one-dimensional spin liquid. At energies above the spin gap, the triplet excitations of the parent compound, Y 2 BaNiO 5 , persist with doping. However, below the gap, we find new excitations with a broad spectrum and characteristic wave vectors that are displaced from the zone boundary by an amount of...