HALDANE-GAP MODES IN THE S = 1 ANTIFERROMAGNETIC CHAIN COMPOUND CSNICL3

For the antiferromagnetically coupled integer-spin Ni2+ chains of CsNiCl3 the Haldane gap is found by neutron scattering to be a singlet-to-triplet spin excitation. It has a 2 periodicity in momentum space with a dispersion relation that falls to a value of order twice the gap energy as Q 2. When the coupled Ni2+ chains undergo the transition to three-dimensional order, a set of longitudinal modes is found to occur that are not present in conventional theory where the excitations are transverse spin waves. Our calculations of the intensities show that near the ordering wave vector (1/3, 1)/3, 1) the new modes agree with the field theory of Affleck but not with spin-wave theory. At larger interchain wave vectors both field theory and spin-wave theory break down. © 1990 The American Physical Society.