Dominance of excitation continuum in the longitudinal spectrum of weakly coupled Heisenberg S=1/2 chains

A low-field spin flop transition in the quasi one-dimensional antiferromagnet \ba is exploited to study the polarization dependence of low-energy magnetic excitations. The measured longitudinal spectrum is best described as single broad continuum, with no sharp ``longitudinal mode'', in apparent contradiction with the commonly used chain-MF/RPA theories. The observed behavior is also quite different than that previously seen in the related \kcuf material, presumably due to a large difference in the relative strength of inter-chain interactions. The results highlight the limitations of the chain-MF/RPA approach.