  The spin dynamics of coupled spin-1/2, antiferromagnetic Heisenberg chains is
predicted to exhibit a novel longitudinal mode at low energies and temperatures
below the Neel temperature. This mode is a dimensional crossover effect and
reveals the presence of a limited amount of long-range antiferromagnetic order
co-existing with quantum fluctuations. In this paper the existence of such a
mode is confirmed in the model material KCuF3 using polarized and unpolarized
inelastic neutron scattering and the longitudinal polarization of the mode is
definitively established. The lineshape is broadened suggesting a reduced
lifetime due to decay into spin-waves. In addition the data shows evidence of
continuum scattering with a lower edge greater than the longitudinal mode
energy. A detailed comparison is made with theoretical predictions and
experimental work on other model materials.
