Longitudinal Magnetic Dynamics and Dimensional Crossover in the Quasi-One-Dimensional, Spin-1/2, Heisenberg Antiferromagnet KCuF3

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.