Longitudinal magnetic dynamics and dimensional crossover in the quasi-one-dimensional spin-12Heisenberg antiferromagnetKCuF3

The spin dynamics of coupled spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chains is predicted to exhibit a longitudinal mode at low energies and temperatures below the Néel temperature. This mode is a dimensional crossover effect and reveals the presence of a limited amount of long-range antiferromagnetic order coexisting with quantum fluctuations. In this paper the existence of such a mode is confirmed in the model material ${\mathrm{KCuF}}_3$ using polarized and unpolarized inelastic neutron scattering, and the longitudinal polarization of the mode is definitively established. The line shape is broadened, suggesting a reduced lifetime due to decay into spin waves. In addition, the data show 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.