Low-temperature study of the static and dynamical magnetic properties of the random one-dimensional antiferromagnet(CD3)4NMncCu1−cCl3

In a recent paper we reported a neutron scattering study of the random one-dimensional (1D) Heisenberg antiferromagnetic ${\left({\mathrm{CD}}_3\right)}_4\mathrm{N}{\mathrm{Mn}}_c{\mathrm{Cu}}_{1-c}{\mathrm{Cl}}_3$, with $c=0.93\mathrm{}$ and $0.85$. The main emphasis was on the static properties. In the present publication we present the results and analyses of extended quasielastic and inelastic neutron scattering experiments at temperatures down to 0.3 K. The low-temperature behavior of the inverse correlation length $\kappa$ and staggered susceptibility $\chi (Q=\pi )$ of the $c=0.93\mathrm{}$ specimen indicates that the exchange $J_{\mathrm{C}\mathrm{u}-\mathrm{C}\mathrm{u}}$ between pairs of ${\mathrm{Cu}}^{++}$ ions is ferromagnetic. Well-defined spin-wave-like excitations are observed for wave vectors larger than a critical wave vector $q_{\mathrm{cr}}$. The low-temperature measurements indicate that $q_{\mathrm{cr}}$ is governed by the percolation limit ${\kappa }_c$ of $\kappa$ itself, indicating that the observed excitations are associated with the pure ${\mathrm{Mn}}^{++}$ segments. We have carried out spin-wave perturbation calculations and computer simulations of the spin-dynamical properties of the dilute classical Heisenberg chain at $T=0\mathrm{}$. These two calculations are in good agreement with each other. No Ising resonances, associated with states at chain ends, were found in these calculations. These resonances occur in similar systems in higher dimensions but are shown not to occur in 1D because of the singular nature of the density of states at the band edges. For $q>\mathrm{}{q}_{\mathrm{cr}}$, the observed inelastic scattering response is quantitatively accounted for by means of the perturbation calculations. For $q\sim q_{\mathrm{cr}}$ the experimentally measured line shapes are in qualitative agreement with the computer simulations.