Dynamic Properties of the Impure Classical Heisenberg Chain

The second, fourth, and sixth moments are calculated exactly of the dynamic local-moment pair correlation function for an impure classical Heisenberg chain, with nearest-neighbor exchange interactions, consisting of two kinds of magnetic ions arranged randomly. By using these moments and by adopting a four-pole approximation, the neutron inelastic magnetic scattering cross section is formulated. Numerical evaluations are performed for (CD 3 ) 4 NMn 1- x Cu x Cl 3 (TMMC: Cu). In the case of finite Cu ++ concentration, both a peak at finite frequency which corresponds to the spin wave excitation and that at zero frequency are obtained in the cross section versus frequency curve calculated at low temperatures for wave numbers not near the center of the Brillouin zone. The results for the spin wave peak reproduce well qualitative features of the recent experimental data. The calculation shows that the spin wave peak for the impure case disappears in the limit of absolute zero temperature.