Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg-spin system

The Coherent Exchange Cluster Approach, developed within two proceeding papers, is applied to dilute quasi two-dimensional Heisenberg spin-systems, consisting of one magnetic and one nonmagnetic alloying component. The level density of spin wave excitations is discussed for concentrations of the magnetic component, which are larger than the critical value, where all excitations become localized. The propagation of the excitations through the disordered system is described by an effective Heisenberg-Hamiltonian with a complex and energy-dependent exchange integral \(\tilde J\) (E). This quantity is determined by the postulate, that the most important matrix elements of the scatteringT-matrix should vanish after averaging over the possible configurations of a scattering cluster, consisting of a central lattice site and its four nearest neighbours. Numerical results are obtained both for the “dilute bond” and “site” problems, respectively; in both cases, the results agree rather well with existing computer simulations for 30 × 30 spin arrays. For the “site” problem, it is necessary to introduce a coherent single ion anisotropy field in addition to the coherent exchange integral: Results in agreement with the analyticity requirements are obtained by a careful choice of the additional selfconsistency equation.