FINITE-SIZE MODIFICATIONS OF THE MAGNETIC-PROPERTIES OF CLUSTERS

The spin-wave spectrum of Heisenberg spin clusters of various structur es (bcc, fcc, and disordered) ranging in size between 9 and 749 spins is calculated by a self-consistent diagonalization of the equation of motion of S+ in real space. The spin-wave spectrum of the clusters is strongly modified relative to the bulk, and the consequent neutron-sca ttering cross section exhibits discretely spaced wave-vector-broadened eigenstates. The implications of the finite size on thermodynamic pro perties, like the temperature dependence of the magnetization and the critical temperature, are also elucidated. We find the temperature dep endence of the cluster magnetization to be well described by an effect ive power law, M(mean) is-proportional-to 1 - BT(alpha), with a size-d ependent, but structure-independent, exponent larger than the bulk val ue. The critical temperature of the clusters is calculated from the sp in-wave spectrum by a method based on the correlation theory and the s pherical approximation generalized to the case of finite systems. A si ze-dependent reduction of the critical temperature by up to 50% for th e smallest clusters is found. The trends found for the model clusters are extrapolated to the size regime of nanoscale particles.