Excitations in randomly diluted ferromagnets

Abstract

The dynamics of a randomly diluted quenched Heisenberg ferromagnet have recently been analyzed by several authors. Within an effective medium type of approach, the correct site aspect of this problem is best given by the recent work of Harris et al. Their theory, which introduces spurious degrees of freedom for the nonmagnetic vacancies and then projects them out by the use of an appropriate pseudopotential, however, works adequately for $K$ vectors out to about halfway to the zone boundary and for low and intermediate concentrations of the nonmagnetic vacancies. For large vacancy concentrations, their results for the magnetic response leak over into the negative-frequency region. Also in their theory the spin-wave stiffness becomes complex for relative vacancy concentrations of order 49%. Here we present a new effective-medium approach to the study of this problem. We avoid the use of additional degrees of freedom for the vacancies by working directly with the equations of motion for the magnetic spins. Effective-medium ansatz is introduced through the use of a generalization of the path coherent-potential-approximation approach introduced by Brouers et al. in their study of random electronic alloys. For low and intermediate vacancy concentrations, our results are found to be of comparable quality to those given by Harris et al. However, unlike in their work, the first three frequency moments of the response are preserved exactly in our work. Moreover, on comparison with "exact" results—obtained via Padé procedures making use of numerically computed frequency moments—we find that our theory continues to yield qualitatively reasonable results even when the vacancy concentration is large, e.g., 60% in a simple-cubic lattice.