Antiferromagnetic magnons in diluted triangular and kagomé lattices.

Abstract

Numerical results are presented for the local field distribution and the distribution of linearized magnon modes in diluted triangular and kagom\'e lattices. A nearest-neighbor antiferromagnetic Heisenberg spin Hamiltonian is assumed, and the linearization is carried out with respect to classical ground states obtained by means of an energy-minimization algorithm. In the case of the triangular lattice, the density of states associated with a 20% vacancy concentration is used to calculate the magnon contribution to the specific heat. With an exchange integral inferred from the Curie-Weiss constant, quantitative agreement is obtained with the experimental results for ${\mathrm{La}}_{0.2}$${\mathrm{Gd}}_{0.8}$${\mathrm{CuO}}_{2}$ reported by Ramirez et al. over the interval 0.1 K\ensuremath{\le}T\ensuremath{\le}0.2 K. The behavior of the diluted kagom\'e lattice is compared with that of the triangular array. In contrast to the latter, the local fields in the diluted kagom\'e lattice take on the discrete values 2JS, JS, and 0. In the case of a 14% vacancy concentration, the distribution of magnon modes resembles that of the fully occupied array with a noncoplanar ground state. The relevance of these results to the behavior of ${\mathrm{SrCr}}_{8}$${\mathrm{Ga}}_{4}$${\mathrm{O}}_{19}$ is discussed.