Abstract
We have studied the static and dynamic magnetic properties of two-dimensional (2D) and quasi-two-dimensional, spin-S, quantum Heisenberg antiferromagnets diluted with spinless vacancies. Using spin-wave theory and the T-matrix approximation we have calculated the staggered magnetization the neutron scattering dynamical structure factor the 2D magnetic correlation length and, for the quasi- (2D) case, the Néel temperature We find that in two dimensions a hydrodynamic description of excitations in terms of spin waves breaks down at wavelengths larger than x being the impurity concentration and a the lattice spacing. We find signatures of localization associated with the scale l, and interpret this scale as the localization length of magnons. The spectral function for momenta consists of two distinct parts: (i) a damped quasiparticle peak at an energy with abnormal damping where is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at For these two structures merge, and the spectrum becomes incoherent. The density of states acquires a constant term, and exhibits an anomalous peak at associated with low-energy localized excitations. These anomalies lead to a substantial enhancement of the magnetic specific heat at low temperatures. Although the dynamical properties are significantly modified, we show that is not the lower critical dimension for this problem. We find that at small x the average staggered magnetization at the magnetic site is where is the zero-point spin deviation and is independent of the value of S; the Néel temperature where is weakly S dependent. Our results are in quantitative agreement with recent Monte Carlo simulations and experimental data for 1, and 5/2. In our approach long-range order persists up to a high concentration of impurities which is above the classical percolation threshold This result suggests that long-range order is stable at small x, and can be lost only around where approximations of our approach become invalid.
- Received 24 July 2001
DOI:https://doi.org/10.1103/PhysRevB.65.104407
©2002 American Physical Society