## 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 M(x,T), the neutron scattering dynamical structure factor S(k, ω), the 2D magnetic correlation length ξ(x,T) and, for the quasi-(2D) case, the Néel temperature T_{N}(x). We find that in two dimensions a hydrodynamic description of excitations in terms of spin waves breaks down at wavelengths larger than l/ãe^{π/4x}, 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 a^{-1}≫k≫l^{-1} consists of two distinct parts: (i) a damped quasiparticle peak at an energy c_{0}k≥ω≫ω_{0}, with abnormal damping Γ_{k}∼x c_{0}k, where ω_{0}∼c_{0}l^{-1}, c_{0} is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at ω∼ω_{0}. For k≲l^{-1} these two structures merge, and the spectrum becomes incoherent. The density of states acquires a constant term, and exhibits an anomalous peak at ω∼ω_{0} associated with low-energy localized excitations. These anomalies lead to a substantial enhancement of the magnetic specific heat C_{M} at low temperatures. Although the dynamical properties are significantly modified, we show that D=2 is not the lower critical dimension for this problem. We find that at small x the average staggered magnetization at the magnetic site is M(x,O)≃S-Δ-Bx, where Δ is the zero-point spin deviation and B≃?0.21 is independent of the value of S; the Néel temperature T_{N}(x)≃(1-A_{s} x) T_{N}(0), where A_{s}=π-2/π+B/(S-Δ) is weakly S dependent. Our results are in quantitative agreement with recent Monte Carlo simulations and experimental data for S=1/2, 1, and 5/2. In our approach long-range order persists up to a high concentration of impurities x_{c} which is above the classical percolation threshold x_{p}≈0.41. This result suggests that long-range order is stable at small x, and can be lost only around x≃x_{p} where approximations of our approach become invalid.

Original language | English |
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Article number | 104407 |

Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 65 |

Issue number | 10 |

DOIs | |

State | Published - 1 Mar 2002 |