Diluted quantum antiferromagnets: Spin excitations and long-range order

A. L. Chernyshev, Yu-Chang Chen, A. H. Castro Neto

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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 TN(x). We find that in two dimensions a hydrodynamic description of excitations in terms of spin waves breaks down at wavelengths larger than l/ãeπ/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 c0k≥ω≫ω0, with abnormal damping Γk∼x c0k, where ω0∼c0l-1, c0 is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at ω∼ω0. 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∼ω0 associated with low-energy localized excitations. These anomalies lead to a substantial enhancement of the magnetic specific heat CM 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 TN(x)≃(1-As x) TN(0), where As=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 xc which is above the classical percolation threshold xp≈0.41. This result suggests that long-range order is stable at small x, and can be lost only around x≃xp where approximations of our approach become invalid.

Original languageEnglish
Article number104407
Pages (from-to)1-23
Number of pages23
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number10
StatePublished - 1 Mar 2002


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