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• W2015241999 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 $mathcal{S}(mathbf{k},ensuremath{omega}),$ the 2D magnetic correlation length $ensuremath{xi}(x,T)$ and, for the quasi- (2D) case, the N'eel 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 $l/aensuremath{sim}{e}^{ensuremath{pi}/4x},$ 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 ${a}^{ensuremath{-}1}ensuremath{gg}kensuremath{gg}{l}^{ensuremath{-}1}$ consists of two distinct parts: (i) a damped quasiparticle peak at an energy ${c}_{0}kensuremath{gtrsim}ensuremath{omega}ensuremath{gg}{ensuremath{omega}}_{0},$ with abnormal damping ${ensuremath{Gamma}}_{k}ensuremath{sim}x{c}_{0}k,$ where ${ensuremath{omega}}_{0}ensuremath{sim}{c}_{0}{l}^{ensuremath{-}1},$ ${c}_{0}$ is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at $ensuremath{omega}ensuremath{sim}{ensuremath{omega}}_{0}.$ For $kensuremath{lesssim}{l}^{ensuremath{-}1}$ these two structures merge, and the spectrum becomes incoherent. The density of states acquires a constant term, and exhibits an anomalous peak at $ensuremath{omega}ensuremath{sim}{ensuremath{omega}}_{0}$ 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 $M(x,0)ensuremath{simeq}Sensuremath{-}ensuremath{Delta}ensuremath{-}Bx,$ where $ensuremath{Delta}$ is the zero-point spin deviation and $Bensuremath{simeq}0.21$ is independent of the value of S; the N'eel temperature ${T}_{N}(x)ensuremath{simeq}(1ensuremath{-}{A}_{s}x) {T}_{N}(0),$ where ${A}_{s}=ensuremath{pi}ensuremath{-}2/ensuremath{pi}+B/(Sensuremath{-}ensuremath{Delta})$ 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 ${x}_{p}ensuremath{approx}0.41.$ This result suggests that long-range order is stable at small x, and can be lost only around $xensuremath{simeq}{x}_{p}$ where approximations of our approach become invalid." @default.
• W2015241999 created "2016-06-24" @default.
• W2015241999 creator A5001361375 @default.
• W2015241999 creator A5009120910 @default.
• W2015241999 creator A5055510120 @default.
• W2015241999 date "2002-02-11" @default.
• W2015241999 modified "2023-09-25" @default.
• W2015241999 title "Diluted quantum antiferromagnets: Spin excitations and long-range order" @default.
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• W2015241999 doi "https://doi.org/10.1103/physrevb.65.104407" @default.
• W2015241999 hasPublicationYear "2002" @default.
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