Diluted quantum antiferromagnets: Spin excitations and long-range order

A. L. Chernyshev, Y. C. Chen, and A. H. Castro Neto
Phys. Rev. B 65, 104407 – Published 11 February 2002
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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 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/aeπ/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 a1kl1 consists of two distinct parts: (i) a damped quasiparticle peak at an energy c0kωω0, with abnormal damping Γkxc0k, where ω0c0l1, c0 is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at ωω0. For kl1 these two structures merge, and the spectrum becomes incoherent. The density of states acquires a constant term, and exhibits an anomalous peak at ωω0 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,0)SΔBx, where Δ is the zero-point spin deviation and B0.21 is independent of the value of S; the Néel temperature TN(x)(1Asx)TN(0), where As=π2/π+B/(SΔ) 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 xp0.41. This result suggests that long-range order is stable at small x, and can be lost only around xxp where approximations of our approach become invalid.

  • Received 24 July 2001

DOI:https://doi.org/10.1103/PhysRevB.65.104407

©2002 American Physical Society

Authors & Affiliations

A. L. Chernyshev1,*, Y. C. Chen2, and A. H. Castro Neto3,†

  • 1Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
  • 2Department of Physics, University of California, Riverside, California 92521
  • 3Department of Physics, Boston University, Boston, Massachusetts 02215

  • *Also at the Institute of Semiconductor Physics, Novosibirsk, Russia.
  • On leave from Department of Physics, University of California, Riverside.

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Vol. 65, Iss. 10 — 1 March 2002

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