Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet

Vajk, O. P.; Mang, P. K.; Greven, M.; Gehring, P. M.; Lynn, J. W.

doi:10.1126/science.1067110

Cited by 145 publications

(211 citation statements)

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“…2 Several materials of current interest are well described by combining random dilution with lattice quantum degrees of freedom, as in a magnetic material in which some quantum spins have been removed by chemical dilution. 3 Aside from its interest as a microscopic description of dilution in materials, percolation is important as the simplest nondeterministic process for generating a "fractal", an object of fractional dimensionality: 4 as explained later in this introduction, there is a geometric phase transition in randomly diluted lattice systems with a fractal structure at the transition point.…”

Section: Introductionmentioning

confidence: 99%

“…5 Finally, the O(2) rotor is qualitatively similar to the nearest-neighbor s = 1/2 antiferromagnetic Heisenberg model in that both have long-range order in two dimensions but only algebraic correlations in one dimension. The diluted Heisenberg model has been studied numerically 3,6,7 and in neutron scattering experiments on La 2 (Zn,Mg) x Cu 1−x O 4 3 .…”

Section: Introductionmentioning

confidence: 99%

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Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

et al. 2006

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Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered 1D bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La2(Zn,Mg)xCu1−xO4.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

et al. 2006

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“…The transition from a renormalized classical to a quantum-disordered state can be triggered by various parameters, including lattice dimerization, frustration and applied field. More recently, special interest has focused on phase transitions driven by geometric randomness of the lattice 3,4 , including site and bond disorder. Strong geometric disorder not only breaks translational invariance and perturbs the ground state of the pure system, but it can also destabilize renormalized classical phases with long-range order (LRO) and drive the system to novel disordered phases.…”

Section: Introductionmentioning

confidence: 99%

“…Site and bond dilution of the square lattice QHAF have been the focus of several recent studies 3,4,13,14,15 , motivated by experiments on antiferromagnetic cuprates doped with nonmagnetic impurities 3,16,17 . From a geometric point of view, bond and site dilution reduce the connectivity of the lattice, ultimately leading to a percolative phase transition 18 beyond which the system is broken up into finite clusters.…”

Section: Introductionmentioning

confidence: 99%

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

Roscilde

Haas

2006

Phys. Rev. B

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We investigate quantum phase transitions in the spin-1/2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a novel quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating cluster with short ranged antiferromagnetic order. In this phase, the low-temperature uniform susceptibility diverges algebraically with non-universal exponents. This is a signature that the novel quantum-disordered phase is a quantum Griffiths phase, as also directly confirmed by the statistical distribution of local gaps. This study thus presents evidence of a genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg antiferromagnet.

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“…Jm, 74.25.Nf, 75.20.Hr, 75.40.Mg The intentional doping of antiferromagnetic materials has become a useful tool in order to study the complicated physics in the context of high temperature superconductivity and quantum magnetism [1,2,3,4,5,6]. Large alternating magnetic moments around static nonmagnetic impurities are observed in Knight shift experiments when a uniform field is applied [3,4,5,6].…”

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Universal Alternating Order around Impurities in Antiferromagnets

et al. 2007

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The study of impurities in antiferromagnets is of considerable interest in condensed matter physics. In this paper we address the elementary question of the effect of vacancies on the orientation of the surrounding magnetic moments in an antiferromagnet. In the presence of a magnetic field, alternating magnetic moments are induced, which can be described by a universal expression that is valid in any ordered antiferromagnet and turns out to be independent of temperature over a large range. The universality is not destroyed by quantum fluctuation, which is demonstrated by quantum Monte Carlo simulations in the two-dimensional Heisenberg antiferromagnet. Physical predictions for finite doping are made, which are relevant for experiments probing Knight shifts and the order parameter.PACS numbers: 75.10. Jm, 74.25.Nf, 75.20.Hr, 75.40.Mg The intentional doping of antiferromagnetic materials has become a useful tool in order to study the complicated physics in the context of high temperature superconductivity and quantum magnetism [1,2,3,4,5,6]. Large alternating magnetic moments around static nonmagnetic impurities are observed in Knight shift experiments when a uniform field is applied [3,4,5,6]. Theoretical studies have shown that vacancies in low-dimensional antiferromagnetic backgrounds give rise to locally enhanced antiferromagnetic correlations [7,8,9,10,11,12,13,14], which strongly depend on the microscopic model and temperature in the low dimensional models.In this work, we show that in generic ordered antiferromagnets the alternating local moments in the vicinity of vacancies can be quantitatively described by a universal expression which only depends on the field B, but is surprisingly independent of temperature, quantum fluctuations, and microscopic details. The mechanism which gives rise to the alternating moments is a local tilting of the order parameter due to the broken sub-lattice symmetry by impurities. In contrast to the pure sample, where the order parameter is always confined in the plane normal to the field, a large alternating order parallel to the field is induced as schematically depicted in Fig. 1. The calculations agree remarkably well with quantum Monte Carlo (QMC) simulations without any adjustable parameters even in two dimensions D = 2, where quantum fluctuations are strongest.The typical antiferromagnetic Hamiltoniandescribes the magnetic behavior realistically even for rather complex materials despite its simplicity. We consider systems with bipartite lattices of dimension D ≥ 2, where the sum in Eq. (1) runs over nearest neighbor sites. Generically, the dominant interaction J > 0 comes from the Coulomb forces via the exchange mechanism and is The spins "cant" with an angle δ towards the field corresponding to a small uniform magnetization. Due to the broken sub-lattice symmetry the order may be "tilted" by an angle α relative to the plane normal to the field corresponding to an induced alternating magnetization around the impurity.therefore isotropic. The rotational symmetry is bro...

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Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet

Cited by 145 publications

References 31 publications

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

Universal Alternating Order around Impurities in Antiferromagnets

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