Hidden order in a frustrated system: Properties of the Heisenberg Kagomé antiferromagnet

Chalker, J. T.; Holdsworth, Peter; Shender, E. F.

doi:10.1103/physrevlett.68.855

Cited by 451 publications

(524 citation statements)

References 19 publications

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“…The "standard" spin correlation function is insensitive to nematic order, so, following Ref. [18], we define a nematic correlation function which is equal to 1 for a coplanar state:…”

Section: Kagome Heisenberg Magnetmentioning

confidence: 99%

spinvert: a program for refinement of paramagnetic diffuse scattering data

Paddison¹,

Stewart²,

Goodwin³

2013

J. Phys.: Condens. Matter

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Abstract. We present a program (SPINVERT; http://spinvert.chem.ox.ac.uk ) for refinement of magnetic diffuse scattering data for frustrated magnets, spin liquids, spin glasses, and other magnetically disordered materials. The approach uses reverse Monte Carlo refinement to fit a large configuration of spins to experimental powder neutron diffraction data. Despite fitting to sphericallyaveraged data, this approach allows the recovery of the three-dimensional magnetic diffuse scattering pattern and the spin-pair correlation function. We illustrate the use of the SPINVERT program with two case studies. First we use simulated powder data for the canonical Heisenberg kagome model to discuss the sensitivity of SPINVERT refinement to both pairwise and higher-order spin correlations. The effect of limited experimental data on the results is also considered. Second, we re-analyse published experimental data on the frustrated system Y 0.5 Ca 0.5 BaCo 4 O 7 . The results from SPINVERT refinement indicate similarities between Y 0.5 Ca 0.5 BaCo 4 O 7 and its parent compound YBaCo 4 O 7 , which were overlooked in previous analysis using powder data.

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“…The "standard" spin correlation function is insensitive to nematic order, so, following Ref. [18], we define a nematic correlation function which is equal to 1 for a coplanar state:…”

Section: Kagome Heisenberg Magnetmentioning

confidence: 99%

spinvert: a program for refinement of paramagnetic diffuse scattering data

Paddison¹,

Stewart²,

Goodwin³

2013

J. Phys.: Condens. Matter

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“…Geometric frustration, for instance, present in two dimensions (2d) on the triangular or kagome lattices or in three dimensions (3d) on the pyrochlore lattice, does not automatically entail the existence of degenerate classical ground states, the hallmark of frustration. While the classical 120 • state of the 2d Heisenberg antiferromagnet on the triangular lattice is unique (up to global rotations and interchange of sublattices), there is a large number of degenerate ground states on the kagome lattice [1]. The fluctuation between many degenerate classical ground states can lead to a suppression of ordering tendencies, resulting in a cooperative paramagnet or classical spin liquid [2,3].…”

mentioning

confidence: 99%

“…The decisive quantity is the free energy F = E − T S, which favors the state(s) that best can exploit the low-energy configurations in its/their vicinity. A famous example of this mechanism is provided by the classical kagome antiferromagnet where coplanar ground-state configurations are favored at low T [1], but other examples, also in higher dimensions, have been reported in the literature [9,12,13]. For other 3d systems, e.g., Heisenberg spins on the pyrochlore lattice, it was shown to be completely * Author to whom correspondence should be addressed: buhrandt@thp.uni-koeln.de absent, resulting in true classical spin liquids at T = 0 [3,14].…”

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confidence: 99%

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Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Buhrandt

Fritz

2014

Phys. Rev. B

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Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin-liquid phase. An intrinsic effect lifting this degeneracy is entropic order by disorder. We present strong evidence that a classical nearest-neighbor Heisenberg model on the swedenborgite lattice exhibits both an extended spin-liquid phase as well as entropic order-by-disorder choosing coplanar configurations after a first-order transition. We argue that this observation renders magnetic insulators such as RBaCo 4 O 7 , where R denotes a rare-earth atom, prime candidates for displaying spin-liquid behavior and entropic order-by-disorder physics due to their large exchange constant.

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“…Their regions of stability were found from considering the free energy at finite temperature which was evaluated using a calculation of the elementary excitations. This was an example of 'order by disorder' that had previously been applied to models with continuous symmetry 30,31 . The method gave the ordering of the phases correctly and also identified the line between them.…”

Section: E Phase Lmentioning

confidence: 99%

The phase diagram of an anisotropic Potts model

Ahmed¹,

Gehring²

2005

J. Phys. A: Math. Gen.

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A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results.We find one region where there are two phase transitions with the lines meeting in a triple point.The orbital ordering that occurs in LaM nO 3 occurs as one of the ordered phases.

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Hidden order in a frustrated system: Properties of the Heisenberg Kagomé antiferromagnet

Cited by 451 publications

References 19 publications

spinvert: a program for refinement of paramagnetic diffuse scattering data

spinvert: a program for refinement of paramagnetic diffuse scattering data

Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

The phase diagram of an anisotropic Potts model

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