Ordering by quantum fluctuations in a strongly frustrated Heisenberg antiferromagnet

Harris, Amanda; Berlinsky, A. J.; Bruder, Christoph

doi:10.1063/1.348098

Cited by 106 publications

(136 citation statements)

References 7 publications

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125

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Order By: Relevance

“…All the theoretical results seem to indicate that for these geometries the classical Heisenberg model with only nearest neighbor interactions does not order at any finite temperature, in agreement with Monte Carlo (MC) results [2,3,4,5,6,7]. There are also a relatively few works which have dealt with the quantum effects in these systems [8]. However, the main interest during last years has been in the classical GFAF.…”

supporting

confidence: 59%

“…However, for the kagomé lattice, the exact value is 11/12, whereas our model predicts a value of 1. In any case, this deviation is expected to occur, as our model does not include the effect of zero modes, which are known to be especially important in the kagomé case, where they give rise to the phenomenon known as order by disorder [5,8]. In contrast, MC data suggest that this mechanism is absent in the Heisenberg pyrochlore.…”

mentioning

confidence: 42%

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Classical generalized constant coupling model for geometrically frustrated antiferromagnets

García-Adeva

Hùber

2001

Phys. Rev. B

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A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagomé lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.

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supporting

confidence: 59%

mentioning

confidence: 42%

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

García-Adeva

Hùber

2001

Phys. Rev. B

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“…Implications for the 3-d pyrochlore magnet: The actual ordering behaviour of the pyrochlore is still far from settled. At this stage [2][3][4][5][6][7][8]24 it appears to be somewhat closer to that of the checkerboard lattice than either of the two is to the kagome case, where there has so far been no strong indication of long-range order of any kind for S = 1/2, and where the large-S state is necessarily non-collinear. We emphasize, however, that details of the ordering we find, such as the pattern of the bond solid or the size of the unit cell, crucially depend on differences between the two lattices -such as spatial dimensionality, the presence of inequivalent links, and short closed loops linking different tetrahedra.…”

mentioning

confidence: 99%

“…Note that the degeneracy of this state is two rather than four, as would be the case for the plaquette state on the square lattice, because of the explicit symmetry breaking introduced by the presence of the plaquettes with crossing interactions. Semiclassics: We now consider the case of large spin S and large κ for SU (2) and Sp(N ), respectively. In either case, one compares the zero-point energy due of the excitations (spin waves and spinons, respectively) of different, classically degenerate ground states.…”

mentioning

confidence: 99%

“…In particular, the Heisenberg pyrochlore antiferromagnet is being studied with view to the question of whether frustration-enhanced quantum fluctuations might lead to unconventional ordering -or complete absence thereof -especially for small values of the quantum spin, S. [2][3][4][5][6][7][8] This model classically is special in that frustration prevents any sort of ordering or dynamical phase transition down to the lowest temperatures, [9][10][11] for which reason it is termed a cooperative paramagnet or classical spin liquid.…”

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confidence: 99%

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Planar Pyrochlore, Quantum Ice and Sliding Ice

Moessner

Tchernyshyov

Sondhi

2004

Journal of Statistical Physics

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We study quantum antiferromagnetism on the highly frustrated checkerboard lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analog of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, S, with a Néel state for large S giving way to a two-fold degenerate valence-bond solid for smaller S. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits long range "anti-ferroelectric" order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry. Introduction: On the heels of recent progress in understanding highly frustrated classical magnets, coupled with a substantial experimental effort, 1 renewed attention is now focused on the behaviour of their quantum counterparts. In particular, the Heisenberg pyrochlore antiferromagnet is being studied with view to the question of whether frustration-enhanced quantum fluctuations might lead to unconventional ordering -or complete absence thereof -especially for small values of the quantum spin, S. 2-8 This model classically is special in that frustration prevents any sort of ordering or dynamical phase transition down to the lowest temperatures, 9-11 for which reason it is termed a cooperative paramagnet or classical spin liquid.The challenge of this problem arises from the small energy scale generated by the frustration: in a semiclassical picture, any linear combination of the classically degenerate ground states -the collection of which is of extensive dimensionality 11 -may be selected as the quantum ground state. For the highly frustrated two-dimensional magnet on the related kagome lattice, exact diagonalisations of small clusters 12 have provided crucial benchmarks. This system has turned out to be particularly well suited to this approach as it appears to have a very short correlation length, although one does find a large number of low-lying singlet excitations.For the pyrochlore magnet, it looks as if such results will elude us for some time to come. The pyrochlore lattice, being three-dimensional, displays a more inclement scaling of the Hilbert space dimension with linear system size. Moreover, its unit cell contains four spins and its structure implies that the smallest system without spurious boundary condition effects contains at least 16 sites.To evade this, attention has shifted to a system which avoids some of these complications, namely the checkerboard lattice (Fig. 1). It is expected to have similar properties to the pyrochlore as it has the same local structure -both can be thought of as networks of corner-sharing tetrahedra. Further, the size and topology of its ground state manifold for Heisenberg magnets are identical to

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Spin-Lattice Coupling in Frustrated Antiferromagnets

Tchernyshyov

Chern

2010

Introduction to Frustrated Magnetism

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We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr 2 O 4 . We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.

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Ordering by quantum fluctuations in a strongly frustrated Heisenberg antiferromagnet

Cited by 106 publications

References 7 publications

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

Planar Pyrochlore, Quantum Ice and Sliding Ice

Spin-Lattice Coupling in Frustrated Antiferromagnets

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