Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbour interaction

Tsuneishi, Daisuke; Ioki, Masayuki; Kawamura, Hikaru

doi:10.1088/0953-8984/19/14/145273

Cited by 21 publications

(37 citation statements)

References 6 publications

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“…About four complex states were identified, including that above mentioned state introduced by Kawamura and collaborators [54][55][56]; a state reminiscent of our double-twist state; a more complex generalization of a conic spiral; and a cuboctahedral spin state that has less than cubic lattice symmetry, thus evading the negative conclusions of Sec. VIII B 1 [58].…”

Section: On To Pyrochlore Lattice?mentioning

confidence: 95%

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Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Sklan

Henley

2013

Phys. Rev. B

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We consider methods to identify the classical ground state for an exchange-coupled Heisenberg antiferromagnet on a non-Bravais lattice with interactions Jij to several neighbor distances. Here we apply this to the unusual "octahedral" lattice in which spins sit on the edge midpoints of a simple cubic lattice. Our approach is informed by the eigenvectors of Jij with largest eigenvalues. We discovered two families of non-coplanar states: (i) two kinds of commensurate state with cubic symmetry, each having twelve sublattices with spins pointing in (1,1,0) directions in spin space (modulo a global rotation); (ii) varieties of incommensurate conic spiral. The latter family is addressed by projecting the three-dimensional lattice to a one-dimensional chain, with a basis of two (or more) sites per unit cell.

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Section: On To Pyrochlore Lattice?mentioning

confidence: 95%

“…The J 1 -J 2 , or J 1 -J 3 pyrochlore, with large antiferromagnetic J 1 , has a noncoplanar and somewhat obscure state that is not fully understood at T = 0 [54][55][56].…”

Section: On To Pyrochlore Lattice?mentioning

confidence: 99%

Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Sklan

Henley

2013

Phys. Rev. B

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“…[48] from the entropically selected ordered phase to the energetically ordered phase as the temperature of the system decreases. Another related example is the Heisenberg J 1 -J 2 model on a pyrochlore lattice where the nearest-neighbor interaction is antiferromagnetic and the second-neighbor coupling ferromagnetic [49]. In this model, there is an intermediate temperature collinear phase which is selected by entropic fluctuations that gives way to a multi-q structure at lower temperatures.…”

Section: B Effect Of Competing Nearest-neighbor Pseudo-dipolar Intermentioning

confidence: 99%

Order-by-disorder in theXYpyrochlore antiferromagnet

2014

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We investigate the properties of the XY pyrochlore antiferromagnet with infinite local 111 planar anisotropy. We identify the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we find that the model exhibits thermal order-by-disorder leading to low-temperature long-range order consisting of discrete magnetic domains. In doing so, we set aside doubts that order-by-disorder survives in the thermodynamic limit in this model. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. With a previously unreported finite-size scaling analysis of Monte Carlo data, we confirm that the transition is first order for the XY model. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions or long-range dipolar interactions to the spin Hamiltonian. Quite interestingly, the resulting state selected by thermal order-by-disorder is metastable below some temperature. We discuss our results in relation to the Er 2 Ti 2 O 7 and Er 2 Sn 2 O 7 pyrochlore antiferromagnets.

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“…In this paper we discuss these questions in the context of a classical Heisenberg antiferromagnet on the pyrochlore lattice with interac-tions going beyond nearest neighbors. Following previous work by Reimers et al 12 and by Tsuneishi et al, 13 we consider the classical Heisenberg antiferromagnet on the pyrochlore lattice with the Hamiltonian…”

Section: Introductionmentioning

confidence: 99%

Partial order from disorder in a classical pyrochlore antiferromagnet

2008

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We investigate theoretically the phase diagram of a classical Heisenberg antiferromagnet on the pyrochlore lattice perturbed by a weak second-neighbor interaction J_2. The huge ground state degeneracy of the nearest-neighbor Heisenberg spins is lifted by J_2 and a magnetically ordered ground state sets in upon approaching zero temperature. We have found a new, partially ordered phase with collinear spins at finite temperatures for a ferromagnetic J_2. In addition to a large nematic order parameter, this intermediate phase also exhibits a layered structure and a bond order that breaks the sublattice symmetry. Thermodynamic phase boundaries separating it from the fully disordered and magnetically ordered states scale as 1.87 J_2 S^2 and 0.26 J_2 S^2 in the limit of small J_2. The phase transitions are discontinuous. We analytically examine the local stability of the collinear state and obtain a boundary T ~ J_2^2/J_1 in agreement with Monte Carlo simulations.Comment: 14 pages revtex, revised phase diagram, references adde

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Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbour interaction

Cited by 21 publications

References 6 publications

Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Order-by-disorder in theXYpyrochlore antiferromagnet

Partial order from disorder in a classical pyrochlore antiferromagnet

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