Ground States of the Classical Antiferromagnet on the Pyrochlore Lattice

Lapa, Matthew F.; Henley, Christopher L.

doi:10.48550/arxiv.1210.6810

Cited by 20 publications

(49 citation statements)

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“…( 11), hence there is no guarantee that the spin configurations with minimum energy satisfy the strong constraint of the unit spin size at each site. Indeed, it gives an upper bound for the classical ground state energy, Moreover the non-coplanar spin configurations can not be found by this method 48,49 . To search for such states, we parametrize each spin in terms of its wave-vector, polar and azimuthal angles and use variational minimization method to find the ground state.…”

Section: Classical Phase Diagram Of Kmh Modelmentioning

confidence: 99%

Zero-temperature phase diagram of the classical Kane-Mele-Heisenberg model

2013

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The classical phase diagram of the Kane-Mele-Heisenberg model is obtained by three complementary methods: Luttinger-Tisza, variational minimization, and the iterative minimization method. Six distinct phases were obtained in the space of the couplings. Three phases are commensurate with long-range ordering, planar Néel states in horizontal plane (phase.I), planar states in the plane vertical to the horizontal plane (phase.VI) and collinear states normal to the horizontal plane (phase.II). However the other three, are infinitely degenerate due to the frustrating competition between the couplings, and characterized by a manifold of incommensurate wave-vectors. These phases are, planar helical states in horizontal plane (phase.III), planar helical states in a vertical plane (phase.IV) and non-coplanar states (phase.V). Employing the linear spin-wave analysis, it is found that the quantum fluctuations select a set of symmetrically equivalent states in phase.III, through the quantum order-by-disorder mechanism. Based on some heuristic arguments is argued that the same scenario may also occur in the other two frustrated phases VI and V.

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Section: Classical Phase Diagram Of Kmh Modelmentioning

confidence: 99%

Zero-temperature phase diagram of the classical Kane-Mele-Heisenberg model

2013

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“…The MC simulations were conducted for T = 0.2 K using single spin updates for continuous spin on pyrochlore lattices (with 16 site cubic unit cells) of size N = 16L 3 for L = 8 (8192 total spins) for a total of 2 × 10 8 steps. Further iterative minimization [35] was performed on the last configuration encountered in the run to obtain the classical spin configuration that corresponds to the nearest local energy minimum. This entire process was performed 400 times for different starting random seeds.…”

Section: Theoretical Simulationsmentioning

confidence: 99%

Multiphase Magnetism in Yb2Ti2O7

Scheie,

Kindervater,

Zhang

et al. 2019

Preprint

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We document the coexistence of ferro-and anti-ferromagnetism in pyrochlore Yb2Ti2O7 using three neutron scattering techniques on stoichiometric crystals: elastic neutron scattering shows a canted ferromagnetic ground state, neutron scattering shows spin wave excitations from both a ferro-and an antiferro-magnetic state, and field and temperature dependent small angle neutron scattering reveals the corresponding anisotropic magnetic domain structure. High-field 111 spin wave fits show that Yb2Ti2O7 is extremely close to an antiferromagnetic phase boundary. Classical Monte Carlo simulations based on the interactions inferrred from high field spin wave measurements confirm ψ2 antiferromagnetism is metastable within the FM ground state.

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“…Already the classical PHAF (i.e., for spin S → ∞) exhibits interesting properties and its study is far from being trivial [4][5][6][7][8][9][10]. Thus, the ground-state manifold is highly degenerate, the model exhibits strong short-range correlations, but it does not exhibit any long-range order, and, because of the huge degeneracy of the ground state, the model is very susceptible to various perturbations.…”

Section: Introductionmentioning

confidence: 99%

Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet

Derzhko,

Hutak,

Krokhmalskii

et al. 2020

Preprint

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The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M. Planck [M. Planck, Verhandl. Dtsch. phys. Ges. 2, 202-204 (1900)] we calculate thermodynamic properties of this model by interpolating between the low-and high-temperature behavior. For that we follow ideas developed in detail by B. Bernu and G. Misguich and use for the interpolation the entropy exploiting sum rules [the "entropy method" (EM)]. We complement the EM results for the specific heat, the entropy, and the susceptibility by corresponding results obtained by the finite-temperature Lanczos method (FTLM) for a finite lattice of N = 32 sites as well as by the high-temperature expansion (HTE) data. We find that due to pronounced finite-size effects the FTLM data for N = 32 are not representative for the infinite system below T ≈ 0.7. A similar restriction to T 0.7 holds for the HTE designed for the infinite PHAF. By contrast, the EM provides reliable data for the whole temperature region for the infinite PHAF. We find evidence for a gapless spectrum leading to a power-law behavior of the specific heat at low T and for a single maximum in c(T ) at T ≈ 0.25. For the susceptibility χ(T ) we find indications of a monotonous increase of χ upon decreasing of T reaching χ0 ≈ 0.1 at T = 0. Moreover, the EM allows to estimate the ground-state energy to e0 ≈ −0.52.

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Ground States of the Classical Antiferromagnet on the Pyrochlore Lattice

Cited by 20 publications

References 0 publications

Zero-temperature phase diagram of the classical Kane-Mele-Heisenberg model

Zero-temperature phase diagram of the classical Kane-Mele-Heisenberg model

Multiphase Magnetism in Yb2Ti2O7

Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet

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