Frustrated Quantum Rare-Earth Pyrochlores

Rau, Jeffrey G.; Gingras, Michel J. P.

doi:10.1146/annurev-conmatphys-022317-110520

Cited by 209 publications

(216 citation statements)

References 155 publications

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“…In the following, we rationalize our observations of octupolar scattering on the basis of the Hamiltonian for rareearth pyrochlores with 'dipole-octupole' doublets ℋ 56 = ∑ 8 99 and # $ transform like magnetic dipoles while # ' behaves as an octupole moment 7,8,24 . We use a simplified version of the generic Hamiltonian considering 99 = 9$ = 0, which still captures the essential physics of octupolar phases.…”

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confidence: 64%

A quantum liquid of magnetic octupoles on the pyrochlore lattice

et al. 2020

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Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles 1 .Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores -a state described by a lattice gauge theory of quantum electrodynamics 2-4 . However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders 5-6 . Here we show that the correlated ground state of a Ce 3+based pyrochlore, Ce2Sn2O7, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipoleoctupole doublets on a pyrochlore lattice 7-8 . The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule. Our work identifies Ce2Sn2O7 as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations. The composite 'dipole-octupole' nature of the degrees of freedom and their evolution as a function of temperature or magnetic field provide new ways of controlling emergent phenomena in quantum materials.

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confidence: 64%

A quantum liquid of magnetic octupoles on the pyrochlore lattice

et al. 2020

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“…Rare-earth pyrochlores have been central to the study of frustrated magnetism, hosting exotic classical and quantum many-body physics, notably emergent gauge fields, and putative quantum spin liquid phases [1][2][3] . A range of these systems is well-described by nearest-neighbour exchange Hamiltonians which, using the symmetries of the pyrochlore lattice, are completely specified by four real coupling constants 4 .…”

Section: Introductionmentioning

confidence: 99%

Analytical theory of pyrochlore cooperative paramagnets

Pandey¹,

Moessner

Castelnovo³

2020

Phys. Rev. B

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The pyrochlore lattice is associated with several potential and actual spin liquid phases as a result of its strong geometric frustration. At finite temperature, these can exhibit an unusually broad cross-over regime to a conventional paramagnet. Here, we study this regime analytically by showing how a single-tetrahedron Hamiltonian can extrapolate beyond the first term of a high-temperature expansion and yield insights into the build-up of correlations. We discuss how this unusual behaviour is brought about by the structure of the eigenspaces of the coupling matrix. Further interesting behaviour can appear for parameter values located near phase transitions: we find coexistence of (111) rods and (220) peaks in the structure factor, as observed in neutron scattering experiments on Yb 2 Ti 2 O 7 .

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“…In particular, for rare-earth pyrochlore oxides with a trivalent 4f magnetic ion, there is a wealth of stoichiometric compounds available in large single-crystal form, necessary for detailed neutron scattering studies. This, along with the synergetic dialogue between theory and experiments, has led to the experimental discovery and the theoretical rationalization of numerous phenomena like spin ice physics, magnetic moment fragmentation, order-by-disorder, fragile splayed-ferromagnetism and candidate spin liquid phenomenology (3,4).…”

Section: Introductionmentioning

confidence: 99%

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

et al. 2019

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We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr 4 O 8 and LiGaCr 4 O 8 , a spiral spin liquid with two-dimensional degeneracy for CuInCr 4 Se 8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr 4 S 8 , LiGaCr 4 S 8 and CuInCr 4 S 8 . The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.

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Frustrated Quantum Rare-Earth Pyrochlores

Cited by 209 publications

References 155 publications

A quantum liquid of magnetic octupoles on the pyrochlore lattice

A quantum liquid of magnetic octupoles on the pyrochlore lattice

Analytical theory of pyrochlore cooperative paramagnets

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

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