How quantum are classical spin ices?

Abstract

The pyrochlore spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are well described by classical Ising models down to very low temperatures. Given the empirical success of this description, the question of the importance of quantum effects in these materials has been mostly ignored. We show that the common wisdom that the strictly Ising moments of Dy3+ and Ho3+ imply strictly Ising interactions is too naive; a more complex argument is needed to explain the close agreement between theory and experiment. From a microscopic picture of the interactions in rare-earth oxides, we show that the high-rank multipolar interactions needed to induce quantum effects are generated only very weakly by super-exchange. Using this framework, we formulate an estimate of the scale of quantum effects in Ho2Ti2O7 and Dy2Ti2O7, finding it to be well below experimentally relevant temperatures. We discuss the implications of these results for realizing quantum spin ice in other materials.

5 pages + 12 pages

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• Why spin ice obeys the ice rules
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• Kagomé ice state in the dipolar spin ice Dy_{2}Ti_{2}O_{7}
• Exchange interaction between $J$-multiplets
• Magnetothermodynamics of the Ising Antiferromagnet Dy2Ge2O7
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Cited by in corpus (54)

• Frustrated quantum rare-earth pyrochlores
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Realization of the kagome spin ice state in a frustrated intermetallic compound
• A quantum liquid of magnetic octupoles on the pyrochlore lattice
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Experimental Insights into Ground State Selection of Quantum XY Pyrochlores
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Crystal field parameters of the rare earth pyrochlores $R_2$Ti${}_2$O${}_7$ ($R$ = Tb, Dy, Ho)
• Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material
• Crystal field Hamiltonian and anisotropy in KErSe2 and CsErSe2
• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Correlated Quantum Tunnelling of Monopoles in Spin Ice
• Quantum versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14
• Spin Ice Thin Film: Surface Ordering, Partial Magnetic Wetting and Emergent Square Ice
• Spin dynamics of the ordered dipolar-octupolar pseudospin-${}^1{/}_2$ pyrochlore Nd${}_2$Zr${}_2$O${}_7$ probed by muon spin relaxation
• Ising exchange interaction in lanthanides and actinides
• Dimensionality and irreversibility of field-induced transitions in SrDy2O4
• Anisotropic exchange Hamiltonian, magnetic phase diagram and domain inversion of Nd${}_2$Zr${}_2$O${}_7$
• Special temperatures in frustrated ferromagnets
• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Phonon-mediated spin-flipping mechanism in the spin ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Monopolar and dipolar relaxation in spin ice Ho${}_2$Ti${}_2$O${}_7$
• Common Glass-Forming Spin-Liquid State in the Pyrochlore Magnets Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Reentrance of disorder in the anisotropic shuriken Ising model
• Dipolar spin ice states with fast monopole hopping rate in CdEr${}_2$X${}_4$ (X = Se, S)
• Crystal-electric-field excitations in a quantum-spin-liquid candidate NaErS${}_2$
• Suppression of Pauling's Residual Entropy in Dilute Spin Ice (Dy${}_{1-x}$Y${}_x$)${}_2$Ti${}_2$O${}_7$
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Fingerprints of quantum spin ice in Raman scattering
• New mechanism of kinetic exchange interaction induced by strong magnetic anisotropy
• Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering
• Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr${}_2$Se${}_4$
• Excitation Spectrum and Spin Hamiltonian of the Frustrated Quantum Ising Magnet Pr${}_3$BWO${}_9$
• Multipolar exchange interaction and complex order in insulating lanthanides
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Field-Induced Ordering in Dipolar Spin Ice
• Deriving quantum spin model for a zigzag-chain ytterbium magnet with anisotropic exchange interactions
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Screening and the Pinch Point Paradox in Spin Ice
• Extremely slow non-equilibrium monopole dynamics in classical spin ice
• Long-wavelength correlations in ferromagnetic titanate pyrochlores as revealed by small angle neutron scattering
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Phonon Thermal Hall Effect in a non-Kramers Paramagnet
• Braided Ising spin-tube physics in a purported kagome magnet
• Tuning interactions in the spin-ice materials Dy${}_2$Ge${}_{2-x}$Si${}_x$O${}_7$ by silicon substitution
• Magnetic field tuning of crystal field levels and vibronic states in Spin-ice Ho${}_2$Ti${}_2$O${}_7$ observed in far-infrared reflectometry
• Observation of Unprecedented Fractional Magnetization Plateaus in a New Shastry-Sutherland Ising Compound
• Nature of ferroelectric transitions in spin ice Ho2Ti2O7 and Dy2Ti2O7
• Thermal Conductivity of Square Ice
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$
• Crossover from string to cluster dynamics following a field quench in spin ice