Frustrated quantum rare-earth pyrochlores

Abstract

In this review we provide an introduction to the physics of a series of frustrated quantum rare-earth pyrochlores. We first give a background on the microscopic single- and two-ion physics of these materials, discussing the origins and properties of their exchange interactions and their minimal low-energy effective models, before outlining what is known about their classical and quantum phases. We then make use of this understanding to discuss four important material examples: Er${}_2$Ti${}_2$O${}_7$, Yb${}_2$Ti${}_2$O${}_7$, Tb${}_2$Ti${}_2$O${}_7$ and Pr${}_2$Zr${}_2$O${}_7$, covering in some detail what is known experimentally and theoretically for each, and summarize some key questions that remain open. Finally, we offer an outlook on some alternative material platforms for realizing similar physics and discuss what we see as prospects for future investigations on these quantum rare-earth pyrochlores.

20 pages, 10 figures. To appear in Annual Reviews of Condensed Matter Physics

References in corpus (37)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Models and Materials for Generalized Kitaev Magnetism
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr${}_2$Zr${}_2$O${}_7$
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Impact of Stoichiometry of Yb2Ti2O7 on its Physical Properties
• Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7
• Exchange interaction between $J$-multiplets
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• Antiferro-quadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Low Energy Electrodynamics of Novel Spin Excitations in the Quantum Spin Ice Yb${}_2$Ti${}_2$O${}_7$
• Synthesis, floating zone crystal growth and characterization of the Quantum Spin Ice $\mathrm{P}{\mathrm{r}}_2\mathrm{Z}{\mathrm{r}}_2{\mathrm{O}}_7$ pyrochlore
• Quantum spin configurations in Tb2Ti2O7
• Physical properties of a candidate quantum spin-ice system Pr2Hf2O7
• A single crystal high-temperature pyrochlore antiferromagnet
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Cluster-glass phase in pyrochlore XY antiferromagnets with quenched disorder
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
• NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7: novel single crystal pyrochlore antiferromagnets
• Double Vibronic process in the quantum spin ice candidate Tb${}_2$Ti${}_2$O${}_7$ revealed by terahertz spectroscopy
• Order Induced by Dilution in Pyrochlore XY Antiferromagnets
• Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
• Magnetic Excitations in the Ground State of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Long-range dynamical magnetic order and spin tunneling in the cooperative paramagnetic states of the pyrochlore analogous spinel antiferromagnets CdYb2X4 (X = S, Se)
• Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Continuum excitation and pseudospin wave in quantum spin-liquid and quadrupole ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Experimental evidence for field induced emergent clock anisotropies in the XY pyrochlore Er${}_2$Ti${}_2$O${}_7$

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• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Magnetic field effects in an octupolar quantum spin liquid candidate
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• Systematic extraction of crystal electric-field effects and quantum magnetic model parameters in triangular rare-earth magnets
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• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
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• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
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• A neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels
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