Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides

Abstract

The effective quantum pseudospin-1/2 model for interacting rare-earth magnetic moments, which are locally described with atomic doublets, is studied theoretically for magnetic pyrochlore oxides. It is derived microscopically for localized Pr^{3+} 4f moments in Pr_2TM_2O_7 (TM = Zr, Sn, Hf, and Ir) by starting from the atomic non-Kramers magnetic doublets and performing the strong-coupling perturbation expansion of the virtual electron transfer between the Pr 4f and O 2p electrons. The most generic form of the nearest-neighbor anisotropic superexchange pseudospin-1/2 Hamiltonian is also constructed from the symmetry properties, which is applicable to Kramers ions Nd^{3+}, Sm^{3+}, and Yb^{3+} potentially showing large quantum effects. The effective model is then studied by means of a classical mean-field theory and the exact diagonalization on a single tetrahedron and on a 16-site cluster. These calculations reveal appreciable quantum fluctuations leading to quantum phase transitions to a quadrupolar state as a melting of spin ice for the Pr^{3+} case. The model also shows a formation of cooperative quadrupole moment and pseudospin chirality on tetrahedrons. A sign of a singlet quantum spin ice is also found in a finite region in the space of coupling constants. The relevance to the experiments is discussed.

18 pages including 14 figures; Comparison with the magnetization curve on Pr2Ir2O7 included; to appear in Phys. Rev. B

References in corpus (9)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Thermal quenches in spin ice
• Ordering of the pyrochlore Ising model with the long-range RKKY interaction
• Quantum 120-degree model on pyrochlore lattice: orbital ordering in MnV2O4
• Weak quasistatic magnetism in the frustrated Kondo lattice Pr_2Ir_2O_7

Cited by in corpus (129)

• Quantum Spin Liquids
• Correlated quantum phenomena in the strong spin-orbit regime
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
• Rare-earth chalcogenides: A large family of triangular lattice spin liquid candidate
• Generic quantum spin ice
• Frustrated quantum rare-earth pyrochlores
• Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb_2Ti_2O_7
• Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• 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
• Magnetic orders and topological phases from f-d exchange in pyrochlore iridates
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Long-range order and spin-liquid states of polycrystalline Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Numerical evidence of quantum melting of spin ice: quantum-classical crossover
• How quantum are classical spin ices?
• The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator YbMgGaO4
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO${}_4$
• A Measure of Monopole Inertia in the Quantum Spin Ice Yb${}_2$Ti${}_2$O${}_7$
• Candidate quantum spin ice in the pyrochlore Pr${}_2$Hf${}_2$O${}_7$
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• Crystal field states in a Quantum Spin Ice]{Crystal field states of Pr${}^{3+}$ in the candidate quantum spin ice Pr${}_2$Sn${}_2$O${}_7$
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• Antiferro-quadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7
• Dynamics of Topological Excitations in a Model Quantum Spin Ice
• Structural and Magnetic Investigations of Single-Crystals of the Neodymium Zirconate Pyrochlore, Nd2Zr2O7
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material
• Competing orders and topology in the global phase diagram of pyrochlore iridates
• Spin liquid correlations, anisotropic exchange and symmetry breaking in Tb2Ti2O7
• Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
• Thermal Hall effects in quantum magnets
• Quadrupole Order in the Frustrated Pyrochlore Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Hidden multipolar orders of dipole-octupole doublets on a triangular lattice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Non-Kondo mechanism for resistivity minimum in spin ice conduction systems
• Static magnetic moments revealed by muon spin relaxation and thermodynamic measurements in quantum spin ice Yb${}_2$Ti${}_2$O${}_7$
• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• New physics in frustrated magnets: Spin ices, monopoles, etc
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Partial up-up-down order with the continuously distributed order parameter in the triangular antiferromagnet TmMgGaO4
• Effective quantum pseudospin-1/2 model for Yb pyrochlore oxides
• Absence of zero-point entropy in a triangular Ising antiferromagnet
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Of chain-based order and quantum spin liquids in dipolar spin ice
• Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields
• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Phonon thermal Hall effect in a metallic spin ice
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Correlated Quantum Tunnelling of Monopoles in Spin Ice
• Magnon interactions in the frustrated pyrochlore ferromagnet Yb${}_2$Ti${}_2$O${}_7$
• Order out of a Coulomb phase and Higgs transtion: frustrated transverse interactions of Nd2Zr2O7
• Spin dynamics of the ordered dipolar-octupolar pseudospin-${}^1{/}_2$ pyrochlore Nd${}_2$Zr${}_2$O${}_7$ probed by muon spin relaxation
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Double Vibronic process in the quantum spin ice candidate Tb${}_2$Ti${}_2$O${}_7$ revealed by terahertz spectroscopy
• Sample independence of magnetoelastic excitations in the rare earth pyrochlore Tb2Ti2O7
• Competing $U(1)$ and ${\mathbb{Z}}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce${}_2$Zr${}_2$O${}_7$
• Electronic transport in the Coulomb phase of the pyrochlore spin ice
• Quantum spin ice under a [111] magnetic field: from pyrochlore to kagomé
• Magnetisation process in Er2Ti2O7 and Tb2Ti2O7 at very low temperature
• Composite spin and quadrupole wave in the ordered phase of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Local Susceptibility of the Yb2Ti2O7 Rare Earth Pyrochlore Computed from a Hamiltonian with Anisotropic Exchange
• Anisotropic exchange Hamiltonian, magnetic phase diagram and domain inversion of Nd${}_2$Zr${}_2$O${}_7$
• Curie-law crossover in spin liquids
• Magnetic properties of triangular lattice antiferromagnets Ba3RB9O18 (R = Yb, Er)
• Theory of magnetostriction for multipolar quantum spin ice in pyrochlore materials
• Evolution of antiferromagnetic domains in the all-in-all-out ordered pyrochlore Nd${}_2$Zr${}_2$O${}_7$
• Spinon walk in quantum spin ice
• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Spectrum of itinerant fractional excitations in quantum spin ice
• Quantum spin liquid and electric quadrupolar states of single crystal Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Low temperature magnetic properties of Nd2Ru2O7
• Gapped ground state in the zigzag pseudospin-1/2 quantum antiferromagnetic chain compound PrTiNbO6
• Spin-orbital liquids in non-Kramers magnet on Kagome lattice
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Fingerprints of quantum spin ice in Raman scattering
• Low-energy spin dynamics in rare-earth perovskite oxides
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Topological thermal Hall effect of "magnetic monopoles" in pyrochlore U(1) spin liquid
• Spectroscopy of spinons in Coulomb quantum spin liquids
• Topological Superconductivity in Metal/Quantum-Spin-Ice Heterostructures
• Magnetic properties and spin dynamics in a spin-orbit driven Jeff= 1/2 triangular lattice antiferromagnet
• Effective point-charge analysis of crystal electric fields -- application to rare-earth pyrochlores and tripod kagome magnets R3Mg2Sb3O14
• Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering
• Experimental signatures of versatile Weyl semimetal in pyrochlore iridate with spin-ice like magnetic orders
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr${}_2$Se${}_4$
• Pseudo-Spin Versus Magnetic Dipole Moment Ordering in the Isosceles Triangular Lattice Material K${}_3$Er(VO${}_4$)${}_2$
• Continuum excitation and pseudospin wave in quantum spin-liquid and quadrupole ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Field induced phase diagram of the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Symmetry breaking via Kondo hybridization: Chiral nematic metal in Pr2Ir2O7
• Ordered ground states of kagome magnets with generic exchange anisotropy
• Spin correlations of quantum-spin-liquid and quadrupole-ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Slow spin tunneling in the paramagnetic phase of the pyrochlore Nd2Sn2O7
• Quadrupole order in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$
• Quantum percolation of monopole paths and the response of quantum spin ice
• Deriving quantum spin model for a zigzag-chain ytterbium magnet with anisotropic exchange interactions
• Ultrasound detection of emergent photons in generic quantum spin ice
• Magnetic field and thermal Hall effect in a pyrochlore U(1) quantum spin liquid
• Exchange interactions in two-state systems: rare earth pyrochlores
• Melting of spin ice state and development of fifth order susceptibility with magnetic field in pyrochlore Tb2Sn2O7
• Thermodynamic properties of quadrupolar states in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• 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
• Hidden phases born of a quantum spin liquid: Application to pyrochlore spin ice
• Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field
• Spin structure factor and thermodynamics in the antiferromagnetic quantum Ising model in the pyrochlore lattice
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Revisiting spin ice physics in the ferromagnetic Ising pyrochlore Pr${}_2$Sn${}_2$O${}_7$
• Exact ground states of frustrated quantum spin systems consisting of spin-dimer units
• Magnetic Monopole Supercurrent through a Quantum Spin Ice Tunnel Junction
• Magnetic-field-induced tunability of spin Hamiltonians: Resonances and Efimov states in Yb${}_2$Ti${}_2$O${}_7$
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• Exact diagonalization for spin-1/2 spin ice pyrochlores
• Phase Diagram of a Spin-ice Kondo Lattice Model in a Breathing Pyrochlore Lattice
• Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\mathrm{T}{\mathrm{b}}_{2+\delta }\mathrm{T}{\mathrm{i}}_{2-\delta }{\mathrm{O}}_7$
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• First-principles design of the spinel iridate Ir2O4 for high-temperature quantum spin ice
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• More bridging ligands activate direct exchange: the case of anisotropic Kitaev effective magnetic interactions
• Disorder and Quantum spin ice