Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules

Abstract

In many quantum magnets especially the rare-earth ones, the low-lying crystal field states are not well separated from the excited ones and thus are insufficient to describe the low-temperature magnetic properties. Inspired by this simple observation, we develop a microscopic theory to describe the magnetic physics due to the collapses of the weak crystal field states. We find two cases where the excited crystal field states should be seriously included into the theory. One case is when the bandwidth of the excited crystal field states is comparable to the crystal field gap. The other case is when the exchange energy gain between the low-lying and excited crystal field states overcomes the crystal field gap. Both cases could drive a phase transition and result in magnetic orders by involving the excited crystal field states. We dub the above physics as upper branch magnetism and phase transition. We discuss the multitude of magnetic phases and the emergent selection rules for the detection of the underlying excitations. We expect our results to help improve the understanding of many rare-earth magnets with weak crystal field gaps such as Tb${}_2$Ti${}_2$O${}_7$ and Tb${}_2$Sn${}_2$O${}_7$, and also provide a complementary perspective to the prevailing local "$J$" physics in $4d$/$5d$ magnets.

arXiv comment9 pages, 4 figures, 2 tables. First two authors contributed equally. Suggestion of experimental relevances is welcome

References in corpus (71)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Magnetic Pyrochlore Oxides
• Correlated quantum phenomena in the strong spin-orbit regime
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Bose-Einstein Condensation in Magnetic Insulators
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Quantum Excitations in Quantum Spin Ice
• Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO${}_4$
• Evidence for a spinon Fermi surface in a triangular lattice quantum spin liquid candidate
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO${}_4$
• A new spin-anisotropic harmonic honeycomb iridate
• Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO${}_4$
• Excitonic Magnetism in Van Vleck-type d^4 Mott Insulators
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• $\mu$SR evidence for the U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO${}_4$
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Generic quantum spin ice
• Crystalline Electric Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO${}_4$
• Frustrated quantum rare-earth pyrochlores
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• An anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets
• Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
• Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides
• Topography of Spin Liquids on a Triangular Lattice
• Quantum Melting of Spin Ice: Emergent Cooperative Quadrupole and Chirality
• Magnetic order and spin fluctuations in the spin liquid Tb$\_2$Sn$\_2$O$\_7$
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate YbMgGaO4
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids
• Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr${}_2$Zr${}_2$O${}_7$
• Investigation of the magnetic structure and crystal field states of pyrochlore antiferromagnet Nd2Zr2O7
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Fluctuations and all-in$-$all-out ordering in dipole-octupole Nd2Zr2O7
• A Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice: FeSc2S4
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Raman scattering from Higgs mode oscillations in the two-dimensional antiferromagnet Ca${}_2$RuO${}_4$
• 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${}_4$
• Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4
• Order by Disorder Spin Wave Gap in the XY Pyrochlore Magnet Er2Ti2O7
• Unconventional Magnetic Ground State in Yb${}_2$Ti${}_2$O${}_7$
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• The effect of spin-orbit coupling on the effective-spin correlation in YbMgGaO4
• Hidden multipolar orders of dipole-octupole doublets on a triangular lattice
• Crystal field states of Tb3+ in the pyrochlore spin liquid Tb2Ti2O7 from neutron spectroscopy
• Reentrant Phase Diagram of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ in $⟨111⟩$ Magnetic Field
• Lack of Evidence for a Singlet Crystal Field Ground State in the Tb2Ti2O7 Magnetic Pyrochlore
• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
• Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7
• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• Magnetic Excitations in Spin-Orbit Coupled $d^4$ Mott Insulator on Square Lattice
• Effective quantum pseudospin-1/2 model for Yb pyrochlore oxides
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Doping-Induced Ferromagnetism and Possible Triplet Pairing in d4 Mott Insulators
• XY Antiferromagnetic Ground State in the Effective S=1/2 Pyrochlore Yb2Ge2O7
• Excitation spectrum and magnetic field effects in a quantum critical spin-orbital system:FeSc${}_2$S${}_4$
• Unstable Spin-Ice Order in the Stuffed Metallic Pyrochlore Pr${}_{2+x}$Ir${}_{2-x}$O${}_{7-\delta }$

Cited by in corpus (11)

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• Induced quantum magnetism in CEF singlet ground state models: Thermodynamics and excitations
• Low Energy Magneto-optics of Tb${}_2$Ti${}_2$O${}_7$ in [111] Magnetic Field
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Universal excitonic superexchange in spin-orbit-coupled Mott insulators
• Emergent transverse-field Ising model in ${\mathbf{d}}^4$ spin-orbit Mott insulators
• Upper branch thermal Hall effect in quantum paramagnets
• Impact of gapped spin-orbit excitons on low energy pseudospin exchange interactions