Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond

Abstract

The rare-earth magnet TmMgGaO${}_4$ is proposed to be an intrinsic quantum Ising magnet described by the antiferromagnetic transverse field Ising model (TFIM) on a triangular lattice, where the relevant degrees of freedom are the non-degenerate dipole-multipole doublets of the Tm${}^{3+}$ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet. We compare this special doublet of Tm${}^{3+}$ with the dipole-octupole Kramers doublet. We study the proposed effective model for the Tm-based triangular lattice and consider the effects of external magnetic fields and finite temperatures. From the "orthogonal operator approach", we show that the TFIM with the three-sublattice intertwined ordered state agrees with the experiments and further clarify the discrepancy in the nubmers of the magnetic sublattices and the measured magnon branches. We make specific predictions for the evolution of the magnetic properties with the external magnetic field. Furthermore, we demonstrate that an emergent U(1) symmetry emerges in thermal melting of the underlying orders and at the criticality, and summarize the previously known signatures related to the finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) physics. We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially the Tm-based materials.

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References in corpus (63)

• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Linear spin wave theory for single-Q incommensurate magnetic structures
• Ising models of quantum frustration
• Supersolid hardcore bosons on the triangular lattice
• Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
• Spin-waves in triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Two-dimensional periodic frustrated Ising models in a transverse field
• Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
• 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
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Dualities and the phase diagram of the $p$-clock model
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Experimental Observation of Bethe Strings
• Evolution of Quantum Fluctuations Near the Quantum Critical Point of the Transverse Field Ising Chain System CoNb${}_2$O${}_6$
• Candidate Quantum Spin Liquid in the Ce\textsuperscript{3+} Pyrochlore Stannate Ce${}_2$Sn${}_2$O${}_7$
• A quantum liquid of magnetic octupoles on the pyrochlore lattice
• Investigation of the magnetic structure and crystal field states of pyrochlore antiferromagnet Nd2Zr2O7
• Fluctuations and all-in$-$all-out ordering in dipole-octupole Nd2Zr2O7
• Hidden Order Behaviour in URu2Si2 (A Critical Review of the Status of Hidden Order in 2014)
• Waves in the unseen : theory of spin excitations in a quantum spin nematic
• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Removing the spin ice cap: magnetic ground states of rare earth tripod kagome lattice Mg${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (RE = Gd, Dy, Er)
• Intertwined dipolar and multipolar order in the triangular-lattice magnet TmMgGaO${}_4$
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Observation of long range magnetic ordering in pyrohafnate Nd2Hf2O7: A neutron diffraction study
• Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in Transverse Magnetic Field
• The quantum origins of moment fragmentation in Nd2Zr2O7
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• Structural and Magnetic Investigations of Single-Crystals of the Neodymium Zirconate Pyrochlore, Nd2Zr2O7
• Quantum criticality of the Ising-like screw chain antiferromagnet SrCo2V2O8 in a transverse magnetic field
• Nd2Sn2O7: an all-in-all-out pyrochlore magnet with no divergence-free field and anomalously slow paramagnetic spin dynamics
• Quantum criticality of two-dimensional quantum magnets with long-range interactions
• Hidden multipolar orders of dipole-octupole doublets on a triangular lattice
• Structural and magnetic properties of two branches of the Tripod Kagome Lattice family A${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb)
• Excitations in the quantum paramagnetic phase of the quasi-one-dimensional Ising magnet CoNb${}_2$O${}_6$ in a transverse field: Geometric frustration and quantum renormalization effects
• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
• Partial up-up-down order with the continuously distributed order parameter in the triangular antiferromagnet TmMgGaO4
• Phase transition of the q-state clock model: duality and tensor renormalization
• Absence of zero-point entropy in a triangular Ising antiferromagnet
• Theory of the Kagome Lattice Ising Antiferromagnet in Weak Transverse Field
• Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields
• Disorder by disorder and flat bands in the kagome transverse field Ising model
• Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices
• Quantum criticality of the transverse-field Ising model with long-range interactions on triangular-lattice cylinders
• Dipolar-Octupolar Ising Antiferromagnetism in Sm${}_2$Ti${}_2$O${}_7$: A Moment Fragmentation Candidate
• Universal Thermodynamic Signature of Self-dual Quantum Critical Points
• Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model
• Possible gapless spin liquid in a rare-earth kagomé lattice magnet Tm${}_3$Sb${}_3$Zn${}_2$O${}_{14}$
• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
• Persisting topological order via geometric frustration
• Melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices
• Dipolar spin ice states with fast monopole hopping rate in CdEr${}_2$X${}_4$ (X = Se, S)
• Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Intermultiplet transitions and magnetic long-range order in Sm-based pyrochlores
• Tomonaga-Luttinger liquid in quasi-one-dimensional antiferromagnet BaCo2V2O8 in magnetic fields
• A neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels
• Slow spin tunneling in the paramagnetic phase of the pyrochlore Nd2Sn2O7
• Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain

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• Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound
• Frustrated Magnetism in Fluoride and Chalcogenide Pyrochlore Lattice Materials
• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
• Quantum dynamics of topological strings in a frustrated Ising antiferromagnet
• Neutron scattering investigation of proposed Kosterlitz-Thouless transitions in the triangular-lattice Ising antiferromagnet TmMgGaO4
• Rare-Earth Chalcogenides: An Inspiring Playground For Exploring Frustrated Magnetism
• Exchange renormalized crystal field excitation in a quantum Ising magnet KTmSe${}_2$
• Field-Tuned Quantum Effects in a Triangular-Lattice Ising Magnet
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Distinguishing thermodynamics and spectroscopy for octupolar U(1) spin liquid of Ce-pyrochlores
• Order-by-disorder and emergent Kosterlitz-Thouless phase in triangular Rydberg array
• Quantum annealing of a frustrated magnet
• Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii physics in the triangular lattice bilayer colbaltate
• Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO${}_4$
• Induced quantum magnetism on a triangular lattice of non-Kramers ions in PrMgAl11O19
• Field tunable BKT and quantum phase transitions in spin-1/2 triangular lattice antiferromagnet
• Doping-induced structural transformation in the spin-1/2 triangular-lattice antiferromagnet Na${}_2$Ba${}_{1-x}$Sr${}_x$Co(PO${}_4$)${}_2$
• Emergent transverse-field Ising model in ${\mathbf{d}}^4$ spin-orbit Mott insulators
• Crystal-Field--Driven Magnetoelectric Coupling in the Non-Kramers Hexaaluminate PrMgAl11O19
• Interplay of frustration and quantum fluctuations in a spin-1/2 anisotropic square lattice
• Theory of magnetism for rare-earth magnets on the Shastry-Sutherland lattice with non-Kramers ions
• Gapless spinon excitations emerging from a multipolar transverse field in the triangular-lattice Ising antiferromagnet NaTmSe2
• Interplay of itinerant electrons and Ising moments in a hybrid honeycomb quantum magnet TmNi${}_3$Al${}_9$
• Three-dimensional Sandglass Magnet with Non-Kramers ions
• Loop Algorithm for Quantum Transverse Ising Model in a Longitudinal Field
• Frustrated Rydberg Atom Arrays Meet Cavity-QED: Emergence of the Superradiant Clock Phase
• Emergent Dispersive Multipolar Excitations in NaErSe${}_2$
• Canted ferromagnetic order in a distorted triangular-lattice magnet Na${}_2$SrCo(VO${}_4$)${}_2$