Quadrupole Order in the Frustrated Pyrochlore Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$

Abstract

A hidden order that emerges in the frustrated pyrochlore Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$ with $T_{\text{c}}=0.53$ K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semi-quantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb${}_2$Ti${}_2$O${}_7$ is most likely a U(1) quantum spin-liquid state.

5 pages, 5 figures, including Supplemental Material

References in corpus (11)

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• Crystal field states of Tb3+ in the pyrochlore spin liquid Tb2Ti2O7 from neutron spectroscopy
• Composite spin and quadrupole wave in the ordered phase of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Mesoscopic correlations in Tb2Ti2O7 spin liquid
• Quantum spin liquid and electric quadrupolar states of single crystal Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Quadrupole order in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$

Cited by in corpus (39)

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• Emergence of nontrivial magnetic excitations in a spin liquid state of kagome volborthite
• Probing hidden spin order with interpretable machine learning
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• Learning multiple order parameters with interpretable machines
• Chirality-driven Hall Transport Phenomena of Spins
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• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Ground state phase diagram of dipolar-octupolar pyrochlores
• Ground state selection under pressure in the quantum pyrochlore magnet Yb2Ti2O7
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• Double Vibronic process in the quantum spin ice candidate Tb${}_2$Ti${}_2$O${}_7$ revealed by terahertz spectroscopy
• Crystal-field states and defect levels in candidate quantum spin ice Ce${}_2$Hf${}_2$O${}_7$
• Quantum spin ice under a [111] magnetic field: from pyrochlore to kagomé
• Probing octupolar hidden order via Janus impurities
• Quantum spin liquid and electric quadrupolar states of single crystal Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Antiferromagnetism and crystalline-electric field excitations in tetragonal NaCeO2
• Neutron Larmor diffraction investigation of the rare earth pyrochlores $R_2$Ti${}_2$O${}_7$ ($R$ = Tb, Dy, Ho)
• Fingerprints of quantum spin ice in Raman scattering
• Strong quantum fluctuations due to competition between magnetic phases in a pyrochlore iridate
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Semi-classical Approach to Quantum Spin Ice
• Continuum excitation and pseudospin wave in quantum spin-liquid and quadrupole ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Terahertz Magneto-optical investigation of quadrupolar spin-lattice effects in magnetically frustrated Tb2Ti2O7
• Spin correlations of quantum-spin-liquid and quadrupole-ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Melting of spin ice state and development of fifth order susceptibility with magnetic field in pyrochlore Tb2Sn2O7
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• Magnetic Monopole Supercurrent through a Quantum Spin Ice Tunnel Junction
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• Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Collective magnetic state induced by charge disorder in the non-Kramers rare-earth pyrochlore Tb${}_2$ScNbO${}_7$
• Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\mathrm{T}{\mathrm{b}}_{2+\delta }\mathrm{T}{\mathrm{i}}_{2-\delta }{\mathrm{O}}_7$
• First-principles design of the spinel iridate Ir2O4 for high-temperature quantum spin ice
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Excitation spectrum and low-temperature magnetism in disordered defect-fluorite Ho2Zr2O7