Quadrupole Order in the Frustrated Pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y}.
A hidden order that emerges in the frustrated pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y} with T_{c}=0.53  K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semiquantitative 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.
Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan.|Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan.
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Takatsu
RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.|Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan.
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Onoda
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
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Kittaka
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
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Kasahara
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
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Kono
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
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Sakakibara
RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.|Department of Applied Physics, University of Tokyo, Bunkyo, Tokyo 113-8656, Japan.
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Kato
Institute Laue Langevin, BP 156, F-38042 Grenoble, France.
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Fåk
Institute Laue Langevin, BP 156, F-38042 Grenoble, France.
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Ollivier
NCNR, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6102, USA.
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Lynn
Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan.
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Taniguchi
Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan.
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Wakita
Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan.
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Kadowaki