2016
DOI: 10.1103/physrevlett.116.217201
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Quadrupole Order in the Frustrated PyrochloreTb2+xTi2xO

Abstract: 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. 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. PACS numbers: 75.40… Show more

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Cited by 58 publications
(104 citation statements)
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“…The studies 7,23,25 of the effective Hamiltonian of Eq. (16) showed that there are two electric quadrupolar states: the PAF state (planar antiferropseudospin) and the PF state (planar ferropseudospin) depending on the two parameters (δ, q) (see Fig.…”
Section: Pseudopin Wavementioning
confidence: 99%
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“…The studies 7,23,25 of the effective Hamiltonian of Eq. (16) showed that there are two electric quadrupolar states: the PAF state (planar antiferropseudospin) and the PF state (planar ferropseudospin) depending on the two parameters (δ, q) (see Fig.…”
Section: Pseudopin Wavementioning
confidence: 99%
“…(17)) along several symmetry directions in the FCC Brillouin zone using the interaction parameters J nn = 1 K, q = 0.85, and δ = 0 adopted in Ref. 23. One can see two flat excitation branches in Fig.…”
Section: Pseudopin Wavementioning
confidence: 99%
“…As a result, phonons (and lattice zero point motions) are now the source of spin fluctuations and by their virtual exchange may give rise to new quantum terms in the effective Hamiltonian of Tb 2 Ti 2 O 7 . Depending on their strength, a long-range quadrupolar order or Coulombphase-like state might be stabilized, provided the Ising term dominates [7, 10,21]. Furthermore, an interesting feature of the vibronic process is that the acoustic phonon crosses the two doublets, which themselves being close in energy, will also partially mix.…”
mentioning
confidence: 99%
“…This signal likely corresponds to fluctuations between the two |± electronic states of the crystal electric field (CEF) ground state doublet. It was interpreted as a signature of interactions between quadrupoles, highlighting the importance of those degrees of freedom [18,[20][21][22]. This is because the non-Kramers nature of Tb 3+ ions prevents magnetic exchange alone from inducing such fluctuations within the Ising-like ground state [22][23][24].…”
mentioning
confidence: 99%
“…Our study covered the temperature range 0.5 K < T < 300 K, as it was convenient to use the 3 He refrigerator to study all three compounds. Recently, it has been suggested that there is a quadrupole ordering transition in Tb 2 Ti 2 O 7 at a temperature of T ≈ 0.5 K [46], only observable in crystals of very high quality or powders. Larmor diffraction could be used to study the transition in a small crystal with directly verified heat capacity-since the signal is proportional to Bragg intensity, even a relatively small sample can be used.…”
Section: Discussionmentioning
confidence: 99%