Quantum spin liquid and electric quadrupolar states of single crystal Tb2+xTi2-xO7+y

Wakita, Mika; Taniguchi, Tadatsugu; Edamoto, H.; Takatsu, Hiroshi; Kadowaki, Hiroko

doi:10.1088/1742-6596/683/1/012023

Cited by 24 publications

(34 citation statements)

References 24 publications

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“…While it is now suggested that Tb 2 Ti 2 O 7 crystals may be inhomogeneous [35], we find that the lattice strain of our Tb 2 Ti 2 O 7 crystal (and LD probes the bulk of a large crystal) is not generally larger than the other two compounds.…”

Section: Discussioncontrasting

confidence: 58%

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

et al. 2016

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In this work, we present a neutron Larmor diffraction study of the rare-earth pyrochlores R 2 Ti 2 O 7 with R = Tb, Dy, Ho. We measured the temperature dependence of the lattice parameter with precision 10 −5 , between 0.5 and 300 K in each of the three compounds. The lattice parameter of the spin ices Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 enters into the derivation of the charge of the emergent magnetic monopole excitations suggested to exist in these materials. We found that throughout the range of applicability of the theory of emergent monopoles in the spin ices there will be no renormalization of the monopole charge due to lattice contraction. In Tb 2 Ti 2 O 7 , strong magnetoelastic interactions have been reported. We found no sign of the previously reported negative thermal expansion, but did observe anomalies in the thermal expansion that can be correlated with previously observed interactions between phonon and crystal-field excitations. Other features in the thermal expansion of all three compounds can be related to previously observed anomalies of the elastic constants, and explained by the phonon band structure of the rare-earth titanates. The temperature dependence of the lattice strain in all three compounds can be correlated with the thermal population of excited crystal-field levels.

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Section: Discussioncontrasting

confidence: 58%

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

et al. 2016

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“…The slight Q-dependence and the non-resolution limited peak-width, ∆E ≫ (∆E) resolution = 0.01 meV, have been one of the puzzling observations of TTO. The present interpretation using the composite spin-quadrupole wave can be an answer 23,24 .…”

Section: Magnetic Spectra Of Polycrystalline Tb2+xti2−xo7+ymentioning

confidence: 62%

Composite Spin and Quadrupole Wave in the Ordered Phase ofTb_2+xTi_2-xO_7+y

Kadowaki

Takatsu

Taniguchi

et al. 2015

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The hidden ordered state of the frustrated pyrochlore oxide Tb2+xTi2−xO7+y is possibly one of the two electric multipolar, or quadrupolar, states of the effective pseudospin-1/2 Hamiltonian derived from crystal-field ground state doublets of non-Kramers Tb 3+ ions. These long-range orders are antiparallel or parallel alignments of transverse pseudospin components representing electric quadrupole moments, which cannot be observed as magnetic Bragg reflections by neutron scattering. However pseudospin waves of these states are composite waves of the magnetic-dipole and electricquadrupole moments, and can be partly observed by inelastic magnetic neutron scattering. We calculate these spin-quadrupole waves using linear spin-wave theory and discuss previously observed low-energy magnetic excitation spectra of a polycrystalline sample with x = 0.005 (Tc = 0.5 K).

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“…1(a)], which suggests that the elusive spin-liquid state of TTO is the U(1) QSL. We emphasize that a high-quality single-crystalline sample with a well-controlled x value [35] enables us to accomplish this work.…”

mentioning

confidence: 99%

“…Polycrystalline and single-crystalline Tb 2+x Ti 2−x O 7+y samples were prepared by a standard solid-state reaction [34] and by a floating zone method [35]. Specific heat was measured by a quasi-adiabatic method down to 0.1 K using a plate-shape crystal with a size of 0.7 × 0.9 × 0.1 mm 3 whose shortest dimension is along a [110] axis.…”

mentioning

confidence: 99%

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Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xO
Takatsu
¹
,
Onoda
²
,
Kittaka
³

et al. 2016
Phys. Rev. Lett.
58
15
89
0
1
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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.Cx, 78.70.Nx, 75.10.Kt, 75.30.Ds Geometrically frustrated magnets have been actively investigated in condensed matter physics [1]. In particular, spin ice (SI), e.g. R 2 Ti 2 O 7 (R = Dy or Ho) [2,3], provides prototypical frustrated Ising magnets with the pyrochlore lattice structure [4], consisting of a three-dimensional network of cornersharing tetrahedra [ Fig. 1(b)]. It displays fascinating features such as a finite zero-point entropy [5] and thermally excited emergent magnetic or SI monopoles [6,7]. An intriguing theoretical proposal for a U(1) quantum spin liquid (QSL) state [8] has been made for variants of SI endowed with quantum spin fluctuations [9][10][11][12][13][14]. The U(1) QSL state [8-10] is characterized by an emergent U(1) gauge field producing gapless fictitious photons and by gapped bosonic spinon excitations carrying the SI magnetic monopole charge [8,9,13,15]. By increasing the transverse interaction, the system can undergo a phase transition from the U(1) QSL to a long range ordered (LRO) state of transverse spins or pseudospins representing electric-quadrupole moments for non-Kramers ions [9][10][11]. This state can be described as a Higgs phase [16][17][18][19][20].In a quest to QSL states in frustrated magnetic systems from both theoretical [21][22][23] and experimental [24,25] viewpoints, an Ising-like pyrochlore Tb 2 Ti 2 O 7 (TTO) is a potential candidate for a U(1) QSL: it has been reported to remain in a fluctuating spin state down to 50 mK without magnetic LRO [26,27]. However, the origin of this spin liquid state of TTO has been elusive for more than a decade despite many investigations (see Refs. [4,13,28] and references therein, and recent Refs. [29-31]), and is still under hot debate [13,28]. To solve this challenging problem of TTO, we start this investigation by postulating that the theoretically-proposed interaction between electric quadrupole moments of non-Kramers ions including Tb 3+ [the fourth term of Eq. interactions between magnetic dipole moments [the first three terms of Eq. (1)] and the perturbation through first excited crystal-field (CF) states [14,32], and by taking another assumption of Jahn-Teller (JT) distortion [28,33]. Under the present postulation, two ground states of off-stoichiometric Tb 2+x Ti 2−x O 7+y samples [34] will possibly be accounted for by the U(1) QSL (x < x c ) and electric quadrupolar (x > x c ) states of Ref. [9].In this Letter, we investigate the hidden order of Tb 2+x Ti 2−x O 7+y (x = 0.005 > x c ), because the electric qua...

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Quantum spin liquid and electric quadrupolar states of single crystal Tb_2+xTi_2-xO_7+y

Cited by 24 publications

References 24 publications

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

Composite Spin and Quadrupole Wave in the Ordered Phase ofTb_2+xTi_2-xO_7+y

Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xO
Takatsu
¹
,
Onoda
²
,
Kittaka
³

et al. 2016
Phys. Rev. Lett.
58
15
89
0
1
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Quantum spin liquid and electric quadrupolar states of single crystal Tb2+xTi2-xO7+y

Cited by 24 publications

References 24 publications

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho

Composite Spin and Quadrupole Wave in the Ordered Phase ofTb2+xTi2-xO7+y

Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xOTakatsu1, Onoda2, Kittaka3 et al. 2016Phys. Rev. Lett.58158901View full textAdd to dashboardCite

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Quantum spin liquid and electric quadrupolar states of single crystal Tb_2+xTi_2-xO_7+y

Composite Spin and Quadrupole Wave in the Ordered Phase ofTb_2+xTi_2-xO_7+y

Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xO
Takatsu
¹
,
Onoda
²
,
Kittaka
³

et al. 2016
Phys. Rev. Lett.
58
15
89
0
1
View full text Add to dashboard Cite