Magnetic-Field Effects on Quadrupolar Ordering in aΓ8-Quartet System CeB6

Shiina, Ryousuke; Shibata, Hiroyuki; Thalmeier, Peter

doi:10.1143/jpsj.66.1741

Cited by 399 publications

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“…The top row of Table I shows the induced dipole perpendicular to the applied field along [111] expected from group theoretical consideration for the quadrupole ordered phase of O 20 or O 22 . 13,14) These perpendicular moments breaking the C 3 symmetry appear on top of the ordinary van Vleck magnetization parallel to the field.…”

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“…[5][6][7][8][9][10][11] In these systems, it is possible that the ground states of the J multiplet split by the cubic crystalline electric field (CEF) are nonmagnetic, i.e., the matrix elements of the magnetic dipole J are identically zero, yet have a degeneracy that allows active higher-order multipoles such as electric quadrupoles or magnetic octupoles. Then various interesting phenomena such as multipole orders [12][13][14] or multichannel Kondo effects 15,16) are expected at low temperatures.These possibilities have indeed been realized in compounds containing Pr 3+ ions with the 4 f 2 electronic configuration. The nine states of the J = 4 ground multiplet are split by a cubic CEF into the Γ 1 nonmagnetic singlet, the Γ 3 nonmagnetic doublet, the Γ 4 magnetic triplet, and the Γ 5 magnetic triplet.…”

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“…If the CEF ground state is the Γ 3 doublet, we encounter an interesting situation that the ground state is nonmagnetic but has nonzero matrix elements for the two types of quadrupoles, O 20 = (3J 2 z −J 2 )/2 and O 22 = √ 3(J 2 x −J 2 y )/2, and one octupole T xyz = ( √ 15/6)J x J y J z , where the bar represents the sum over the possible permutations of the indices x, y, and z. 13) The series of compounds PrT 2 X 20 (T : transition metal, X: Zn or Al) provides particularly interesting examples of the Γ 3 CEF ground states. 4) As shown in Fig.…”

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“…Therefore, two of the 3c sites, denoted Table I. Field-induced dipole for magnetic fields along the 111 direction in the quadrupole ordered phase 13) and number of split NMR lines from the 3c site.…”

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NMR Observation of Ferro-Quadrupole Order in PrTi₂Al₂₀

et al. 2016

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We report the results of 27 Al-NMR measurements on a single crystal of PrTi 2 Al 20 . This compound shows a phase transition near 2 K associated with the quadrupole degree of freedom of Pr ions, for which the ground state of the crystalline electric field is a nonmagnetic doublet. When a magnetic field is applied along the 111 direction, the NMR lines split upon entering the low-temperature phase, indicating the breaking of the three fold rotation symmetry due to the field-induced magnetic dipole perpendicular to the field. This provides microscopic evidence for a ferro order of the O 20 quadrupole. Although a first-order transition is expected theoretically, the line splitting evolves continuously within the experimental resolution.KEYWORDS: PrTi 2 Al 20 , NMR, quadrupole order, symmetry breaking Multipoles of f electrons in rare-earth compounds show a wide variety of phenomena. [1][2][3][4] In particular, non-Kramers rare-earth ions with an even number of f electrons in a cubic environment have been attracting strong interest recently. [5][6][7][8][9][10][11] In these systems, it is possible that the ground states of the J multiplet split by the cubic crystalline electric field (CEF) are nonmagnetic, i.e., the matrix elements of the magnetic dipole J are identically zero, yet have a degeneracy that allows active higher-order multipoles such as electric quadrupoles or magnetic octupoles. Then various interesting phenomena such as multipole orders [12][13][14] or multichannel Kondo effects 15,16) are expected at low temperatures.These possibilities have indeed been realized in compounds containing Pr 3+ ions with the 4 f 2 electronic configuration. The nine states of the J = 4 ground multiplet are split by a cubic CEF into the Γ 1 nonmagnetic singlet, the Γ 3 nonmagnetic doublet, the Γ 4 magnetic triplet, and the Γ 5 magnetic triplet. If the CEF ground state is the Γ 3 doublet, we encounter an interesting situation that the ground state is nonmagnetic but has nonzero matrix elements for the two types of quadrupoles, O 20 = (3J 2 z −J 2 )/2 and O 22 = √ 3(J 2 x −J 2 y )/2, and one octupole T xyz = ( √ 15/6)J x J y J z , where the bar represents the sum over the possible permutations of the indices x, y, and z. 13) The series of compounds PrT 2 X 20 (T : transition metal, X: Zn or Al) provides particularly interesting examples of the Γ 3 CEF ground states. 4) As shown in Fig. 1 [18][19][20][21] all of which also show superconductivity. [21][22][23][24][25][26] Various measurements indicate that the Al-based materials are characterized by stronger hybridization between conduction and f electrons than the Zn-based materials, leading to anomalous transport properties and their pronounced pressure depen- * E-mail : taka.taniguchi@issp.u-tokyo.ac.jp dence. 4,[23][24][25][26][27][28][29][30] In this paper, we focus on PrTi 2 Al 20 . The magnetic susceptibility for H 111 is nearly independent of temperature below 20 K, indicating van Vleck paramagnetism with a nonmagnetic CEF ground state. 29) Specific heat measurements ...

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NMR Observation of Ferro-Quadrupole Order in PrTi₂Al₂₀

et al. 2016

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“…23,24,25 In the Γ 8 ground-state multiplet, octupoles exist as independent moments besides dipole and quadrupole moments. 26 Then, phenomenological theories have been developed under the assumption that octupole ordering occurs. Note that direct detection of octupole ordering is very difficult, since the octupole moment directly couples to neither a magnetic field nor lattice distortions.…”

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Multipole ordering inf-electron systems on the basis of aj−jcoupling scheme

Kubo

Hotta

2005

Phys. Rev. B

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We investigate microscopic aspects of multipole ordering in f -electron systems with emphasis on the effect of lattice structure. For the purpose, first we construct f -electron models on three kinds of lattices, simple cubic (sc), bcc, and fcc, by including f -electron hopping through (f f σ) bonding in a tight-binding approximation on the basis of a j-j coupling scheme. Then, an effective model is derived in the strong-coupling limit for each lattice structure with the use of second-order perturbation theory with respect to (f f σ). By applying mean-field theory to such effective models, we find different types of multipole ordered state depending on the lattice structure. For the sc lattice, a Γ3g antiferro-quadrupole transition occurs at a finite temperature and as further lowering temperature, we find another transition to a ferromagnetic state. For the bcc lattice, a Γ2u antiferrooctupole ordering occurs first, and then, a ferromagnetic phase transition follows it. Finally, for the fcc lattice, we find a single phase transition to the longitudinal triple-q Γ5u octupole ordering.

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