Multipole ordering in f electron systems

Sakakibara, Toshiro; Tayama, Takashi; Tenya, Kenichi; Yokoyama, M.; Arima, Hiroshi; Aoki, Dai; Ōnuki, Yoshichika; Kletowski, Z.; Kunii, S.

doi:10.1016/s0022-3697(02)00151-8

Cited by 12 publications

(15 citation statements)

References 16 publications

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“…Therefore, octupole moments, which break the time reversal symmetry, become a candidate for the order parameter in phase IV. 9,10) Since the cubic symmetry is broken, and since the anisotropy develops in the magnetization under uniaxial pressure, 11,12) the order parameter should have an anisotropic nature. Thus the Γ 5u -type, among all octupole moments, is the most plausible candidate for the order parameter in the phase IV.…”

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confidence: 99%

Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆

Kubo

Kuramoto

2003

J. Phys. Soc. Jpn.

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Possible order parameters of the phase IV in CexLa1-xB6 are discussed with special attention to the lattice distortion recently observed. A \Gamma_{5u}-type octupole order with finite wave number is proposed as the origin of the distortion along the [111] direction. The \Gamma_8 crystalline electric field (CEF) level splits into three levels by a mean field with the \Gamma_{5u} symmetry. The ground and highest singlets have the same quadrupole moment, while the intermediate doublet has an opposite sign. It is shown that any collinear order of \Gamma_{5u}-type octupole moment accompanies the \Gamma_{5g}-type ferro-quadrupole order, and the coupling of the quadrupole moment with the lattice induces the distortion. The cusp in the magnetization at the phase transition is reproduced, but the internal magnetic field due to the octupole moment is smaller than the observed one by an order of magnitude.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp

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confidence: 99%

Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆

Kubo

Kuramoto

2003

J. Phys. Soc. Jpn.

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“…26,27 These features are analogous to those in the phase IV of Ce 1−x La x B 6 with x ∼ 0.7, where the antiferro octupole order has been proposed, 28,29 and confirmed by various measurements. [30][31][32] The cubic symmetry in Ce 1−x La x B 6 allows pure octupoles which should have zero internal field at the Ce nucleus site, but with finite off-center field which has recently be detected by neutron scattering.…”

Section: Bilinear Coupling Of Dipoles and Octupoles In Smru 4 P 12mentioning

confidence: 99%

“…Then the presence of critical point at finite temperature and field requires another model which is certainly more complicated than the one given by eq. (32). Within the Landau phenomenology, we have been unable to find a model with the desired property; the second transition, if real, always starts from zero temperature instead of a critical point at finite temperature.…”

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confidence: 92%

Toward Identification of Order Parameters in Skutterudites –a Wonderland of Strong Correlation Physics–

Kuramoto

Kiss

2008

J. Phys. Soc. Jpn.

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Current status is described toward identifying unconventional order parameters in filled skutterudites with unique ordering phenomena. The order parameters in PrFe 4 P 12 and PrRu 4 P 12 are discussed in relation to associated crystalline electric field (CEF) states and angular form factors. By phenomenological Landau analysis, it is shown that a scalar order model explains most properties in both PrFe 4 P 12 and PrRu 4 P 12 with very different magnetic properties. In particular, the highly anisotropic susceptibility induced by uniaxial pressure in PrFe 4 P 12 is explained in terms of two types of couplings. In the case of SmRu 4 P 12 , the main order parameter at low field is identified as magnetic octupoles. A microscopic mechanism is proposed how the dipole and octupole degrees of freedom mix under the point group T h of skutterudites.

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“…In particular, it has been recognized that cubic systems with Γ8 crystalline electric field ground states frequently exhibit higher-order multipole ordering due to their high symmetry. Indeed, octupole ordering has been proposed to reconcile experimental observations for CexLa1−xB6 [1,2,3,4,5] and NpO2 [6,7,8,9]. To understand the origin of such multipole ordering from a unified view point, it is important to analyze a simple microscopic model with correct f -electron symmetry.…”

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confidence: 99%

Multipole ordering in f-electron systems

Kubo

Hotta

2006

Physica B: Condensed Matter

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In order to investigate multipole ordering in f -electron systems from a microscopic viewpoint, we study the so-called Γ8 models on three kinds of lattices, simple cubic (sc), bcc, and fcc, based on a j-j coupling scheme with f -electron hopping integrals through (f f σ) bonding. From the Γ8 model, we derive an effective model for each lattice structure by using the second-order perturbation theory with respect to (f f σ). By further applying mean-field theory to the effective model, we find a Γ3g antiferro-quadrupole transition for the sc lattice, a Γ2u antiferro-octupole transition for the bcc lattice, and a longitudinal triple-q Γ5u octupole transition for the fcc lattice.Key words: multipole ordering, j-j coupling scheme, Γ8 crystalline electric field ground state PACS: 75.30. Et; 71.10.Fd; 75.40.Cx In recent decades, various kinds of magnetic and orbital ordering have been found in f -electron systems. In particular, it has been recognized that cubic systems with Γ8 crystalline electric field ground states frequently exhibit higher-order multipole ordering due to their high symmetry. Indeed, octupole ordering has been proposed to reconcile experimental observations for CexLa1−xB6 [1,2,3,4,5] and NpO2 [6,7,8,9]. To understand the origin of such multipole ordering from a unified view point, it is important to analyze a simple microscopic model with correct f -electron symmetry.In this paper, we study the so-called Γ8 models on three kinds of lattices, simple cubic (sc), bcc, and fcc, based on a j-j coupling scheme. For the description of the model, we define annihilation operators in the second-quantized form for Γ8 electrons with α and β orbitals as f rα↑ = 5/6a r5/2 + 1/6a r−3/2 , f rα↓ = 5/6a r−5/2 + 1/6a r3/2 , f rβ↑ = a r1/2 , and f rβ↓ = a r−1/2 , where arj z is the annihilation operator for an electron with the z-component jz of the total angular momentum j=5/2 at site r.In the tight-binding approximation, the model Hamiltonian is given by [10] * Corresponding author.where µ is a vector connecting nearest-neighbor sites, t µ τ σ;τ ′ σ ′ is the hopping integral of an electron with (τ ′ , σ ′ ) at site r+µ to the (τ, σ) state at r through (f f σ) bonding [11], nrτσ =f † rτ σ frτσ, and nrτ = σ nrτσ. The coupling constants U , U ′ , J, and J ′ denote the intra-orbital, inter-orbital, exchange, and pair-hopping interactions, respectively. Note that the form of t µ τ σ;τ ′ σ ′ characterizes the lattice structure. By using the second-order perturbation theory with respect to (f f σ) including only the lowest energy Γ5 triplet among the intermediate states, we obtain effective multipole interactions for each lattice structure. The detail of the effective models will be reported elsewhere, and here we report the ordered state obtained in the mean-field theory.For sc lattice, a Γ3g antiferro quadrupole (AFQ) transition occurs at a finite temperature, and as lowering temperature further, we find another transition to

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Multipole ordering in f electron systems

Cited by 12 publications

References 16 publications

Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆

Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆

Toward Identification of Order Parameters in Skutterudites –a Wonderland of Strong Correlation Physics–

Multipole ordering in f-electron systems

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Multipole ordering in f electron systems

Cited by 12 publications

References 16 publications

Lattice Distortion and Octupole Ordering Model in CexLa1-xB6

Lattice Distortion and Octupole Ordering Model in CexLa1-xB6

Toward Identification of Order Parameters in Skutterudites –a Wonderland of Strong Correlation Physics–

Multipole ordering in f-electron systems

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Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆

Lattice Distortion and Octupole Ordering Model in Ce_xLa_1-xB₆