Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 
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Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

doi:10.1103/physrevb.97.024414

Cited by 41 publications

(12 citation statements)

References 45 publications

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“…Once the systems undergo phase transitions causing inversion symmetry breaking, order parameters are represented by unconventional odd-parity multipoles, such as magnetic toroidal dipole [5][6][7][8][9], magnetic quadrupole [10][11][12], electric toroidal quadrupole [13,14], and electric octupole [15][16][17]. In previous studies, such odd-parity multipoles have often been described by the staggered (antiferroic) alignment of even-parity multipoles on a crystal structure without local inversion symmetry at an atomic site; prototypes are the zigzag chain [7,18], honeycomb structure [6,8], and diamond structure [19,20]. Such odd-parity multipoles formed by an antiferroic alignment of the even-parity multipoles like magnetic dipole and electric quadrupole are denoted as cluster odd-parity multipoles.…”

Section: Introductionmentioning

confidence: 99%

NQR and NMR spectra in the odd-parity multipole material CeCoSi

Yatsushiro

Hayami

2020

Phys. Rev. B

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We theoretically study NQR and NMR spectra in the presence of odd-parity multipoles originating from staggered antiferromagnetic and antiferroquadrupole orderings. For the f-electron metal, CeCoSi, which is a candidate hosting odd-parity multipoles, we derive an effective hyperfine field acting on Co nucleus generated from electronic origin multipole moments at Ce ion under zero and nonzero magnetic fields. We elucidate that emergent odd-parity multipoles give rise to sublattice-dependent spectral splittings in NQR and NMR through the effective hyperfine coupling in the absence of the global inversion symmetry. We mainly examine behaviors of the NQR and NMR spectra in three odd-parity multipole ordered states: a y-type magnetic toroidal dipole order with a staggered x-type antiferromagnetic structure, an xy-type electric toroidal quadrupole order with a staggered x 2 − y 2-type antiferroquadrupole structure, and a z-type electric dipole order with a staggered 3z 2 − r 2type antiferroquadrupole structure. We show that different odd-parity multipole orders lead to different fielddependent spectral splittings in NMR, while only the xy-type electric toroidal quadrupole order exhibits the NQR spectral splitting. We also present possible sublattice-dependent spectral splittings for all the odd-parity multipole orders potentially activated in low-energy crystal-field levels, which will be useful to identify oddparity order parameters in CeCoSi by NQR and NMR measurements.

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Section: Introductionmentioning

confidence: 99%

NQR and NMR spectra in the odd-parity multipole material CeCoSi

Yatsushiro

Hayami

2020

Phys. Rev. B

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“…Experiments have indeed discovered an oddparity nematic metal in Cd 2 Re 2 O 7 below T c ∼ 200 K via optical second-harmonic generation [16]. Other proposed materials for hosting multipolar orders include A 2 OsO 4 (with A = K,Rb,Cs) [17].However, to the best of our knowledge, there have been no clear d-orbital candidates for hosting octupolar or-ders. Indeed, there appears to be no microscopic understanding of what are the key ingredients to potentially stabilize such octupolar phases.…”

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confidence: 97%

Octupolar order in d -orbital Mott insulators

2020

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Motivated by experimental and theoretical interest in realizing multipolar orders in d-orbital materials, we discuss the quantum magnetism of J = 2 ions on the face-centered cubic lattice which can be realized in spin-orbit coupled oxides with 5d 2 transition metal ions. Based on the crystal field environment, we argue for a splitting of the J = 2 multiplet, leading to a low lying non-Kramers doublet which hosts quadrupolar and octupolar moments. We discuss a microscopic mechanism whereby the combined perturbative effects of orbital repulsion and antiferromagnetic Heisenberg spin interactions leads to ferro-octupolar coupling between neighboring sites, and stabilizes ferrooctupolar order. This same mechanism is also shown to disfavor quadrupolar ordering. We study spin dynamics in the ferro-octupolar state using a slave-boson approach, uncovering a gapped and dispersive magnetic exciton. For sufficiently strong magnetic exchange, the dispersive exciton can condense, leading to conventional type-I antiferromagnetic order which can preempt octupolar order. Our proposal for ferrooctupolar order, with specific results in the context of a model Hamiltonian, provides a comprehensive understanding of thermodynamics, µSR, X-ray diffraction, and inelastic neutron scattering measurements on a range of cubic 5d 2 double perovskite materials including Ba2ZnOsO6, Ba2CaOsO6, and Ba2MgOsO6. Our proposal for exciton condensation leading to type-I magnetic ordering is argued to be relevant to materials such as Sr2MgOsO6.PACS numbers: 75.25.aj, 75.40.Gb, 75.70.Tj Multipolar symmetry-breaking orders have been extensively discussed in f -orbital based lanthanide and actinide compounds, which host ions where spin-orbit coupling (SOC) is a dominant energy scale [1]. For instance, the "hidden order" state of URu 2 Si 2 has been proposed to host hexadecapolar symmetry breaking [2]. Another well-known example is cubic NpO 2 [3-6], where a large body of experiments have been reconciled in terms of a primary antiferro-triakontadipolar (rank-5 magnetic multipolar) symmetry breaking which drives secondary antiferro-quadrupolar order. In certain pyrochlore magnets, all-in all-out magnetic order has been proposed to lead to "effective octupoles" on tetrahedra [7]. Ongoing experimental [8-10] and theoretical investigations [11][12][13][14] of PrTi 2 Al 20 and PrV 2 Al 20 have also uncovered quadrupolar and ferro-octupolar orders.Recently, unconventional multipolar orders have also been proposed in d-orbital metals to occur as Pomeranchuk instabilities of spin-orbit coupled Fermi surfaces [15]. Specifically, metallic oxides which have d-orbital ions with large SOC, such as LiOsO 3 and Cd 2 Re 2 O 7 , have been proposed as potential candidates to realize this physics [15]. Experiments have indeed discovered an oddparity nematic metal in Cd 2 Re 2 O 7 below T c ∼ 200 K via optical second-harmonic generation [16]. Other proposed materials for hosting multipolar orders include A 2 OsO 4 (with A = K,Rb,Cs) [17].However, to the best of our knowledg...

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“…Multipolar orders have been extensively studied in f -electron compounds [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] where spin-orbit coupling and interactions dominate over weaker crystal field effects. However, there is growing evidence for such exotic "higher multipoles" in a wide range of heavy d-orbital metals such as LiOsO 3 and Cd 2 Re 2 O 7 which may exhibit odd-parity nematic orders [17,18], or quadrupolar orders as proposed in A 2 OsO 4 (with A = K,Rb,Cs) [19].…”

Section: Introductionmentioning

confidence: 99%

Octupolar order and Ising quantum criticality tuned by strain and dimensionality: Application to $d$-orbital Mott insulators

Voleti,

Haldar,

Paramekanti

2021

Preprint

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Recent experiments have discovered multipolar orders in a variety of d-orbital Mott insulators. Motivated by uncovering the exchange interactions which underlie octupolar order proposed in the osmate double perovskites, we study a two-site model using exact diagonalization on a five-orbital Hamiltonian, incorporating spin-orbit coupling (SOC) and interactions, and including both intraorbital and inter-orbital hopping. Using an exact Schrieffer-Wolff transformation, we then extract an effective pseudospin Hamiltonian for the non-Kramers doublets, uncovering dominant ferrooctupolar coupling driven by the interplay of two distinct intra-orbital hopping terms. Using classical Monte Carlo simulations on the face-centered cubic lattice, we obtain a ferrooctupolar transition temperature which is in good agreement with experiments on the osmate double perovskites. We also explore the impact of uniaxial strain and dimensional tuning via ultrathin films, which are shown to induce a transverse field on the Ising octupolar order. This suppresses Tc and potentially allows one to access octupolar Ising quantum critical points. We discuss possible implications of our results for a broader class of materials which may host such non-Kramers doublet ions.

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Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 5d transition metal oxides AOsO4(A=

Cited by 41 publications

References 45 publications

NQR and NMR spectra in the odd-parity multipole material CeCoSi

NQR and NMR spectra in the odd-parity multipole material CeCoSi

Octupolar order in d -orbital Mott insulators

Octupolar order and Ising quantum criticality tuned by strain and dimensionality: Application to $d$-orbital Mott insulators

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