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Kohgi, M.; Iwasa, Kazuaki; Mignot, J.-M.; Fåk, B.; Gegenwart, P.; Lang, Michael; Ochiai, Akira; Aoki, Hidekazu; Suzuki, Takashi

doi:10.1103/physrevlett.86.2439

Cited by 130 publications

(79 citation statements)

References 15 publications

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“…Similar behavior has been observed in Cu-benzoate, 27-29 Yb4As3, 30 and KCuGaF6 31 and well explained by the presence of staggered Dzyaloshinskii-Moriya (DM) interactions. 32,33 We think that a similar mechanism applies to the present compound.…”

Section: Discussionsupporting

confidence: 52%

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)

2015

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ABSTRACT:A new spin-1/2 quasi-one-dimensional antiferromagnet KCuMoO4(OH) is prepared by the hydrothermal method. The crystal structures of KCuMoO4(OH) and the already-known Na-analogue, NaCuMoO4(OH), are isotypic, comprising chains of Cu 2+ ions in edge-sharing CuO4(OH)2 octahedra. Despite the structural similarity, their magnetic properties are quite different because of the different arrangements of dx 2 -y 2 orbitals carrying spins. For NaCuMoO4(OH), dx 2 -y 2 orbitals are linked by superexchange couplings via two bridging oxide ions, which gives a ferromagnetic nearestneighbor interaction J1 of -51 K and an antiferromagnetic next-nearest-neighbor interaction J2 of 36 K in the chain. In contrast, a staggered dx 2 -y 2 orbital arrangement in KCuMoO4(OH) results in superexchange couplings via only one bridging oxide ion, which makes J1 antiferromagnetic as large as 238 K and J2 negligible. This comparison between the two isotypic compounds demonstrates an important role of orbital arrangements in determining the magnetic properties of cuprates. IntroductionQuantum spin systems attract much attention because quantum fluctuations may suppress conventional magnetic order and can induce exotic states such as a spin liquid. 1, 2 The most promising candidates are found in compounds that contain Cu 2+ ions with spin 1/2. The Cu 2+ ion has a d 9 electronic configuration with one unpaired electron occupying either the dx 2 -y 2 or dz 2 orbital in the octahedral crystal field. This degeneracy is eventually lifted by lowering symmetry due to the Jahn-Teller effect: when two opposite ligands move away and the other four ligands come closer, the dx 2 -y 2 orbital is selected to carry the spin, whereas the dz 2 orbital is selected in the opposite case. Since this Jahn-Teller energy is quite large, either distortion of octahedra always occurs in actual compounds. Since magnetic interactions between neighboring Cu spins are caused by superexchange interactions via overlapping between Cu d orbitals and O ligand p orbitals, the arrangements of the Cu d orbitals and their connections via ligands are important to determine the magnetic properties of cuprates.Among many cuprates, a rich variety of crystal structures are found in natural minerals and their synthetic analogues. Recently, for example, many copper minerals with Cu 2+ ions in the kagome geometry have been focused on from the viewpoint of quantum magnetism: Volborthite (Cu3V2O7(OH)2•2H2O), [3][4][5] Herbertsmithite (Zn1-xCu3+x(OH)6Cl2), 6 Vesignieite (BaCu3V2O8(OH)2), 7 and so on. Besides, there are a lot of minerals where Cu 2+ forms one-dimensional (1D) chains, such as Chalcanthite (CuSO4•5H2O), 8 Linarite (PbCuSO4(OH)2), 9 and Natrochalcite (NaCu2(SO4)2(OH)•H2O). 10 Natrochalcite also has many synthetic analogues of ACu2(SO4)2(OH) •H2O (A

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Section: Discussionsupporting

confidence: 52%

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)

2015

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“…Recently, more attention has been paid to theoretical studies of exactly solvable quantum spin models involving nearest-, next-nearest-neighbor interactions, and multiple spin exchange models, etc [3][4][5][6][7][8][9][10]. Those models are closer to real quasi-one-dimensional magnets [11][12][13] comparing to standard ones with only nearest-neighbor couplings. Furthermore, it has been shown that quantum spin models can be simulated in artificial quantum system with controllable parameters.…”

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confidence: 99%

Topological Characterization of Extended Quantum Ising Models

2015

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We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.PACS numbers: 03.65. Vf, 75.10.Jm, 05.70.Fh, Introduction. Characterizing the quantum phase transitions (QPTs) is of central significance to both condensed matter physics and quantum information science. QPTs occur only at zero temperature due to the competition between different parameters describing the interactions of the system. A quantitative understanding of the second-order QPT is that the ground state undergoes qualitative changes when an external parameter passes through quantum critical points (QCPs).There are two prototypical models, Bose-Hubbard model and transverse-field Ising model, based on which the concept and characteristic of QPTs can be well demonstrated. However, among the two, only the transverse-field Ising model is exactly solvable [1], so as to be a unique paradigm for understanding the QPTs. Recently, more attention has been paid to theoretical studies of exactly solvable quantum spin models involving nearest-, next-nearest-neighbor interactions, and multiple spin exchange models, etc [3][4][5][6][7][8][9][10]. Those models are closer to real quasi-one-dimensional magnets [11][12][13] comparing to standard ones with only nearest-neighbor couplings. Furthermore, it has been shown that quantum spin models can be simulated in artificial quantum system with controllable parameters. Quantum simulation of spin chain can be experimentally realized through neutral atoms stored in an optical lattice [14,15], trapped ions [16][17][18][19][20][21][22][23][24] and NMR simulator [25]. This system often serves as a test bed for applying new ideas and methods to quantum phase transitions.A fundamental question is whether QPTs in Ising model can have a connection to some topological characterizations. It is interesting to note in this context that some simple Ising models have been found to exhibit topological characterization [26][27][28][29]. The purpose of the present work is to shed some light upon the relation between QPTs and a geometrical parameter characterizing the phase diagram, through the investigation of a class of quantum Ising models.In this work, we present an extended quantum Ising

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“…Recently some novel magnetic properties were discovered in a variety of quasi-one dimensional materials, such as copper benzoate Cu(C 6 D 5 COO) 2 3D 2 O[1, 2], Yb 4 As 3 [3,4,5] and BaCu 2 Si 2 O 7 [6]. In these materials, the Dzyaloshinskii-Moriya (DM) interaction [7,8,9] plays an important role, especially in an applied magnetic field.…”

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confidence: 99%

“…In particular, for metallic materials, e.g. Yb 4 As 3 [3], one could use external fields to modulate the magnetic transport properties which is one of the focal points for the spintronics.…”

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Effects of the Dzyaloshinskii-Moriya Interaction on Low-Energy Magnetic Excitations in Copper Benzoate

et al. 2003

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We have investigated the physical effects of the Dzyaloshinskii-Moriya (DM) interaction in copper benzoate. In the low field limit, the spin gap is found to vary as H 2/3 ln 1/6 (J/µBHs) (Hs: an effective staggered field induced by the external field H) in agreement with the prediction of conformal field theory, while the staggered magnetization varies as H 1/3 and the ln 1/3 (J/µBHs) correction predicted by conformal field theory is not confirmed. The linear scaling behavior between the momentum shift and the magnetization is broken. We have determined the coupling constant of the DM interaction and have given a complete quantitative account for the field dependence of the spin gaps along all three principal axes, without resorting to additional interactions like interchain coupling. A crossover to strong applied field behavior is predicted for further experimental verification. . In these materials, the Dzyaloshinskii-Moriya (DM) interaction [7,8,9] plays an important role, especially in an applied magnetic field. This has stimulated extensive investigation on the physical properties of the DM interaction. However, this interaction is rather difficult to handle analytically, which has brought much uncertainty in the interpretation of experimental data and has limited our understanding of many interesting quantum phenomena of low-dimensional magnetic materials.For copper benzoate, Dender et al [1,2] found that the spin excitation gap shows a peculiar field dependence, ∆ ∼ H 0.65 , in low fields. On the contrary, excitations remain gapless in the S=1/2 Heisenberg model below a critical field. Oshikawa and Affleck (OA) suggested that this field dependence of the gap is due to a staggered magnetic field induced by the DM interaction in addition to the staggered g-factor in a uniform field [9,10]. However, a satisfactory explanation for the field-dependence of the energy gaps in all three directions is still lacking [11,12]. It was argued that the inconsistency between the experimental data and theoretical results might be due to the neglect of the interchain coupling and/or anisotropic interaction terms in the low-field effective model used by Oshikawa and Affleck [9,11]. We believe this issue can be clarified by a thorough study of the DM interaction and a direct comparison with experiments.Copper benzoate is a quasi-1D spin-1/2 antiferromagnetic Heisenberg system. The chain direction is the caxis. It contains two types of alternating and slightly tilted CuO 8 octahedra. This leads to two inequivalent Cu ++ ions and an alternating DM coupling [13]. In an applied field, copper benzoate can be modeled by the following Hamiltonian,( 1) where the three terms in the summation are the antiferromagnetic Heisenberg, DM and Zeeman splitting interactions, respectively. The exchange coupling constant J, determined from the neutron scattering measurements, is about 1.57meV. The DM interaction is much weaker than the Heisenberg term. The D-vector, primarily aligned along the a ′′ axis, will be determined numerically. g u and ...

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Staggered Field Effect on the One-DimensionalS=12AntiferromagnetYb4

Cited by 130 publications

References 15 publications

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)

Topological Characterization of Extended Quantum Ising Models

Effects of the Dzyaloshinskii-Moriya Interaction on Low-Energy Magnetic Excitations in Copper Benzoate

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Staggered Field Effect on the One-DimensionalS=12AntiferromagnetYb4

Cited by 130 publications

References 15 publications

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO4(OH) (A = Na, K)

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO4(OH) (A = Na, K)

Topological Characterization of Extended Quantum Ising Models

Effects of the Dzyaloshinskii-Moriya Interaction on Low-Energy Magnetic Excitations in Copper Benzoate

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Product

Resources

About

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO₄(OH) (A = Na, K)