Reexamination of Finite-Lattice Extrapolation of Haldane Gaps

Nakano, Hiroki; Terai, Akira

doi:10.1143/jpsj.78.014003

Cited by 72 publications

(71 citation statements)

References 12 publications

(21 reference statements)

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“…To achieve calculations of large clusters, a part of Lanczos diagonalizations has been carried out using the MPI-parallelized code, which was originally developed in the study of the Haldane gaps. 12 The usefulness of our program was confirmed in large-scale parallelized calculations. 13,14 For a finite-size system, the magnetization process is determined by the magnetization increase from M to M + 1 at the field…”

Section: Model Hamiltonians and Methodsmentioning

confidence: 71%

Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space

2014

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Motivated by a recent finding of a spin-flop phenomenon in a system without anisotropy in spin space reported in the S = 1/2 Heisenberg antiferromagnet on the square-kagome lattice, we study the S = 1/2 Heisenberg antiferromagnets on two other lattices composed of vertex-sharing triangles by the numerical diagonalization method. One is a novel lattice including a shuriken shape with four teeth; the other is the kagome lattice with √ 3 × √ 3-structure distortion, which includes a shuriken shape with six teeth. We find in the magnetization processes of these systems that a magnetization jump accompanied by a spin-flop phenomenon occurs at the higher-field-side edge of the magnetization plateau at one-third the height of saturation. This finding indicates that the spin-flop phenomenon found in the isotropic system on the square-kagome lattice is not an exceptional case.

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Section: Model Hamiltonians and Methodsmentioning

confidence: 71%

Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space

2014

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“…Part of the Lanczos diagonalizations were carried out using the MPI-parallelized code, which was originally developed in the study of Haldane gaps. 45 The usefulness of our program was previously confirmed in large-scale parallelized calculations. 19,27,46 The magnetization process for a finite-size system is obtained by considering the magnetization increase from M to M + 1 in the field…”

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confidence: 61%

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Nakano

Sakai

2015

J. Phys. Soc. Jpn.

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The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S = 1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.Frustrated spin systems have attracted much attention from many condensed-matter physicists. One of the fascinating systems among them is the kagome-lattice Heisenberg antiferromagnet. Unfortunately, our understanding of this system is still far from complete in spite of many experimental and theoretical studies. In the S = 1/2 system, in particular, discoveries of several realistic materials such as herbertsmithite, 1, 2 volborthite, 3, 4 and vesignieite 5, 6 have accelerated theoretical studies. 7-29 However, there remain some unresolved issues; one of them is the spin-gap problem of whether the spin excitation above the singlet ground state is gapped or gapless.On the other hand, fewer studies on S > 1/2 cases have been carried out. As candidate S = 1 kagome-lattice systems, m-MPYNM·BF 4 , 30, 31, 33 and KV 3 Ge 2 O 9 34 are known. Theoretical studies 9, 35-39 for the S = 1 case are also limited. Studies on the S > 1 cases have only started recently; candidate kagome-lattice systems of Cs 2 Mn 3 LiF 12 40 for S = 2 and NaBa 2 Mn 3 F 11 41 for S = 5/2 have been reported, together with theoretical studies 42-44 as well as an analysis based on the semiclassical limit. 13 Under these circumstances, then, we are faced with a question: do any systematic behaviors exist in the spin-S kagome-lattice Heisenberg antiferromagnet under magnetic fields? The purpose of this letter is to extract such systematic behavior of the magnetization processes of this model for various S by numerical-diagonalization calculations that are unbiased against approximations. With the same motivation, Zhitomirsky recently investigated the frustrated Heisenberg model under magnetic fields by real-space perturbation theory taking into account fluctuations around a classical configuration. 44 He found that in the magnetization process of the kagome-lattice antiferromagnet, the so-called uud state is stable at one-third of the height of the saturation, at which a magnetization plateau appears irrespective of the value of S. He also derived an expression for the 1/S expansion for both the edge fields of this height. The comparison between the * E-mail: hnakano@sci.u-hyogo.ac.jp † present numerical-diagonalization results and the results from real-space perturbation theory should contribute to our understanding of the frustration effect in the kagome-lattice antiferromagnet.The Hamiltonian that we study in this research is given by H = H 0 + H Zeeman , whereandHere, S i denotes the spin operator at site i, where the sites are th...

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“…4 Specifically, while the half-integer spin chains were indeed described by the preceding work, 2,3,5-8 the integer spin chain possessed an energy gap, 4 where ∆ S=1 ≈ 0.41J for S = 1 LCHAs without anisotropic terms. [9][10][11] Here, J(> 0) is the nearest-neighbor intrachain magnetic superexchange parameter, and the spin Hamiltonian, which defines the notation for J, λ, D, E, and g, is…”

Section: Introductionmentioning

confidence: 99%

Antiferromagnetic order in single crystals of theS=2quasi-one-dimensional chainMnCl3(bpy)

et al. 2016

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A suite of experimental tools, including high-field magnetization and electron spin resonance (ESR) studies in magnetic fields of up to 50 T and heat capacity studies up to 9 T, have revealed antiferromagnetic order in single crystals of the Heisenberg S = 2 chain compound MnCl3(bpy), where bpy is 2,2 ′ -bipyridine. The Néel temperature, which depends on the strength of the applied magnetic field and its orientation with respect to the crystalline axes that was revealed by heat capacity measurements, is near 11.5 K in zero field. The spin-flop transition is identified in the magnetization curve acquired at 1.7 K and at µoH c SF = 24 T along the c-axis. The transition field HSF is lower than that expected from the previous antiferromagnetic resonance (AFMR) studies on a powder sample. The identification of the long-range antiferromagnetic order resolves an earlier report by Granroth et al. [Phys. Rev. Lett. 77, 1616(1996] that identified MnCl3(bpy) as an S = 2 Haldane system down to 40 mK. The ESR studies identify a wide-range of antiferromagnetic resonance modes that provide additional microscopic information about the g-values (ga * = 2.09, g b = 1.92, and gc = 2.07), the zero-field splitting constants, D = −1.5 K and E = −0.17 K when the nearest-neighbor spin interaction J/kB = 31.2 K, which is evaluated from fitting the susceptibility, and the anisotropy of this compound (easy-axis is the c-axis, the second easy-axis is the b-axis, and the hard axis is the a * -axis), when using a standard (two-sublattices) AFMR analysis that does not quantitatively reproduce the observed H

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Reexamination of Finite-Lattice Extrapolation of Haldane Gaps

Cited by 72 publications

References 12 publications

Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space

Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Antiferromagnetic order in single crystals of theS=2quasi-one-dimensional chainMnCl3(bpy)

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