Soft modes, gaps, and magnetization plateaus in one-dimensional spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>antiferromagnetic Heisenberg models

Fledderjohann, A.; Gerhardt, C.; Karbach, Michael; Mütter, K.-H.; Wießner, R.M.

doi:10.1103/physrevb.59.991

Cited by 19 publications

(26 citation statements)

References 26 publications

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“…For example, it has been shown (see e.g. [15,24]) that an M = 1/2 plateau can appear if a nextnearest neighbour interaction is added to the dimerized chain, (1) with p = 2 (for generalizations of this situation see [25]). This phenomenon can be also understood within the strong-coupling analysis [15][16][17][18] if one goes to first order, i.e.…”

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Strong-coupling approach to the magnetization process of polymerized quantum spin chains

Honecker

1999

Phys. Rev. B

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Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaux as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion how the universality classes associated to the transitions at the boundaries of magnetization plateaux arise in many cases from a first order strong-coupling effective Hamiltonian.PACS numbers: 75.10. Jm, 75.40.Cx, 75.45.+j, 75.60.Ej Quantum spin systems at low (or zero) temperatures can exhibit plateaux in their magnetization curves when subjected to strong external fields. Such phenomena in quasi-one-dimensional systems have recently been the subject of intense interest. In one dimension, there is an intriguing interplay between theoretical progress on a systematic understanding of the underlying mechanisms (see e.g. [1]) and an increasing number of experiments (see e.g. [2,3]) on materials which are believed to be predominantly one-dimensional.Here we study polymerized spin-S quantum spin chains in a magnetic field. Their Hamiltonian is given bywhere we assume periodicity of the coupling constants with period p, i.e.We will mostly concentrate on spin S = 1/2 and the antiferromagnetic regime J x ≥ 0. The zero-temperature magnetization process of the S = 1/2 polymerized chains (1) was studied in [4] using finite-size diagonalization and a perturbative bosonization analysis around the case of equal coupling constants J x = J (apart from this and the dimerized case, only some trimerized [5,6] and quadrumerized [7] cases seem to have been studied in the literature). Here we wish to complete the picture by discussing the 'strong-coupling' limit where at least one coupling constant is small with respect to the others, i.e. J x0 → 0. As is known e.g. from studies of spin-ladders [8,9], the magnetization process is easy to understand if some J x0 = 0. In this limit, the chain (1) decouples into clusters of p spins. These 'strongly coupled' clusters magnetize independently such that at zero temperature the magnetization M can only take finitely many values. For spin S they are subject to the quantization conditionwith a normalization such that the magnetization has saturation values M = ±1. This quantization condition was obtained (for S = 1/2) in [4] and is a special case of a more general condition written down in [9]. In particular the latter was also motivated by considering a limit in which the system decouples into clusters of finitely many spins. In fact, this counting argument is completely independent of the internal coupling inside the cluster of the p spins. The quantization condition (3) is therefore insensitive to details of the model. However, not only the tr...

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confidence: 99%

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

Honecker

1999

Phys. Rev. B

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“…Necessary conditions for the occurence of plateaus have been formulated by Oshikawa et al [1] employing a generalization of the Lieb-Schultz-Mattis theorem: for a spin-S chain with a magnetic unit cell containing q magnetic moments this feature can appear at rational values M with integer q(S − M ). The existence of these phenomena in a variety of models has been established by numerical and analytical studies of various lowdimensional magnetic insulators including spin chains, spin ladders and systems with multi spin exchange or exchange anisotropies [2][3][4][5][6][7][8][9][10][11][12][13]. Very recently, several experimental observations of such magnetization plateaus at non-zero M have been reported [14][15][16].…”

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Doping-Induced Magnetization Plateaus

Frahm

Sobiella

1999

Phys. Rev. Lett.

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The low temperature magnetization process of antiferromagnetic spin-S chains doped with mobile spin-(S − 1/2) carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase which exists for a large range of carrier concentrations x the zero temperature magnetization is determined by x alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behaviour at the edges of these plateaus is studied in detail. 75.10.Jm, 75.10.Lp, 71.10.Pm Synthetization of new magnetic materials and availability of very high magnetic fields provide new possibilities to study the magnetization process of lowdimensional quantum spin systems. In particular socalled spin liquids realized in quasi-one dimensional antiferromagnetic systems such as spin chains, spin ladders and exchange-alternating spin chains attract much interest at present due to the possible occurence of magnetization plateaus associated with gapped excitations. In addition to saturated magnetization M s such plateaus, i.e. regions where the magnetization does not depend on the magnetic field for sufficiently low temperatures, are admissible from topological considerations at certain fractions of M s depending on the value of the spin of the substance and the translational symmetry of the ground state. Necessary conditions for the occurence of plateaus have been formulated by Oshikawa et al.[1] employing a generalization of the Lieb-Schultz-Mattis theorem: for a spin-S chain with a magnetic unit cell containing q magnetic moments this feature can appear at rational values M with integer q(S − M ). The existence of these phenomena in a variety of models has been established by numerical and analytical studies of various lowdimensional magnetic insulators including spin chains, spin ladders and systems with multi spin exchange or exchange anisotropies [2][3][4][5][6][7][8][9][10][11][12][13]. Very recently, several experimental observations of such magnetization plateaus at non-zero M have been reported [14][15][16].A common feature in these systems is that the plateaus in the magnetization curves appear at certain simple fractions of the maximal value M s as a consequence of their topological origin. In this letter we report on a mechanism leading to gaps for magnetic excitations at magnetizations which can be controlled by suitable preparation of the sample, namely doping. We study this phenomenon in the framework of a recently introduced class of integrable models for doped Heisenberg chains which may be used as a basis for studies of certain features of doped transition metal oxides [17,18]. Starting from the doubleexchange model [19] a strong ferromagnetic Hund's rule coupling between the spins of the itinerant e g electrons and localized quantum spins (S−1/2) arising from the t 2g electrons allows to introduce an effective Hamiltonian on a restricted Hilbert space with maximally allow...

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“…This result is also corroborated by the absence of a magnetization plateau in our model in small magnetic fields 18 . For an alternating NN exchange, a magnetization plateau is observed in small magnetic fields, but for alternating NNN exchange, it is only observed in high fields 18,19 .…”

Section: Effective Low-energy Theory and Renormalization Group Anmentioning

confidence: 99%

Ground state and excitation of an asymmetric spin ladder model

2003

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We perform a systematic investigation on an asymmetric zig-zag spin ladder with inter-leg exchange J1 and different exchange integrals J2 ± δ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gorden model by using bosonization. Renormalization group analysis shows that the Heisenberg critical point flows to an intermediatecoupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing J2 = J1/2, we find, as a function of δ, a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange δ, the gap size of excitations is found to decrease with increasing δ. We also extend our study to a two-dimensional double layer model with an exactly known ground state.

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Soft modes, gaps, and magnetization plateaus in one-dimensional spin-12antiferromagnetic Heisenberg models

Cited by 19 publications

References 26 publications

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

Doping-Induced Magnetization Plateaus

Ground state and excitation of an asymmetric spin ladder model

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