Fractalization drives crystalline states in a frustrated spin system

Sebastian, Suchitra E.; Harrison, N.; Sengupta, Pinaki; Batista, Cristian D.; Francoual, S.; Palm, E.; Murphy, T. P.; Marcano, N.; Dąbkowska, H. A.; Gaulin, B. D.

doi:10.1073/pnas.0804320105

Cited by 88 publications

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References 32 publications

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“…A famous example is the Shastry-Sutherland model (SSM) [2], which is believed to accurately capture the physics of the orthogonal-dimer antiferromagnet SrCu 2 (BO 3 ) 2 . A big effort has been invested in understanding the appearance of various magnetization plateaus observed in experiments [3][4][5][6][7][8][9][10][11][12][13]. Early on it was found that the SSM has almost localized triplet excitations [5,14] which suggests that each plateau corresponds to a particular crystal of localized triplets.…”

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Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

2014

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Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz = 2. Finally, we discuss the role of competing domain-wall and supersolid phases as well as that of additional anisotropic interactions. PACS numbers: 75.10.Jm, 75.40.Mg, 75.10.Kt, Predicting the phases of frustrated spin systems is one of the major challenges in theoretical condensed matter physics [1]. A famous example is the Shastry-Sutherland model (SSM) [2], which is believed to accurately capture the physics of the orthogonal-dimer antiferromagnet SrCu 2 (BO 3 ) 2 . A big effort has been invested in understanding the appearance of various magnetization plateaus observed in experiments [3][4][5][6][7][8][9][10][11][12][13]. Early on it was found that the SSM has almost localized triplet excitations [5,14] which suggests that each plateau corresponds to a particular crystal of localized triplets. This viewpoint has been supported by many analytical and (approximate) numerical studies over the last 15 years [14][15][16][17][18][19][20][21][22][23][24][25].The SSM is given by the Hamiltonianwhere the i, j bonds with coupling strength J build an array of orthogonal dimers while the bonds with coupling J denote inter-dimer couplings, and h the strength of the external magnetic field. The main result of this Letter is that -in contrast to the standard belief -the plateaus are not crystals of S z = 1 triplets (see Fig. 1(a)), but of S z = 2 bound states of triplets, which form a pinwheel pattern as shown in Fig. 1(b), and which are shown to be stable even if they are localized. Bound states have previously been predicted to be relevant in the dilute limit of excitations [16,[26][27][28][29], but not for the formation of crystals. The only hint so far that bound states can form crystals was found in a one-dimensional analog -a SSM spin tube [30]. It is also shown that the crystals formed by the bound states naturally explain the sequence of magnetization plateaus observed in SrCu 2 (BO 3 ) 2 . In particular, the 2/15 plateau is made of a simple and regular pattern of bound states, in contrast to the more complicated patterns of triplets which were previously suggested [12,21,24].Method -Our results have been obtained with infinite projected entangled-pair states (iPEPS) -a variational tensornetwork ansatz to represent a two-dimensional wave function in the thermodynamic limit [31][32][33]. It consists of a cell of tensors which is periodically repeated on the lattice, where ...

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Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

2014

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“…We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 MnCoO 6 . [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges.…”

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“…Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca 3 Co 2 O 6 . We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 Introduction.-Geometric frustration, low-dimensionality, and quantum fluctuations can lead to exotic phase transitions and states of matter [1,2] such as the field-induced magnetization plateaus of SrCu 2 (BO 3 ) 2 [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges.…”

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Formation of Magnetic Microphases inCa3Co2O6

Kamiya

Batista

2012

Phys. Rev. Lett.

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We study a frustrated quantum Ising model relevant for Ca 3 Co 2 O 6 that consists of a triangular lattice of weakly-coupled ferromagnetic (FM) chains. According to our quantum Monte Carlo (QMC) simulations, the chains become FM and form a three-sublattice "up-up-down" structure for T ≤ T CI . In contrast, long-period spin-density-wave (SDW) microphases are stabilized along the chains for T CI < T < T c . Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca 3 Co 2 O 6 . We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 MnCoO 6 . [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges. This compound exhibits field-induced magnetization steps whose heights depend on the field sweep history and rate [12][13][14][15][16]. We will show that this out-of-equilibrium behavior has its roots in exotic equilibrium properties that can be extended to the related multiferroic compound Ca 3 Co 2−x Mn x O 6 [17][18][19][20][21][22].The Co 3+ ions (Co II) on the trigonal prism sites of Ca 3 Co 2 O 6 contain 3d 6 localized electrons that generate an S = 2 spin with large Ising-like anisotropy [23][24][25][26]. These ions form a triangular lattice of FM Ising chains along the caxis (Fig. 1) and the structure comprises three sublattices of layers stacked along the c-axis in an ABCABC . . . configuration. Although the AFM inter-chain couplings J 2 and J 3 [27] [ Fig. 1(a)] are an order of magnitude smaller than the intrachain FM exchange, |J 1 | = 2 × 10 K [23, 27], we will show that they strongly affect the intra-chain spin correlations over a window of temperatures below T c .The initial interest in Ca 3 Co 2 O 6 was triggered by the observation of out-of-equilibrium magnetization steps measured below ∼ 8 K and ∼ 3.6 T that appear at regular field intervals. Previous works invoked a "rigid-chain model": every chain is replaced by a single Ising spin by assuming [28][29][30][31][32]. Each spin of the resulting triangular lattice Ising model (TLIM), represents the magnetization of the whole chain and it is flipped if gµ B H overcomes its molecular field. Within this simplified framework, the regular field intervals result from the equally-spaced discrete molecular field spectrum [28]. However, this 2D scenario was challenged by the recent discovery of long-wavelength intra-chain spindensity-wave (SDW) ordering below T c 25 K [16,33,34]. Motivated by this discovery, Chapon initiated the study of a more realistic 3D lattice model by using a random-phase approximation (RPA) which is only valid close to T = T c [35].By combining QMC simulations and mean field (MF) solu-

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“…Unlike the celebrated case of quantum spin-1/2 Cu 2+ ions in the insulating compound SrCu 2 (BO 3 ) 2 , which realizes the collective dimer singlet ground state predicted for the SSL [10,11], RB 4 has large classical f moments with magnetic interactions mediated by itinerant electrons. Despite this, just as SrCu 2 (BO 3 ) 2 exhibits a series of fractional magnetization plateaus as a function of the magnetic field H with M/M S = 1/q (q here is an integer from 2 to 9, M is the * lindaye@mit.edu magnetization, and M S is the saturation M) [11][12][13][14], RB 4 also shows magnetization plateaus of unusual structure [15][16][17][18]. A particularly interesting limit is the trivalent R = Er and Tm, where a strong Ising single-ion anisotropy exists such that the f -electron moments may be described within up/down twofold degrees of freedom locked perpendicular to the SSL plane and the plateau transitions arise from complex spin-flip processes [19][20][21][22].…”

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Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides

Suzuki

Checkelsky

2017

Phys. Rev. B

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In the presence of a magnetic field frustrated spin systems may exhibit plateaus at fractional values of saturation magnetization. Such plateau states are stabilized by classical and quantum mechanisms including order by disorder, triplon crystallization, and various competing order effects. In the case of electrically conducting systems, free electrons represent an incisive probe for the plateau states. Here we study the electrical transport of Ising-type rare-earth tetraborides RB 4 (R = Er, Tm), a metallic Shastry-Sutherland lattice showing magnetization plateaus. We find that the longitudinal and transverse resistivities reflect scattering with both the static and the dynamic plateau structure. We model these results consistently with the expected strong uniaxial anisotropy on a quantitative level, providing a framework for the study of plateau states in metallic frustrated systems.

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Fractalization drives crystalline states in a frustrated spin system

Cited by 88 publications

References 32 publications

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

Formation of Magnetic Microphases inCa3Co2O6

Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides

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