Low-Lying Magnetic Excitation of the Shastry-Sutherland Model

Totsuka, Keisuke; Miyahara, Shin; Ueda, Kazuo

doi:10.1103/physrevlett.86.520

Cited by 58 publications

(80 citation statements)

References 18 publications

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“…These states, as observed in particular by ESR, 43 Raman scattering, 6,10 far-infrared spectroscopy, 30 and neutron scattering 5,44 have been analyzed so far within the framework of the Shastry-Sutherland model, [45][46][47] but should be affected by Dzyaloshinskii-Moriya interactions. This may explain the splittings observed 44 and resolve the issue of "localization" versus "delocalization" of these excitations.…”

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confidence: 99%

Magnon dispersion and anisotropies inSrCu2(BO3)2

et al. 2007

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We study the dispersion of the magnons ͑triplet states͒ in SrCu 2 ͑BO 3 ͒ 2 including all symmetry-allowed Dzyaloshinskii-Moriya interactions ͓J. Phys. Chem. Solids 4, 241 ͑1958͒; Phys. Rev. 120, 91 ͑1960͔͒. We can reduce the complexity of the general Hamiltonian to a simpler form by appropriate rotations of the spin operators. The resulting Hamiltonian is studied by both perturbation theory and exact numerical diagonalization on a 32-site cluster. We argue that the dispersion is dominated by Dzyaloshinskii-Moriya interactions. We point out which combinations of these anisotropies affect the dispersion to linear order, and extract their magnitudes.

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Section: Discussionmentioning

confidence: 99%

Magnon dispersion and anisotropies inSrCu2(BO3)2

et al. 2007

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“…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].…”

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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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“…In addition to the triplon bands, we find a new field-independent and comparatively dispersive feature that hybridizes with them. We identify this mode as a singlet bound state of two triplons 20 . Its presence is a manifestation of the strong interactions between triplons and a precursor of the complex crystals of bound states 11 that give rise to the magnetization plateaux at higher fields.…”

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“…The angular momentum is taken up by the lattice, highlighting the importance of spin-orbit coupling to the existence of antisymmetric exchange. The above method may be used to study S = 1 and S = 2 two-triplon bound states 20 . Within the model these naturally lie at higher energies than the lowest energy singlet sector.…”

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“…In summary, we obtain six triplon bands since there exist two dimers in the unit cell. The bond-operator representation leads to cubic and quartic interaction terms between the triplons (see Methods) which are responsible for a tower of bound states 9,20 . To study the bound states in the singlet sector, as motivated by the experiment, we follow and extend the results of ref.…”

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Topological triplon modes and bound states in a Shastry–Sutherland magnet

McClarty¹,

Krüger²,

Guidi³

et al. 2017

Nature Phys

109

102

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The twin discoveries of the quantum Hall e ect 1 , in the 1980s, and of topological band insulators 2 , in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side e ects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals [3][4][5][6] , in the vibrational modes of crystals 7 , and in the excitations of ordered magnets 8 . Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu 2 (BO 3 ) 2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.The quantum magnet SrCu 2 (BO 3 ) 2 is famous in the magnetism community 9 especially for its rich in-field phase diagram reflected in a series of magnetization plateaux 10,11 . The material is composed of layers of strongly interacting S = 1/2 copper moments arranged on the lattice illustrated in Fig. 1. Nearest-neighbour moments bind together in pairs (dimers), forming quantum mechanical singlets. Neighbouring dimers have an orthogonal arrangement ( Fig. 1).Most magnetic materials undergo a transition into long-range magnetic order, so the fact that the ground state of this material is both interacting and with only short-range correlations is remarkable: a consequence of the frustrating effect of the Shastry-Sutherland lattice geometry 12,13 . The lattice geometry of SrCu 2 (BO 3 ) 2 is also responsible for ensuring that the excited states of the magnet-called triplons-are almost flat across the Brillouin zone [14][15][16] . The predominant contribution to the weak dispersion of these modes is due to subleading magnetic exchange couplings which are antisymmetric Dzyaloshinskii-Moriya (DM) interactions 17,18 . These DM interactions are responsible for complex hopping amplitudes of the triplons which may then pick up Berry phases around closed paths. Their role is therefore similar to that of spin-orbit coupling in electronic topological insulators. Based on a theoretical model of non-interacting triplons, Romhanyi et al.19 predicted that in a small magnetic field the triplon bands of SrCu 2 (BO 3 ) 2 acquire a nontrivial topological invariant, called a Chern number, which implies the existence of chiral magnetic edge states.In this Letter, we present new inelastic neutron scattering (INS) results exploring the low-energy magnetic excitations of SrCu 2 (BO 3 ) 2 in small magnetic fields of up to 2.8 T perpendicular to the dimer planes. This provides unprecedented insight into the nat...

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Low-Lying Magnetic Excitation of the Shastry-Sutherland Model

Cited by 58 publications

References 18 publications

Magnon dispersion and anisotropies inSrCu2(BO3)2

Magnon dispersion and anisotropies inSrCu2(BO3)2

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

Topological triplon modes and bound states in a Shastry–Sutherland magnet

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