Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0004111 · Journal of the Physical Society of Japan

Two-Triplet-Dimer Excitation Spectra in the Shastry-Sutherland Model for SrCu 2(BO 3) 2

Yoshiyuki Fukumoto

Published Sep 1, 2000• 41 citations
arXivHTMLPDF

Abstract

By using the perturbation expansion up to the fifth order, we study the two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by the correlated hopping and the long-range interactions between triplet-dimers play an essential role. It is found that the dispersion relations for first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry qualitatively explain the second-lowest branch observed in the neutron inelastic scattering experiment. It is also predicted that the second-lowest branch consists of two components, p_x- and p_y-states, with slightly different excitation energies. The origin of the singlet mode at 3.7meV observed in the Raman scattering experiment is also discussed.

DOI
10.1143/jpsj.69.2755

Related papers

Direct Evidence for the Localized Single-Triplet Excitations and the Dispersive Multitriplet Excitations in SrCu 2 ( BO 3 ) 2

Hiroshi Kageyama, Masakazu Nishi, N. Aso +6 more

We performed inelastic neutron scattering on the 2D Shastry-Sutherland system SrCu2(11BO3)2 with an exact dimer ground state. Three energy levels at around 3, 5, and 9 meV were observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispersionless with a bandwidth of 0.2 meV at most, showing a significant constraint on a single-triplet hopping owing to the orthogonality of the neighboring dimers. In contrast, the correlated two-triplet excitations at 5 meV exhibit a more dispersive behavior.

arXiv:cond-mat/0005342•Physical Review Letters•Jun 19, 2000•204 citations

Correlated Decay of Triplet Excitations in the Shastry-Sutherland Compound SrCu2(BO3)2

Mohamed Zayed, Christian Rüegg, Th. Strässle +9 more

The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu(2)(BO(3))(2) is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature, while the integrated spectral weight can be explained by an isolated dimer model up to 10 K. Analyzing this anomalous spectral line shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the underlying mechanism through a simple yet quantitatively accurate model of correlated decay of triplons: an excited triplon is long lived if no thermally populated triplons are nearby but decays quickly if there are. The phenomenon is a direct consequence of frustration induced triplon localization in the Shastry-Sutherland lattice.

arXiv:1408.3135•Physical Review Letters•Aug 5, 2014•24 citations

Symmetries and triplet dispersion in a modified Shastry-Sutherland model for SrCu2(BO3)2

Christian Knetter, Erwin Müller-Hartmann, Götz Silvester Uhrig +1 more

We investigate the one-triplet dispersion in a modified Shastry-Sutherland model for SrCu 2 (BO 3 ) 2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy-quanta-conserving block diagonal Hamiltonian eff . The dispersion splits into two branches which are nearly degenerate. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k = 0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small | k | and compare our results to inelastic neutron scattering data.

arXiv:cond-mat/0009402•Journal of Physics Condensed Matter•Oct 5, 2000•15 citations

MAGNETIC EXCITATION OF ORTHOGONAL DIMER HEISENBERG SPIN SYSTEM FOR SrCu 2( BO 3)2

Shin Miyahara, Kiyohito Totsuka, Kazuhiro Ueda

SrCu 2( BO 3)2 is a new two-dimensional spin gap system and the magnetic behaviour of this compound is explained well by the two-dimensional orthogonal dimer Heisenberg model. Recently several excitations have been observed by inelastic neutron scattering and other experiments. We study features of these excitations by Lanczos method and perturbation technique. A triplet excitation has an almost localised nature. This localised character is observed as an almost flat band in neutron scattering. On the other hand, bound states of two triplet excitations, which have dispersive character, are stable in contrast to ordinary magnetic systems. We calculate the dynamic structure factor by a Lanczos method in finite systems and compare our results with experiments.

International Journal of Modern Physics B•Nov 10, 2003•0 citations

Theory of the orthogonal dimer Heisenberg spin model for SrCu 2 (BO 3 ) 2

Shin Miyahara, Kazuo Ueda

The magnetic properties of SrCu 2 (BO 3 ) 2 are reviewed from a theoretical point of view. SrCu 2 (BO 3 ) 2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu 2 (BO 3 ) 2 . In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu 2 (BO 3 ) 2 . The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.

Journal of Physics Condensed Matter•Feb 24, 2003•248 citations

High Energy-Resolution Inelastic Neutron Scattering Experiments on Triplet Bound State Excitations in SrCu2(BO3)2

Naofumi Aso, Hiroshi Kageyama, Katsuyuki Nukui +4 more

In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.

Journal of the Physical Society of Japan•Aug 1, 2005•8 citations
By using the perturbation expansion up to the fifth order, we study the two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by the correlated hopping and the long-range interactions between triplet-dimers play an essential role. It is found that the dispersion relations for first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry qualitatively explain the second-lowest branch observed in the neutron inelastic scattering experiment. It is also predicted that the second-lowest branch consists of two components, p_x- and p_y-states, with slightly different excitation energies. The origin of the singlet mode at 3.7meV observed in the Raman scattering experiment is also discussed.
We performed inelastic neutron scattering on the 2D Shastry-Sutherland system SrCu2(11BO3)2 with an exact dimer ground state. Three energy levels at around 3, 5, and 9 meV were observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispersionless with a bandwidth of 0.2 meV at most, showing a significant constraint on a single-triplet hopping owing to the orthogonality of the neighboring dimers. In contrast, the correlated two-triplet excitations at 5 meV exhibit a more dispersive behavior.
The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu(2)(BO(3))(2) is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature, while the integrated spectral weight can be explained by an isolated dimer model up to 10 K. Analyzing this anomalous spectral line shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the underlying mechanism through a simple yet quantitatively accurate model of correlated decay of triplons: an excited triplon is long lived if no thermally populated triplons are nearby but decays quickly if there are. The phenomenon is a direct consequence of frustration induced triplon localization in the Shastry-Sutherland lattice.
We investigate the one-triplet dispersion in a modified Shastry-Sutherland model for SrCu 2 (BO 3 ) 2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy-quanta-conserving block diagonal Hamiltonian eff . The dispersion splits into two branches which are nearly degenerate. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k = 0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small | k | and compare our results to inelastic neutron scattering data.
SrCu 2( BO 3)2 is a new two-dimensional spin gap system and the magnetic behaviour of this compound is explained well by the two-dimensional orthogonal dimer Heisenberg model. Recently several excitations have been observed by inelastic neutron scattering and other experiments. We study features of these excitations by Lanczos method and perturbation technique. A triplet excitation has an almost localised nature. This localised character is observed as an almost flat band in neutron scattering. On the other hand, bound states of two triplet excitations, which have dispersive character, are stable in contrast to ordinary magnetic systems. We calculate the dynamic structure factor by a Lanczos method in finite systems and compare our results with experiments.
The magnetic properties of SrCu 2 (BO 3 ) 2 are reviewed from a theoretical point of view. SrCu 2 (BO 3 ) 2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu 2 (BO 3 ) 2 . In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu 2 (BO 3 ) 2 . The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.
In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.