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Anomalous thermal broadening in the Shastry-Sutherland model and SrCu2(BO3)2

Z. Q. Wang, Paul McClarty, Dobromila Dankova, A. Honecker, A. Wietek

Published Jan 15, 2026• 0 citations
OpenAlex

Abstract

In the quantum magnet SrCu2(BO3)2, an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap A using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu2(BO3)2 are captured by the spin S = 1/2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper [Phys. Rev. B 113, 024406 (2026)]. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap A to the single triplon excitations at the experimentally relevant model parameters.

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In the quantum magnet SrCu 2 ( BO 3 ) 2 , an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap Δ using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu 2 ( BO 3 ) 2 are captured by the spin S = 1 / 2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper []. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap Δ to the single triplon excitations at the experimentally relevant model parameters.

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Theory of Magnetization Plateaux in the Shastry-Sutherland Model

Julien Dorier, Kai Phillip Schmidt, Frédéric Mila

Motivated by the remarkable properties of SrCu2(BO3) 2 in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at 2/9, 1/6, 1/9, and 2/15 upon increasing the interdimer coupling. We predict that a 1/6 plateau should be present in SrCu2(BO3)2, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below 1/3. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on SrCu2(BO3) 2.

arXiv:0806.3406•Physical Review Letters•Dec 19, 2008•94 citations
In the quantum magnet SrCu2(BO3)2, an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap A using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu2(BO3)2 are captured by the spin S = 1/2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper [Phys. Rev. B 113, 024406 (2026)]. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap A to the single triplon excitations at the experimentally relevant model parameters.
In the quantum magnet SrCu 2 ( BO 3 ) 2 , an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap Δ using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu 2 ( BO 3 ) 2 are captured by the spin S = 1 / 2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper []. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap Δ to the single triplon excitations at the experimentally relevant model parameters.
Anomalous thermal broadening in the Shastry-Sutherland model and SrCu2(_2(2​(BO3)2_3)_23​)2​
The quantum magnet SrCu2(_2(2​(BO3)2_3)_23​)2​ and its remarkably accurate theoretical description, the spin-1/21/21/2 Shastry-Sutherland model, host a variety of intriguing phenomena such as a dimer ground state with a nearly flat band of triplon excitations, a series of magnetization plateaux, and a possible pressure-induced deconfined quantum critical point. One open puzzle originating from inelastic neutron scattering and Raman experiments is the anomalous broadening of the triplon modes at relatively low temperatures compared to the triplon gap ΔΔΔ. We demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. To this end, we develop a numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately. Perturbative calculations identify the origin of this phenomenon as a small energy scale compared to ΔΔΔ between single triplon and bound triplon states at the experimentally relevant model parameters.
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.
Abstract The Shastry–Sutherland compound SrCu2(BO3)2constituting orthogonally coupled dimers harbors anS = 0 singlet ground state. The confluence of strong interdimer interaction and frustration engenders a spectrum of low-energy excitations including localized triplons as well as singlet and triplet bound states. Their dynamics are controlled by an external magnetic field and temperature. Here, we employ high-field Raman spectroscopy to map the field and temperature evolution of such bosonic composite quasiparticles on approaching the 1/8 magnetization plateau. Our study unveils that the magnetic field and thermal fluctuations show remarkably similar effects in melting the singlet bound states, but are disparate in their effects on the fine spectral shapes. This, together with the anti-crossing of two singlet bound states in the intermediate fieldB = 10 − 16 T, is discussed in terms of the correlated dynamics of frustrated, interacting bosons.
Low dimensional quantum magnets which display a collective singlet ground state and a gap in their magnetic excitation spectrum provide a framework for much exotic phase behavior in new materials, with high temperature superconductivity being the best appreciated example. Neutron scattering techniques can be applied to study a wide variety of problems in condensed matter physics. These techniques are particularly useful as applied to understanding the magnetic properties of quantum magnets that display exotic phases. SrCu2(BO3)2, is a rare example of a two-dimensional quantum magnet for which an exact theoretical solution describing its ground state is known to be a collective singlet. Previous high resolution neutron scattering measurements identified the most prominent features of the spin excitation spectrum in SrCu2(BO3)2, including the presence of one and two triplet excitations and weak dispersion characteristic of subleading terms in the spin Hamiltonian. The resemblance between the spin gap behavior in the Mott insulator SrCu2(BO3)2 and that associated with high temperature superconductors motivated the consideration of the significance of doping in order to understand the properties of this quantum magnetic system. For this reason, a series of neutron scattering studies on doped SrCu2(BO3)2 were initiated. These series of investigations began with the performance of neutron scattering measurements on a SrCu(2-x)Mgx(BO3)2 single crystal in order to introduce magnetic vacancies to the system. These results revealed the presence of new spin excitations within the singlet-triplet gap of this system. Application of a magnetic field induces Zeeman-split states associated with un-paired spins which exist as a consequence of doping with quenched non-magnetic impurities. Additional substantial broadening of both the one and two triplet excitations is observed in the doped system as compared to the pure system. Theoretical calculations are shown to qualitatively account for these features. These studies were extended to neutron scattering measurements on Sr(1-x)LaxCu2(BO3)2, with an aim of introducing charged carriers into this system. The broadening of the one and two triplet excitations is observed and compared to the thermally induced finite lifetime of the pure system. The temperature dependence of this broadening in Sr(1-x)LaxCu2(BO3)2 is different compared to that observed in both SrCu2(BO3)2 and SrCu(2-x)Mgx(BO3)2. It has also been suggested that there is a relation between the spin-lattice interaction in SrCu2(BO3)2 and the magnetic dynamics at low temperatures and high magnetic fields. For this reason there has been increased interest in the study of the crystalline structure and vibrational modes of SrCu2(BO3)2. In order to investigate the role of the lattice in the formation of the singlet ground state in SrCu2(BO3)2, a series of low and high energy neutron scattering measurements were carried out on this system to study both the crystalline structure as well as the normal modes of vibration of the lattice, the transverse acoustic and optical phonons. Transverse acoustic phonons with energies comparable to and higher than the onset of the two triplet continuum show substantially increased lifetimes on entering the singlet ground state below ~ 10 K. This may indicate the removal of the decay channel for the phonons due to the gapping of the spin excitation spectrum in SrCu2(BO3)2 at low temperatures. In high energy inelastic neutron scattering we observe broadening of optic phonons in the ~ 52 to 65 meV region on entering the low temperature singlet ground state. Additionally, the magnetic properties of CuMoO4, which is a triclinic quantum magnet system based on S=1/2 moments at the Cu2+ site, were studied using elastic and inelastic neutron scattering experiments. This material exhibits a first order structural phase transition at ~ 190 K as well as a magnetic phase transition at ~ 1.75 K. We were primarily interested in the low temperature magnetic properties of this material. Magnetization and heat capacity measurements as well as elastic and inelastic neutron scattering measurements were conducted on this system within the low temperature ordered phase. These studies confirm that this material has a magnetic phase transition at ~ 1.7 K. Neutron scattering results indicate that this magnetically ordered phase is characterized by a doubling of the a axis. Inelastic neutron scattering measurements revealed a gapped magnetic excitation spectrum in zero magnetic field, which could be filled in by the application of magnetic fields approaching 7 T.
Motivated by the remarkable properties of SrCu2(BO3) 2 in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at 2/9, 1/6, 1/9, and 2/15 upon increasing the interdimer coupling. We predict that a 1/6 plateau should be present in SrCu2(BO3)2, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below 1/3. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on SrCu2(BO3) 2.