We have studied spin excitation spectra in the Shastry-Sutherland model compound $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ . One is $a$ -polarized and creates an intradimer dynamic DM along the $c$ axis. The other is $c$ -polarized and creates an intradimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ anticross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and interdimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static interdimer DM in the $c$ -direction ${d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ splits the triplet state sublevels in zero field [C\'epas et al., Phys. Rev. Lett. 87, 167205 (2001)]. The static intradimer DM in the $(ab)$ plane (perpendicular to the dimer axis) ${d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, allowed by the buckling of $\mathrm{Cu}\mathrm{B}{\mathrm{O}}_{3}$ planes, couples the triplet state to the $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ singlet as is seen from the avoided crossing.We have studied spin excitation spectra in the Shastry-Sutherland model compound $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$. One is $a$-polarized and creates an intradimer dynamic DM along the $c$ axis. The other is $c$-polarized and creates an intradimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ anticross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and interdimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static interdimer DM in the $c$-direction ${d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ splits the triplet state sublevels in zero field [C\'epas et al., Phys. Rev. Lett. 87, 167205 (2001)]. The static intradimer DM in the $(ab)$ plane (perpendicular to the dimer axis) ${d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, allowed by the buckling of $\mathrm{Cu}\mathrm{B}{\mathrm{O}}_{3}$ planes, couples the triplet state to the $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ singlet as is seen from the avoided crossing.

arXiv:cond-mat/0405434Physical Review BOct 27, 200431 citations

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

Z. Q. Wang, Paul McClarty, Dobromila Dankova +2 more

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 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.

Jan 15, 20260 citations

We have studied spin excitation spectra in the Shastry-Sutherland model compound

\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}

in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in

\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}

. One is

a

-polarized and creates an intradimer dynamic DM along the

c

axis. The other is

c

-polarized and creates an intradimer dynamic DM interaction, it is in the

(ab)

plane and perpendicular to the dimer axis. Singlet levels at 21.5 and $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ anticross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and interdimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static interdimer DM in the

c

-direction ${d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ splits the triplet state sublevels in zero field [C\'epas et al., Phys. Rev. Lett. 87, 167205 (2001)]. The static intradimer DM in the

(ab)

plane (perpendicular to the dimer axis) ${d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, allowed by the buckling of

\mathrm{Cu}\mathrm{B}{\mathrm{O}}_{3}

planes, couples the triplet state to the $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ singlet as is seen from the avoided crossing.