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arXiv:cond-mat/0405434 · Physical Review B

Far-infrared spectroscopy of spin excitations and Dzyaloshinskii-Moriya interactions in the Shastry-Sutherland compound SrCu2(BO3)2

T. Rõõm, D. Hüvonen, U. Nagel, Jungseek Hwang, T. Timusk, Hiroshi Kageyama

Published Oct 27, 2004• 31 citations
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Abstract

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.

DOI
10.1103/physrevb.70.144417

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We have studied spin excitation spectra in the Shastry-Sutherland model compound SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at 24cm\ensuremath−124\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}24cm\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 SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​. One is aaa-polarized and creates an intradimer dynamic DM along the ccc axis. The other is ccc-polarized and creates an intradimer dynamic DM interaction, it is in the (ab)(ab)(ab) plane and perpendicular to the dimer axis. Singlet levels at 21.5 and 28.6cm\ensuremath−128.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}28.6cm\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 ccc-direction d1=0.7cm\ensuremath−1{d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}d1​=0.7cm\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)(ab)(ab) plane (perpendicular to the dimer axis) d2=1.8cm\ensuremath−1{d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}d2​=1.8cm\ensuremath−1, allowed by the buckling of CuBO3\mathrm{Cu}\mathrm{B}{\mathrm{O}}_{3}CuBO3​ planes, couples the triplet state to the 28.6cm\ensuremath−128.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}28.6cm\ensuremath−1 singlet as is seen from the avoided crossing.
We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ as a function of magnetic field BBB. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a nonzero Dz{D}_{z}Dz​ component is required to explain the low frequency ESR lines for $B\ensuremath{\Vert}c$. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.
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.
In this paper we would like to review the zero field inelastic neutron scattering results obtained by using both the thermal and cold neutron triple axis instrument. The first single triplet state at around 3 meV is split due to the Dzyaloshinski-Moriya (DM) inter-dimer interaction with both the out-of-plane and in-plane components. The splitting between the Sz = ±1 states is of the order of 0.3 meV. The two triplets bound states also form a very flat bands at 4.9, 5.5 and 6.3 meV with finite line width of the order and/or twice of the DM splitting. Finally the higher energy range up to 13 meV can be also characterized by three rather broad, but flat bands at around 8, 10 and 12 meV with the line width roughly three times the DM splitting. These excitations can be probably assigned to three and more triplets bound state excitations.
The field- and frequency-dependence of Electron Spin Resonance (ESR) in the Shastry–Sutherland lattice with small Dzyaloshinsky–Moriya (DM) interaction is studied by the direct numerical estimation of the Kubo formula. Beside the strong paramagnetic resonance, we find the resonance due to the transitions between the triplet and singlet levels which are prohibited in the case without the DM interaction. Furthermore, we find the resonance which is distributed in a wide range of the field for a specific frequency, which corresponds to the transition between the states with the same magnetization.
Raman light scattering of the two-dimensional quantum spin system SrCu2(BO3)(2) shows a rich structure in the magnetic excitation spectrum, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of SrCu2(BO3)(2) is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound.
The orthogonal dimer structure of the SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ spin-1/2 magnet provides a realization of the Shastry--Sutherland model. Using a dimer-product variational wave function, we map out the phase diagram of the Shastry--Sutherland model including anisotropies. Based on the variational solution, we construct a bond-wave approach to obtain the excitation spectra as a function of the magnetic field. The characteristic features of the experimentally measured neutron and ESR spectra are reproduced, like the anisotropy-induced zero-field splittings and the persistent gap at higher fields.