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arXiv:cond-mat/0407632 · Physical Review B

Electron spin resonance of SrCu2(BO3)2 at high magnetic fields

Samir El Shawish, J. Bonča, Cristian D. Batista, Igor Sega

Published Jan 12, 2005• 10 citations
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Abstract

We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ as a function of magnetic field $B$. 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 ${D}_{z}$ 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.

DOI
10.1103/physrevb.71.014413

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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∥cB\ensuremath{\Vert}cB\ensuremath∥c. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.
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.
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 $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ 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 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 $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ 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 ccc-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)(ab)(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 CuBO3\mathrm{Cu}\mathrm{B}{\mathrm{O}}_{3}CuBO3​ 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.
Using finite temperature Lanczos technique on finite clusters we calculate dynamical spin structure factor 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 wave vector and temperature. At low temperatures the peak belonging to the lowest spin excitations is split due to spin anisotropy, in accord with the experimental data. Unusual temperature dependence of calculated spectra is as well in agreement with inelastic neutron scattering measurements. Normalized peak intensities of the single-triplet peak are q\mathbf{q}q independent, their temperature dependence is analyzed in terms of thermodynamic quantities.
High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu2_{2}2​(BO3_{3}3​)2_{2}2​. With frequencies below 1 THz, ESR signals associated with transitions from the singlet ground state to the one-triplet excited states and the two-triplet bound state were observed at pressures up to 2.1 GPa. We obtained directly the pressure dependence of the gap energies, finding a clear first-order phase transition at Pc=1.85±0.05P_{c}=1.85\pm0.05Pc​=1.85±0.05 GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- (J′J'J′) and intra-dimer (JJJ) exchange interactions considering the Dzyaloshinski-Moriya interaction. Thus this system undergoes a first-order quantum phase transition from the dimer singlet phase to a plaquette singlet phase above the ratio (J′/J)c=0.660±0.003(J'/J)_{c}=0.660\pm0.003(J′/J)c​=0.660±0.003.
We study magnetic excitations for anisotropic spin dimer systems. We present a theory that describes not only the lowest-lying excitation mode but also higher-lying modes of the spin dimers, where the latter modes are important for quantum phase transitions driven by magnetic field and pressure in spin-gapped systems. As the most intriguing application, we calculate electron spin resonance (ESR) intensity in the presence of Dzyaloshinskii–Moriya (DM) interaction, which couples the local triplet with the singlet states of the dimer. The ESR intensities under various configurations of the DM interactions are reported in both disordered and field-induced ordered phases, which are very useful for the analysis of high-field ESR data.