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Physical Review B

Dynamic spin structure factor of SrCu2(BO3)2 at finite temperatures

Samir El Shawish, J. Bonča, Igor Sega

Published Nov 7, 2005• 8 citations
Publisher

Abstract

Using finite temperature Lanczos technique on finite clusters we calculate dynamical spin structure factor of the quasi-two-dimensional dimer spin liquid $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ 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 $\mathbf{q}$ independent, their temperature dependence is analyzed in terms of thermodynamic quantities.

DOI
10.1103/physrevb.72.184409

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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.
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.
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.
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.
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ and many other highly frustrated spin systems.
Abstract Quantum magnets admit more than one classical limit and N-level systems with strong single-ion anisotropy are expected to be described by a classical approximation based on SU(N) coherent states. Here we test this hypothesis by modeling finite temperature inelastic neutron scattering (INS) data of the effective spin-one antiferromagnet Ba2FeSi2O7. The measured dynamic structure factor is calculated with a generalized Landau-Lifshitz dynamics for SU(3) spins. Unlike the traditional classical limit based on SU(2) coherent states, the results obtained with classical SU(3) spins are in good agreement with the measured temperature-dependent spectrum. The SU(3) approach developed here provides a general framework to understand the broad class of materials comprising weakly coupled antiferromagnetic dimers, trimers, or tetramers, and magnets with strong single-ion anisotropy.