Canadian Journal of Physics

SrCu2(BO3)2 – a two-dimensional spin liquid

Christian Knetter, Alexander Bühler, R.R.P. Singh, E. Müller‐Hartmann, Götz Silvester Uhrig

Published Jan 1, 2001• 0 citations

Abstract

We study an extended Shastry-Sutherland model for SrCu2(BO3)2 and analyze the low lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations.The derivation of the 1-magnon dispersion (elementary triplets) is discussed.Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets.Our high order results allow to fix the model parameters for SrCu2(BO3)2 precisely: J1 = 6.16(10)meV, x := J2/J1 = 0.603(3), J ⊥ = 1.3(2)meV.To our knowledge this is the first quantitative treatment of bound states in a true 2d model.

DOI: 10.1139/cjp-79-11-12-1565

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Canadian Journal of Physics

SrCu2(BO3)2 – a two-dimensional spin liquid

Christian Knetter, Alexander Bühler, R.R.P. Singh, E. Müller‐Hartmann, Götz Silvester Uhrig

Published Jan 1, 2001• 0 citations

Publisher

Abstract

DOI: 10.1139/cjp-79-11-12-1565

Related papers

SrCu2(BO3)2 – a two-dimensional spin liquid

Christian Knetter, Alexander Bühler, R RP Singh +2 more

We study an extended ShastrySutherland model for SrCu2(BO3)2 and analyze the low-lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations. The derivation of the one-magnon dispersion (elementary triplets) is discussed. Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets. Our high-order results allow us to fix the model parameters for SrCu2(BO3)2 precisely: J1 = 6.16(10) meV, x := J2/J1 = 0.603(3), J[Formula: see text] =1.3(2) meV. To our knowledge this is the first quantitative treatment of bound states in a true 2D model. PACS Nos.: 75.40Gb, 75.30Kz, 75.50Ee, 75.10JmWe study an extended ShastrySutherland model for SrCu2(BO3)2 and analyze the low-lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations. The derivation of the one-magnon dispersion (elementary triplets) is discussed. Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets. Our high-order results allow us to fix the model parameters for SrCu2(BO3)2 precisely: J1 = 6.16(10) meV, x := J2/J1 = 0.603(3), J[Formula: see text] =1.3(2) meV. To our knowledge this is the first quantitative treatment of bound states in a true 2D model. PACS Nos.: 75.40Gb, 75.30Kz, 75.50Ee, 75.10Jm

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In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.

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Magnetization Plateaus in the Shastry-Sutherland Model for SrCu2(BO3)2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation

Yoshiyuki Fukumoto

Magnetization plateaus in the Shastry-Sutherland model for ${\rm SrCu_2(BO_3)_2}$ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with $S^{\rm tot}_z=1$ in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.Magnetization plateaus in the Shastry-Sutherland model for ${\rm SrCu_2(BO_3)_2}$ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with $S^{\rm tot}_z=1$ in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.

arXiv:cond-mat/0012396Journal of the Physical Society of JapanMay 15, 200125 citations

({J}_{2}/{J}_{1}{)}^{14}

] permit one to fix the parameters of

{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}

precisely:

{J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6.16(10)\mathrm{meV}

, $x\ensuremath{\mathrel{:=}}{J}_{2}/{J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.603(3)$, ${J}_{\ensuremath{\perp}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.3(2)\mathrm{meV}$. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at

x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.63

indicates a transition towards another phase. The possible nature of this phase is discussed.

Magnetization plateaus in the Shastry-Sutherland model for

{\rm SrCu_2(BO_3)_2}

are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with

S^{\rm tot}_z=1

in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.