arXiv:cond-mat/0009403 · Canadian Journal of Physics

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

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

Published Dec 1, 2001• 0 citations

Abstract

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, 75.10Jm

DOI: 10.1139/p01-091

Related papers

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

Christian Knetter, Alexander Bühler, R.R.P. Singh +2 more

Canadian Journal of PhysicsJan 1, 20010 citations

Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model

Christian Knetter, Alexander Bühler, E. Müller‐Hartmann +1 more

arXiv:cond-mat/0005322Physical Review LettersOct 30, 2000146 citations

Symmetries and triplet dispersion in a modified Shastry-Sutherland model for SrCu2(BO3)2

Christian Knetter, Erwin Müller-Hartmann, Götz Silvester Uhrig +1 more

arXiv:cond-mat/0009402Journal of Physics Condensed MatterOct 5, 200015 citations

Magnetization plateaux and bound states of the Shastry–Sutherland model for SrCu2(BO3)2

Tsutomu Momoi, Kiyohito Totsuka

Canadian Journal of PhysicsDec 1, 20010 citations

High Energy-Resolution Inelastic Neutron Scattering Experiments on Triplet Bound State Excitations in SrCu2(BO3)2

Naofumi Aso, Hiroshi Kageyama, Katsuyuki Nukui +4 more

Journal of the Physical Society of JapanAug 1, 20058 citations

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

Yoshiyuki Fukumoto

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

arXiv:cond-mat/0009403 · Canadian Journal of Physics

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

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

Published Dec 1, 2001• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1139/p01-091

Related papers

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

Christian Knetter, Alexander Bühler, R.R.P. Singh +2 more

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.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.

Canadian Journal of PhysicsJan 1, 20010 citations

Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model

Christian Knetter, Alexander Bühler, E. Müller‐Hartmann +1 more

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to $({J}_{2}/{J}_{1}{)}^{14}$ ] 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.Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to $({J}_{2}/{J}_{1}{)}^{14}$] 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.

arXiv:cond-mat/0005322Physical Review LettersOct 30, 2000146 citations

Symmetries and triplet dispersion in a modified Shastry-Sutherland model for SrCu2(BO3)2

Christian Knetter, Erwin Müller-Hartmann, Götz Silvester Uhrig +1 more

We investigate the one-triplet dispersion in a modified Shastry-Sutherland model for SrCu 2 (BO 3 ) 2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy-quanta-conserving block diagonal Hamiltonian eff . The dispersion splits into two branches which are nearly degenerate. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k = 0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small | k | and compare our results to inelastic neutron scattering data.We investigate the one-triplet dispersion in a modified Shastry-Sutherland model for SrCu 2 (BO 3 ) 2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy-quanta-conserving block diagonal Hamiltonian eff . The dispersion splits into two branches which are nearly degenerate. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k = 0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small | k | and compare our results to inelastic neutron scattering data.

arXiv:cond-mat/0009402Journal of Physics Condensed MatterOct 5, 200015 citations

Magnetization plateaux and bound states of the Shastry–Sutherland model for SrCu2(BO3)2

Tsutomu Momoi, Kiyohito Totsuka

In this paper, we briefly review our recent studies of the Heisenberg anti-ferromagnet on the ShastrySutherland lattice for SrCu2(BO3)2 under magnetic fields. Treating magnetic excitations promoted by the field as Bose particles and using a strong-coupling expansion, we derived an effective Hamiltonian for the magnetic particles. Anisotropic repulsive interactions between particles induce "insulating" states with a stripe spin-density wave structure at magnetization m/msat = 1/3 and with a checkerboard structure at 1/2, and thereby form magnetization plateaux. We also demonstrated how the unique geometry of the ShastrySutherland lattice affects dynamical properties and makes a novel type of quintuplet (S = 2) bound states condense for very small magnetization. PACS Nos.: 75.50-y, 75.60Ej, 75.10JmIn this paper, we briefly review our recent studies of the Heisenberg anti-ferromagnet on the ShastrySutherland lattice for SrCu2(BO3)2 under magnetic fields. Treating magnetic excitations promoted by the field as Bose particles and using a strong-coupling expansion, we derived an effective Hamiltonian for the magnetic particles. Anisotropic repulsive interactions between particles induce "insulating" states with a stripe spin-density wave structure at magnetization m/msat = 1/3 and with a checkerboard structure at 1/2, and thereby form magnetization plateaux. We also demonstrated how the unique geometry of the ShastrySutherland lattice affects dynamical properties and makes a novel type of quintuplet (S = 2) bound states condense for very small magnetization. PACS Nos.: 75.50-y, 75.60Ej, 75.10Jm

Canadian Journal of PhysicsDec 1, 20010 citations

High Energy-Resolution Inelastic Neutron Scattering Experiments on Triplet Bound State Excitations in SrCu2(BO3)2

Naofumi Aso, Hiroshi Kageyama, Katsuyuki Nukui +4 more

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.

Journal of the Physical Society of JapanAug 1, 20058 citations

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.