Thermodynamic Properties of the Shastry Sutherland Model

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Thermodynamic Properties of the Shastry
Sutherland Model
Janez Bonca Physics Department, FMF, University
of Ljubljana, J. Stefan Institute, Ljubljana,
SLOVENIA
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• Collaborators
• S. El Shawish and I. Sega, J. Stefan Inst.,
  Ljubljana, Slovenia
• C. D. Batista, M. Jaime, N. Harrison, G.A. Jorge,
  LANL T-11, NHMFL, USA
• R. Stern, NICPB, Tallin, Estonia
• H.A. Dabkowska, B.D. Gaulin, Mc Master Univ.,
  Hamilton, Canada

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Introduction

• Structure and symmetry properties of SrCu2(BO3)2
• The Sutherlad Shastry model
• Finite Temperature Lanczos method
• Specific heath results and comparison with
  experiment
• Spin structure factor at zero and finite
  temperatures and comparison with ESR and INS
  measurements
• Finite doping with nonmagnetic impurities

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SrCu2(BO3)2
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SrCu2(BO3)2
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Space group of the CuBO3 plane
Point group
Including time-reversal at H0
Hgt0
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Shastry-Sutherland model
Shastry Sutherland Physica 108B (1981) 1069
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Complete model
Tslt395K
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Symmetry of DM term
sx
y
1
Inversion Symmetry
sy
x
2
Mirror Symmetry
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Computation
Allowed tilted square lattices
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FTLM High -T expansion

• Thermal average over the canonical ensemble

Combination of high- temperature expansion and
random sampling
J. Jaklic and P. Prelovšek, Adv. Phys. 49, 1
(2000). J. Jaklic and P. Prelovšek, Phys. Rev.
Lett. 77, 892 (1996). J. Bonca and P. Prelovšek,
Phys. Rev. B 67, 085103 (2002).
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FTLM High -T expansion

• Thermal average in the canonical ensemble

Only Nst5000 can be done exactly
Instead, we perform High-T expansion of Exp(-? H)
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FTLM High T expansion cont
M - of Lanczos steps Mgtk

• The error is of the order of ?M1
• Expansion remains exact at T-gt0

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Random sampling
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Implementation of HTML
We join HTE and random sampling
A special case H,A0 ?
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Finite-size effects, Tfs
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Thermodyamic properties
Entropy density
Specific heat
Uniform susceptibility
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Model parameters
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Uniform Susceptibility
T(K)
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Specific heat
G.A.Jorge, R.Stern, M. Jaime, N. Harrison, J.
Bonca, S. El Shawish, C.D Batista, H.A.
Dabkowska, and B.D. Gaulin,PRB 71, 092403, (2005).
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Energy spectrum
3
4
2
1
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ESR spectrum
H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243
(2003).
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Spin Structure Factor S. El Shwaish, J. Bonca,
C.D.Batista, and I. Sega, PRB 71, 014413 (2005)
Non-symmetry breaking D
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Symmetry breaking D
T0
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Effect of Dx and Dy terms
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Finite T calculations
T0
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Finite T calculations
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H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243
(2003).
Bc
Ba
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Neutron Scattering
Knetter, PRL 92, 027204 (2004)
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Neutron Scattering
S. El Shawish, J. Bonca, and I. Sega, PRB
72,184409 (2005).
Comparison of FTLM with Kageyama et al. PRL,
84 5876 (2000).
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Neutron Scattering
Comparison of FTLM with B.D. Gaulin et al.
PRL, 93 267202 (2004).
S. El Shawish, J. Bonca, and I. Sega, PRB
72,184409 (2005).
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Neutron Scattering
FTLM results
Comparison of FTLM with B.D. Gaulin et al.
PRL, 93 267202 (2004).
Experiment
T1.4K
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Dimer model J0,JD34K
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Neutron Scattering
S. El Shawish, J. Bonca, and I. Sega, PRB
72,184409 (2005).
Comparison of FTLM with B.D. Gaulin et al.
PRL, 93 267202 (2004).
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Finite Doping Sr Cu2-xMx(BO3)2, MZn,Mg
J/J0.62
N32, Nh1
Leung Cheng,PRB 69, 180403, (2005)
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Uniform susceptibility co
K.Kudo et al. cond-mat/0409178
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Spin Structure Factor Sr Cu2-xMx(BO3)2,
X2n
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Conclusions

• FT simulations of Cv show good agreement with
  experimental data when symmetry breaking DM term
  is of the order of Dz5K. G.A.Jorge, R.Stern, M.
  Jaime, N. Harrison, J. Bonca, S. El Shawish, C.D
  Batista, H.A. Dabkowska, and B.D. Gaulin,PRB 71,
  092403, (2005).
• ESR spectra can be reproduced only with finite
  value of symmetry breaking Dz open question
  (structural phase transition, phonons). S. El
  Shwaish, J. Bonca, C.D.Batista, and I. Sega, PRB
  71, 014413 (2005).
• Good agreement with neutron-scattering data. S.
  El Shawish, J. Bonca, and I. Sega, PRB 72,184409
  (2005).
• Results a finite doping show filling up of the
  spin gap.