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www-f1.ijs.si/~bonca LAW3M-05 Janez Bonča Physics Department, FMF, University of Ljubljana, J. Stefan Institute, Ljubljana, SLOVENIA Thermodynamic Properties of the Shastry Sutherland Model
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www-f1.ijs.si/~bonca LAW3M-05 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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www-f1.ijs.si/~bonca LAW3M-05 Introduction Structure and symmetry properties of SrCu 2 (BO 3 ) 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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www-f1.ijs.si/~bonca LAW3M-05 SrCu 2 (BO 3 ) 2
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www-f1.ijs.si/~bonca LAW3M-05 SrCu 2 (BO 3 ) 2
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www-f1.ijs.si/~bonca LAW3M-05 Space group of the CuBO 3 plane: Point group: Including time- reversal at H=0: H>0:
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www-f1.ijs.si/~bonca LAW3M-05 Shastry-Sutherland model: Shastry & Sutherland Physica 108B (1981) 1069
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www-f1.ijs.si/~bonca LAW3M-05 Complete model: Ts<395K
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www-f1.ijs.si/~bonca LAW3M-05 Symmetry of DM term 1 2 sysy sxsx x y Inversion Symmetry: Mirror Symmetry:
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www-f1.ijs.si/~bonca LAW3M-05 Computation: Allowed tilted square lattices:
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www-f1.ijs.si/~bonca LAW3M-05 FTLM: High -T expansion Thermal average over the canonical ensemble Combination of high- temperature expansion and random sampling J. Jaklič and P. Prelovšek, Adv. Phys. 49, 1 (2000). J. Jaklič and P. Prelovšek, Phys. Rev. Lett. 77, 892 (1996). J. Bonča and P. Prelovšek, Phys. Rev. B 67, 085103 (2002).
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www-f1.ijs.si/~bonca LAW3M-05 Thermal average in the canonical ensemble Only N st ~5000 can be done exactly Instead, we perform High-T expansion of Exp(- H) FTLM: High -T expansion
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www-f1.ijs.si/~bonca LAW3M-05 M - # of Lanczos steps M>k The error is of the order of M+1 Expansion remains exact at T->0 FTLM: High –T expansion cont
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www-f1.ijs.si/~bonca LAW3M-05 Random sampling
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www-f1.ijs.si/~bonca LAW3M-05 We join HTE and random sampling A special case: [H,A]=0 Implementation of HTML
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www-f1.ijs.si/~bonca LAW3M-05 Finite-size effects, T fs
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www-f1.ijs.si/~bonca LAW3M-05 Thermodyamic properties: Entropy density: Specific heat: Uniform susceptibility:
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www-f1.ijs.si/~bonca LAW3M-05 Model parameters
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www-f1.ijs.si/~bonca LAW3M-05 Uniform Susceptibility T(K)
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www-f1.ijs.si/~bonca LAW3M-05 Specific heat G.A.Jorge, R.Stern, M. Jaime, N. Harrison, J. Bonča, S. El Shawish, C.D Batista, H.A. Dabkowska, and B.D. Gaulin,PRB 71, 092403, (2005).
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www-f1.ijs.si/~bonca LAW3M-05 Energy spectrum 1 2 3 4
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www-f1.ijs.si/~bonca LAW3M-05 ESR spectrum H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243 (2003).
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www-f1.ijs.si/~bonca LAW3M-05 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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www-f1.ijs.si/~bonca LAW3M-05 Symmetry breaking D: T=0
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www-f1.ijs.si/~bonca LAW3M-05 Effect of D x and D y terms
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www-f1.ijs.si/~bonca LAW3M-05 Finite –T calculations T=0
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www-f1.ijs.si/~bonca LAW3M-05 Finite –T calculations
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www-f1.ijs.si/~bonca LAW3M-05 B||c B||a H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243 (2003).
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www-f1.ijs.si/~bonca LAW3M-05 Neutron Scattering Knetter, PRL 92, 027204 (2004)
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www-f1.ijs.si/~bonca LAW3M-05 Neutron Scattering Comparison of FTLM with: Kageyama et al. PRL, 84 5876 (2000). S. El Shawish, J. Bonča, and I. Sega, PRB 72,184409 (2005).
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www-f1.ijs.si/~bonca LAW3M-05 Neutron Scattering Comparison of FTLM with: B.D. Gaulin et al. PRL, 93 267202 (2004). S. El Shawish, J. Bonča, and I. Sega, PRB 72,184409 (2005).
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www-f1.ijs.si/~bonca LAW3M-05 Neutron Scattering Comparison of FTLM with: B.D. Gaulin et al. PRL, 93 267202 (2004). T=1.4K FTLM results Experiment
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www-f1.ijs.si/~bonca LAW3M-05 Dimer model: J’=0,J= D =34K
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www-f1.ijs.si/~bonca LAW3M-05 Neutron Scattering Comparison of FTLM with: B.D. Gaulin et al. PRL, 93 267202 (2004). S. El Shawish, J. Bonča, and I. Sega, PRB 72,184409 (2005).
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www-f1.ijs.si/~bonca LAW3M-05 Finite Doping Sr Cu 2-x M x (BO 3 ) 2, M=Zn,Mg Leung & Cheng,PRB 69, 180403, (2005) N=32, Nh=1 J’/J=0.62
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www-f1.ijs.si/~bonca LAW3M-05 Uniform susceptibility c o K.Kudo et al. cond-mat/0409178
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www-f1.ijs.si/~bonca LAW3M-05 Spin Structure Factor Sr Cu 2-x M x (BO 3 ) 2, X=2n
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www-f1.ijs.si/~bonca LAW3M-05 Conclusions FT simulations of Cv show good agreement with experimental data when symmetry breaking DM term is of the order of Dz~5K. G.A.Jorge, R.Stern, M. Jaime, N. Harrison, J. Bonča, 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. Bonča, and I. Sega, PRB 72,184409 (2005). Results a finite doping show filling up of the spin gap.
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