Thermodynamic Properties of the Shastry Sutherland Model

Janez Bonča 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 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 www-f1.ijs.si/~bonca LAW3M-05

SrCu

2

(BO

3

)

2 www-f1.ijs.si/~bonca LAW3M-05

SrCu

2

(BO

3

)

2 www-f1.ijs.si/~bonca LAW3M-05

Space group of the CuBO

3

plane:

Point group: Including time reversal at H=0: H>0: www-f1.ijs.si/~bonca LAW3M-05

Shastry-Sutherland model:

Shastry & Sutherland Physica 108B (1981) 1069 www-f1.ijs.si/~bonca LAW3M-05

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Complete model:

Ts<395K LAW3M-05

Symmetry of DM term

y s x 1 Inversion Symmetry: s y 2 Mirror Symmetry: x www-f1.ijs.si/~bonca LAW3M-05

Computation:

Allowed tilted square lattices: 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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Thermodyamic properties:

Entropy density: Specific heat: Uniform susceptibility: www-f1.ijs.si/~bonca LAW3M-05

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Model parameters

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Uniform Susceptibility

www-f1.ijs.si/~bonca T(K) 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 1

Energy spectrum

3 4 2 LAW3M-05

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: www-f1.ijs.si/~bonca LAW3M-05

Symmetry breaking D: www-f1.ijs.si/~bonca T=0 LAW3M-05

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Effect of D

x

and D

y

terms

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H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243 (2003).

B||c B||a www-f1.ijs.si/~bonca LAW3M-05

Neutron Scattering

Knetter, PRL 92, 027204 (2004) www-f1.ijs.si/~bonca LAW3M-05

Neutron Scattering

S. El Shawish, J. Bonča, 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. Bonča, and I. Sega, PRB 72,184409 (2005).

LAW3M-05 www-f1.ijs.si/~bonca

Neutron Scattering

FTLM results Comparison of FTLM with: B.D. Gaulin et al. PRL, 93 267202 (2004).

Experiment www-f1.ijs.si/~bonca T=1.4K

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Neutron Scattering

S. El Shawish, J. Bonča, 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 Cu 2-x M x (BO 3 ) 2, M=Zn,Mg J’/J=0.62

N=32, Nh=1 Leung & Cheng,PRB 69, 180403, (2005) www-f1.ijs.si/~bonca LAW3M-05

Uniform susceptibility

c o www-f1.ijs.si/~bonca K.Kudo et al.

cond-mat/0409178 LAW3M-05

www-f1.ijs.si/~bonca Spin Structure Factor Sr Cu 2-x M x (BO 3 ) 2, X=2n 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. B.D. Gaulin, G.A.Jorge, R.Stern, M. Jaime, N. Harrison, J. Bonča, S. El Shawish, C.D Batista, H.A. Dabkowska, and 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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