2. 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

3. 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

4. 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

5. www-f1.ijs.si/~bonca LAW3M-05 SrCu 2 (BO 3 ) 2

6. www-f1.ijs.si/~bonca LAW3M-05 SrCu 2 (BO 3 ) 2

7. www-f1.ijs.si/~bonca LAW3M-05 Space group of the CuBO 3 plane: Point group: Including time- reversal at H=0: H>0:

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

9. www-f1.ijs.si/~bonca LAW3M-05 Complete model: Ts<395K

10. www-f1.ijs.si/~bonca LAW3M-05 Symmetry of DM term 1 2 sysy sxsx x y Inversion Symmetry: Mirror Symmetry:

11. www-f1.ijs.si/~bonca LAW3M-05 Computation: Allowed tilted square lattices:

12. 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).

13. 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

14. 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

15. www-f1.ijs.si/~bonca LAW3M-05 Random sampling

16. www-f1.ijs.si/~bonca LAW3M-05 We join HTE and random sampling A special case: [H,A]=0  Implementation of HTML

17. www-f1.ijs.si/~bonca LAW3M-05 Finite-size effects, T fs

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

19. www-f1.ijs.si/~bonca LAW3M-05 Model parameters

20. www-f1.ijs.si/~bonca LAW3M-05 Uniform Susceptibility T(K)

21. 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).

22. www-f1.ijs.si/~bonca LAW3M-05 Energy spectrum 1 2 3 4

23. www-f1.ijs.si/~bonca LAW3M-05 ESR spectrum H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243 (2003).

24. 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:

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

26. www-f1.ijs.si/~bonca LAW3M-05 Effect of D x and D y terms

27. www-f1.ijs.si/~bonca LAW3M-05 Finite –T calculations T=0

28. www-f1.ijs.si/~bonca LAW3M-05 Finite –T calculations

29. www-f1.ijs.si/~bonca LAW3M-05 B||c B||a H. Nojiri, et al.,J. Phys. Soc. Jpn. 72, 3243 (2003).

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

31. 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).

32. 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).

33. 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

34. www-f1.ijs.si/~bonca LAW3M-05 Dimer model: J’=0,J= D =34K

35. 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).

36. 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

37. www-f1.ijs.si/~bonca LAW3M-05 Uniform susceptibility c o K.Kudo et al. cond-mat/0409178

38. www-f1.ijs.si/~bonca LAW3M-05 Spin Structure Factor Sr Cu 2-x M x (BO 3 ) 2, X=2n

39. 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.