Dynamic properties of the Shastry-Sutherland model at by xiaopangnv

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									           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
        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 H=0:


   H>0:
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              Shastry-Sutherland model:



                           Shastry & Sutherland
                            Physica 108B (1981)
                                   1069




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                       Complete model:



                       Ts<395K




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                                  sx
       Symmetry of DM term 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. 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:


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                       Model parameters




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                       Uniform Susceptibility




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                                 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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                           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:




                                  T=0




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                 Effect of Dx and Dy terms




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




                                B||c                           B||a




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       Neutron Scattering

                       Knetter, PRL
                       92, 027204 (2004)




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       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).



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       Neutron Scattering
                                     FTLM results

      Comparison of
      FTLM with:

      B.D. Gaulin et al.
      PRL, 93
      267202 (2004). Experiment




                            T=1.4K
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                            S. El Shawish, J. Bonča,
                                  and I. Sega,
       Neutron Scattering   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,
                M=Zn,Mg


                       J’/J=0.62




                                         N=32, Nh=1




                  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, X=2n




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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 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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