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Frustrated Quantum Magnets in Strong Magnetic Fields

Frustrated Quantum Magnets in Strong Magnetic Fields. F. Mila Institute of Theoretical Physics Ecole Polytechnique F édérale de Lausanne Switzerland. Collaborators. Theorists. S. Miyahara (Lausanne  Tokyo) F. Becca (Lausanne  Trieste) B. Kumar (Lausanne). Experimentalists.

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Frustrated Quantum Magnets in Strong Magnetic Fields

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  1. Frustrated Quantum Magnets in StrongMagnetic Fields F. Mila Institute of Theoretical Physics Ecole Polytechnique Fédérale de Lausanne Switzerland

  2. Collaborators Theorists S. Miyahara(Lausanne  Tokyo) F. Becca (Lausanne  Trieste) B. Kumar (Lausanne) Experimentalists M. Takigawa, K. Kodama (ISSP, Tokyo) C. Berthier, M. Horvatic (Grenoble) Chemists H. Kageyama, Y. Ueda (ISSP, Tokyo)

  3. Scope • Introduction to Frustrated Quantum Magnets • Dimers + Frustration  Magnetization plateaux • Other anomalies in SrCu2(BO3)2  Dzyaloshinskii-Moriya interactions  Correlated hopping • Conclusions/Perspectives

  4. Quantum magnets: 2 paradigms H=∑(i,j) JijSi.Sj S=1/2,1,… Long-range order Spin gap J J’ Singlet-triplet gap Goldstone modes: Spin waves Δ=J’+O(J) (J«J’)

  5. Defining frustration Frustration = infinite degeneracy of classical ground state Shastry-Sutherland Model J1 J2 J2<2J1 J2>2J1 Effect of quantum fluctuations?

  6. Quantum approach 1) Quantum treatment of local bricks 2) Pertubative treatment of inter-brick coupling Coupled triangles Coupled dimers 2 degrees of freedom Frustrated motion of triplets Low-lying singlets Magnetization plateaux SrCu2(BO3)2 Spin ½ kagome

  7. Dimers in a magnetic field Isolated dimers Coupled dimers

  8. Magnetization of spin ladders Chaboussant et al, EPJB ‘98 CuHpCl NB: CuHpCl might not be a simple ladder (Stone et al, cond-mat/0103023)

  9. Frustrated ladders Metal-insulator transition for V=2t (J’=J/3)

  10. Magnetization Plateau D. Cabra et al, PRL ‘97 K. Totsuka, PRB ‘98 T. Tonegawa et al, PRB ‘99 F. Mila, EPJB ‘98 Kinetic energy Metal-insulator transition Frustration Magnetization plateau Repulsion

  11. Frustrated Coupled Dimers Triplet Hopping Triplet Repulsion

  12. Magnetization of SrCu2(BO3)2 Kageyama et al, PRL ‘99

  13. Shastry-Sutherland model J’/J ' .63 Ground-state Product of singlets on J-bonds (Shastry, Sutherland, ’81) Triplets Almost immobile and repulsive (Miyahara et al, ’99) Plateaux (Miyahara et al, ’00)

  14. Symmetry breaking inside plateaux Miyahara et al, ’00 Hard-core bosons with repulsion

  15. NMR at 1/8-plateau At least 11 different sites! K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca, F. Mila, Science ‘02

  16. Magnetization opposite to field Magnetization in field direction Magnetization profile at 1/8 Symmetrybreaking 16 sites/unit cell 8-fold degenerate GS Lattice distortion Selection of one GS Friedel-like oscillations NMR pattern

  17. Further anomalies I Δ∕gμB Kodama et al, unpublished Kodama et al, Science ‘02 • The magnetization raises too early • The gap does not close (see also ESR, Nojiri et al, 1999) • 3) The magnetization jumps before plateau

  18. Further anomalies II Tsujii et al,’03 4) No Bose condensation below plateau

  19. Possible sources of deviation • Correlated hopping of triplets  Bound states • Spin-lattice coupling • Dzyaloshinskii-Moriya interactions D.(SixSj)  Inter-dimer (D’) Intra-dimer(D)

  20. Evidence of intra-dimer DM Hs=H1-H2≠0 Hext=6.9 T Staggered magnetization Kodama et al, unpublished

  21. D 1 2 Dzyaloshinskii-Moriya interactions H D: intra-dimer DM

  22. High-field effects of intra-dimer DM D=0.034 D’=-0.02 gs=0.023 (ED, 24 sites) Kodama, Miyahara, et al, unpublished

  23. Properties around 1/8 plateau Exact diagonalizations? Not appropriate! Huge finite-size effects at the plateaux!  Effective hard-core boson model

  24. Pertubative derivation Momoi and Totsuka, PRB’01 3rd order in J’/J

  25. Mean-field phase diagram Momoi-Totsuka, ‘01 Plateaux only at 1/3 and 1/2

  26. Semi-phenomenological approach t’ it B. Kumar, F. Mila, unpublished

  27. Mean-field (<b>, <b+>,<b+b>) Next step: include <bb> and <b+b+>

  28. Conclusions/Perspectives Magnetization of SrCu2(BO3)2: Remarkably rich and complex behaviour • Triplet reduced mobility and repulsion Magnetization plateaus • Intra-dimer DM interaction  Staggered magnetization  Early raise of uniform magnetization  Persistence of gap

  29. Openissues • Magnetization jump before 1/8 plateau? • Difference of behaviour below and above 1/8 plateau? • Consequences of correlated hopping?  Pairing? • Dip of the gap just before plateau?

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