Frustrated Quantum Magnets in Strong Magnetic Fields

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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. - PowerPoint PPT Presentation

Text of Frustrated Quantum Magnets in Strong Magnetic Fields

  • Frustrated Quantum Magnets in StrongMagnetic FieldsF. MilaInstitute of Theoretical PhysicsEcole Polytechnique Fdrale de LausanneSwitzerland

  • CollaboratorsTheoristsS. Miyahara (Lausanne Tokyo)F. Becca (Lausanne Trieste)B. Kumar (Lausanne)

    ExperimentalistsM. Takigawa, K. Kodama (ISSP, Tokyo)C. Berthier, M. Horvatic (Grenoble)ChemistsH. Kageyama, Y. Ueda (ISSP, Tokyo)

  • ScopeIntroduction to Frustrated Quantum Magnets

    Dimers + Frustration Magnetization plateaux

    Other anomalies in SrCu2(BO3)2 Dzyaloshinskii-Moriya interactions Correlated hopping


  • Quantum magnets: 2 paradigmsLong-range orderSpin gapGoldstone modes: Spin wavesSinglet-triplet gapJJ=J+O(J) (JJ)H=(i,j) Jij Si.Sj S=1/2,1,

  • Defining frustrationFrustration = infinite degeneracy of classical ground stateShastry-Sutherland ModelEffect of quantum fluctuations?J1J2J22J1

  • Quantum approach1) Quantum treatment of local bricks2) Pertubative treatment of inter-brick couplingCoupled dimersCoupled trianglesFrustrated motion of tripletsMagnetization plateauxSrCu2(BO3)22 degrees of freedomLow-lying singletsSpin kagome

  • Dimers in a magnetic fieldIsolated dimersCoupled dimers

  • Magnetization of spin laddersCuHpClChaboussant et al, EPJB 98NB: CuHpCl might not be a simple ladder (Stone et al, cond-mat/0103023)

  • Frustrated laddersMetal-insulator transition for V=2t (J=J/3)

  • Magnetization PlateauD. Cabra et al, PRL 97K. Totsuka, PRB 98T. Tonegawa et al, PRB 99F. Mila, EPJB 98FrustrationKinetic energyRepulsionMetal-insulator transitionMagnetization plateau

  • Frustrated Coupled DimersTriplet HoppingTriplet Repulsion

  • Magnetization of SrCu2(BO3)2Kageyama et al, PRL 99

  • Shastry-Sutherland modelGround-state Product of singlets on J-bonds (Shastry, Sutherland, 81)Triplets Almost immobile and repulsive (Miyahara et al, 99)(Miyahara et al, 00)PlateauxJ/J ' .63

  • Symmetry breaking inside plateauxMiyahara et al, 00Hard-core bosonswith repulsion

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

  • Magnetization profile at 1/8Symmetry breaking16 sites/unit cell8-fold degenerate GSLattice distortionSelection of one GSFriedel-likeoscillationsNMR pattern

  • Further anomalies IThe magnetization raises too earlyThe gap does not close (see also ESR, Nojiri et al, 1999)3) The magnetization jumps before plateauKodama et al, Science 02Kodama et al, unpublishedgB

  • Further anomalies IITsujii et al,034) No Bose condensation below plateau

  • Possible sources of deviationCorrelated hopping of triplets Bound statesSpin-lattice coupling Dzyaloshinskii-Moriya interactions D.(SixSj) Inter-dimer (D) Intra-dimer (D)

  • Evidence of intra-dimer DMHext=6.9 TKodama et al, unpublishedHs=H1-H20Staggeredmagnetization

  • Dzyaloshinskii-Moriya interactionsHD: intra-dimer DM

  • High-field effects of intra-dimer DMKodama, Miyahara, et al, unpublishedD=0.034 D=-0.02 gs=0.023 (ED, 24 sites)

  • Properties around 1/8 plateauExact diagonalizations?Not appropriate!Huge finite-size effects at the plateaux! Effective hard-core boson model

  • Pertubative derivationMomoi and Totsuka, PRB013rd order in J/J

  • Mean-field phase diagramMomoi-Totsuka, 01Plateaux onlyat 1/3 and 1/2

  • Semi-phenomenological approachB. Kumar, F. Mila, unpublishedtit

  • Mean-field (, ,)Next step: include and

  • Conclusions/PerspectivesTriplet reduced mobility and repulsion Magnetization plateausIntra-dimer DM interaction Staggered magnetization Early raise of uniform magnetization Persistence of gap Magnetization of SrCu2(BO3)2:Remarkably rich and complex behaviour

  • 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?Open issues