Frustrated Quantum Magnets in Strong Magnetic Fields
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Transcript of Frustrated Quantum Magnets in Strong Magnetic Fields
Frustrated Quantum Frustrated Quantum Magnets in StrongMagnets in Strong
Magnetic FieldsMagnetic Fields
F. MilaF. MilaInstitute of Theoretical PhysicsInstitute of Theoretical Physics
Ecole Polytechnique FEcole Polytechnique Fédérale de édérale de LausanneLausanne
SwitzerlandSwitzerland
CollaboratorsCollaboratorsTheorists
S. Miyahara (Lausanne Tokyo)F. Becca (Lausanne Trieste)B. Kumar (Lausanne)
ExperimentalistsM. Takigawa, K. Kodama (ISSP, Tokyo)C. Berthier, M. Horvatic (Grenoble)Chemists
H. Kageyama, Y. Ueda (ISSP, Tokyo)
ScopeScope• Introduction to Frustrated Quantum MagnetsIntroduction to Frustrated Quantum Magnets
• Dimers + Frustration Dimers + Frustration Magnetization plateaux Magnetization plateaux
• Other anomalies in SrCuOther anomalies in SrCu22(BO(BO33))22
Dzyaloshinskii-Moriya interactions Correlated hopping
• Conclusions/PerspectivesConclusions/Perspectives
Quantum magnets: 2 Quantum magnets: 2 paradigmsparadigms
Long-range order Spin gap
Goldstone modes: Spin waves
Singlet-triplet gap
J’J
Δ=J’+O(J) (J«J’)
H=∑(i,j) Jij Si.Sj S=1/2,1,…
Defining frustrationDefining frustrationFrustration = infinite degeneracy of classical ground state
Shastry-Sutherland ModelShastry-Sutherland Model
Effect of quantum fluctuations?
J1J2
J2<2J1 J2>2J1
Quantum approachQuantum approach1) Quantum treatment of local bricks
2) Pertubative treatment of inter-brick coupling
Coupled dimers Coupled triangles
Frustrated motion of triplets
Magnetization plateaux
SrCuSrCu2(BO(BO3))2
2 degrees of freedom
Low-lying singlets
Spin ½ kagomeSpin ½ kagome
Dimers in a magnetic Dimers in a magnetic fieldfield
Isolated dimersCoupled dimers
Magnetization of spin Magnetization of spin laddersladders
CuHpCl Chaboussant et al, EPJB ‘98
NB: CuHpCl might not be a simple ladder (Stone et al, cond-mat/0103023)
Frustrated laddersFrustrated ladders
Metal-insulator transition for V=2t (J’=J/3)
Magnetization PlateauMagnetization Plateau
D. Cabra et al, PRL ‘97K. Totsuka, PRB ‘98
T. Tonegawa et al, PRB ‘99F. Mila, EPJB ‘98
Frustration
Kinetic energy
Repulsion
Metal-insulator transition
Magnetization plateau
Frustrated Coupled Frustrated Coupled DimersDimers
Triplet Hopping Triplet Repulsion
Magnetization of Magnetization of SrCuSrCu2(BO(BO3))2
Kageyama et al, PRL ‘99
Shastry-Sutherland Shastry-Sutherland modelmodel
Ground-state Product of singlets on J-bonds (Shastry, Sutherland, ’81)
Triplets Almost immobile and repulsive (Miyahara et al, ’99)(Miyahara et al, ’00)Plateaux
J’/J ' .63
Symmetry breaking inside Symmetry breaking inside plateauxplateaux
Miyahara et al, ’00
Hard-core bosonswith repulsion
NMR at 1/8-plateauNMR 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
Magnetization profile at 1/8Magnetization profile at 1/8Symmetry breaking
16 sites/unit cell8-fold degenerate GS
Lattice distortionSelection of one GS
Magnetization in field direction
Magnetization opposite to field
Friedel-likeoscillationsNMR pattern
Further anomalies IFurther anomalies I
1)The magnetization raises too early2)The gap does not close (see also ESR, Nojiri et al,
1999)3) The magnetization jumps before plateau
Kodama et al, Science ‘02 Kodama et al, unpublished
Δ∕gμB
Further anomalies IIFurther anomalies II
Tsujii et al,’03
4) No Bose condensation below plateau
Possible sources of Possible sources of deviationdeviation
• Correlated hopping of triplets Correlated hopping of triplets Bound statesBound states• Spin-lattice coupling Spin-lattice coupling • Dzyaloshinskii-Moriya interactions D.Dzyaloshinskii-Moriya interactions D.
(S(SixSxSj)) Inter-dimer (D’)Inter-dimer (D’) Intra-dimerIntra-dimer (D)(D)
Evidence of intra-dimer DMEvidence of intra-dimer DM
Hext=6.9 T
Kodama et al, unpublished
Hs=H1-H2≠0
Staggeredmagnetization
Dzyaloshinskii-Moriya Dzyaloshinskii-Moriya interactionsinteractions
H
D1 2
D: intra-dimer DM
High-field effects of intra-dimer High-field effects of intra-dimer DMDM
Kodama, Miyahara, et al, unpublishedD=0.034 D’=-0.02 gs=0.023 (ED, 24 sites)
Properties around 1/8 Properties around 1/8 plateauplateau
Exact diagonalizations?
Not appropriate!
Huge finite-size effects at the plateaux!
Effective hard-core boson model
Pertubative Pertubative derivationderivation
Momoi and Totsuka, PRB’01
3rd order in J’/J
Mean-field phase diagramMean-field phase diagram
Momoi-Totsuka, ‘01
Plateaux onlyat 1/3 and 1/2
B. Kumar, F. Mila, unpublished
t’
it
Semi-phenomenological Semi-phenomenological approachapproach
Mean-field (<b>, <bMean-field (<b>, <b++>,<b>,<b++b>)b>)
Next step: include <bb> and <b+b+>
Conclusions/Conclusions/PerspectivesPerspectives
Magnetization of SrCu2(BO3)2:Remarkably rich and complex behaviour
• Triplet reduced mobility and repulsion Triplet reduced mobility and repulsion Magnetization plateausMagnetization plateaus
• Intra-dimer DM interaction Intra-dimer DM interaction Staggered magnetization Staggered magnetization Early raise of uniform magnetization Early raise of uniform magnetization Persistence of gap Persistence of gap
OpenOpen issuesissues
• Magnetization jump before 1/8 plateau?Magnetization jump before 1/8 plateau?• Difference of behaviour below and Difference of behaviour below and
above 1/8 plateau?above 1/8 plateau?• Consequences of correlated hopping?Consequences of correlated hopping? Pairing?Pairing?• Dip of the gap just before plateau?Dip of the gap just before plateau?