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Frustrated Antiferromagnets at High Fields: BEC in Degenerate Spectra. George Jackeli. Institute for Theoretical Physics, EPFL, Lausanne. In collaboration with: Mike Zhitomirsky PRL 93, 017201 (2004). Les Houches, June 2006. √. Summary. Outline. √. - PowerPoint PPT Presentation
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Frustrated Antiferromagnets at High Fields:
BEC in Degenerate Spectra
George Jackeli
In collaboration with: Mike Zhitomirsky
PRL 93, 017201 (2004)
Institute for Theoretical Physics,EPFL, Lausanne
Les Houches, June 2006
Outline
Heisenberg AFM near saturation field: Bose gas analogy
The case of frustration: how to lift the degeneracy
Frustrated Models with lines of minima:
I. J1-J2 AFM at its critical point
II. AFM on FCC lattice
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√
Summary √
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AFM near the Saturation Field
H>Hc H<Hc
Mapping to a Bose gas
The Dilute Bose Gas
Effective interaction:
Expansion in gas parameter
Results:
Examples of Frustrated Magnets
Impossible to satisfy simultaneously every pairwise interactions
Geometrical frustration Competing interactions
Infinitely many classical ground states
Degeneracy is typically lifted by “order-out-of-disorder” mechanism: Ordering by fluctuations
By quantum fluctuations:Different zero point energy
By thermal fluctuations:Entropic lowering of free energy
The Case of Frustration
Macroscopic degeneracy below Hc√√ Anomalous spectra above Hc:
Continuous set of minima
Possible way out: Lift the degeneracy dynamically
Locate the minimum of Interaction:
Magnons condense at wv Q at which they less interact
Where do magnons condense?
The Models with Lines of Minima: I. J1-J2 AFM at its critical point
J1>2J2 : Q=(,) J1<2J2 Q=(,)/(,)
J1=2J2Magnon spectrum for
Interaction vertex GS Energy: Nonanalytic
Magnetization Curve: Singular
Single gapless mode
II. AFM on FCC Lattice
Lines of minima at
Magnon spectrum at saturation field
Interaction vertex
GS Energy Magnetization Curve
Single-Q state 3-Q state
GS Energy functional
Temperature vs Field Phase Diagram
Hartree term from Therm. Fluc. Self-consistent gap equation.
Magnetic analog ofWeak Crystallization
Thermal Fluctuations Induce 1st Order Transition
Conclusions
The spectrum has unique Goldstone mode at ordering wv away from it the gap is generated
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√ The degeneracy can be lifted dynamically by dressed magnon interaction
√ Singularity in magnetization curve
√ Rich H-T phase diagram
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