Frustrated Antiferromagnets at High Fields:

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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
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Outline
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Heisenberg AFM near saturation field Bose gas
analogy
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The case of frustration how to lift the
degeneracy
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Frustrated Models with lines of minima
I. J1-J2 AFM at its critical point II. AFM
on FCC lattice
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AFM near the Saturation Field
HgtHc
HltHc
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The Dilute Bose Gas
Effective interaction
Expansion in gas parameter
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Examples of Frustrated Magnets
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
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The Case of Frustration
Where do magnons condense?
Possible way out Lift the degeneracy dynamically
Locate the minimum of Interaction
Magnons condense at wv Q at which they less
interact
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The Models with Lines of Minima I. J1-J2
AFM at its critical point
J1gt2J2 Q(p,p)
J1lt2J2 Q(p,0)/(0,p)
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II. AFM on FCC Lattice
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GS Energy functional
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Temperature vs Field Phase Diagram
Magnetic analog of Weak Crystallization
Thermal Fluctuations Induce 1st Order
Transition
Hartree term from Therm. Fluc.
Self-consistent gap equation.
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Conclusions
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The spectrum has unique Goldstone mode at
ordering wv away from it the gap is
generated