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