1. Institute for Theoretical Physics,
Frustrated Antiferromagnets at High Fields:
BEC in Degenerate Spectra
George Jackeli
Institute for Theoretical Physics,
EPFL, Lausanne
In collaboration with:
Mike Zhitomirsky
PRL 93, (2004)
Les Houches, June 2006

2. √ √ √ √ 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
Summary √

3. AFM near the Saturation Field
H>Hc
H<Hc
Mapping to a Bose gas

4. The Dilute Bose Gas Effective interaction: Expansion in gas parameter
Results:

5. Examples of Frustrated Magnets
Geometrical frustration
Competing interactions
Impossible to satisfy simultaneously
every pairwise 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

6. √ The Case of Frustration Macroscopic degeneracy below Hc
Anomalous spectra above Hc:
Continuous set of minima
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

7. The Models with Lines of Minima:
I. J1-J2 AFM at its critical point
J1>2J2 : Q=(p,p)
J1<2J2 Q=(p,0)/(0,p)

8. J1=2J2
Magnon spectrum for
Interaction vertex
GS Energy: Nonanalytic
Magnetization Curve: Singular
Single gapless mode

9. II. AFM on FCC Lattice Magnon spectrum at saturation field
Lines of minima at
Interaction vertex

10. GS Energy functional
Single-Q state
3-Q state
Magnetization Curve
GS Energy

11. 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.

12. √ √ √ √ Conclusions The degeneracy can be lifted dynamically
by dressed magnon interaction √
The spectrum has unique Goldstone mode at ordering wv
away from it the gap is generated √
Singularity in magnetization curve √
Rich H-T phase diagram