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Frustrated Antiferromagnets at High Fields: BEC in Degenerate Spectra

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. √.

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Frustrated Antiferromagnets at High Fields: BEC in Degenerate Spectra

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  1. 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

  2. √ Summary 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

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

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

  5. Geometrical frustration Impossible to satisfy simultaneously every pairwise interactions 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

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

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

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

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

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

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