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, 017201 (2004) 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 Summary √

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 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

√ 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

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)

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

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

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

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.

√ √ √ √ 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