Spinons, Solitons, and Breathers in Quasi-one-dimensional Magnets

1. Frustrated Magnetism & Heavy Fermions Spinons, Solitons, and Breathers in Quasi-one-dimensional Magnets Collin Broholm Johns Hopkins University & NIST Center for Neutron Research SCES 2004 Karlsruhe, Germany 7/29/2004 PPHMF-IV

2. Overview • Introduction • Frustrated magnetism in insulators • Order from competing interactions • Near critical systems • Quantum liquids • Metals with frustrated magnetism • Spinel vanadates • Spinels with rare earth ions • Frustration in heavy fermions? • Conclusions

3. Acknowledgements Ni3V2O8 G. Lawes, M. Kenzelmann, N. Rogado, K. H. Kim, G. A. Jorge, R. J. Cava, A. Aharony, O. Entin-Wohlman, A. B. Harris, T. Yildirim, Q. Z. Huang, S. Park, and A. P. Ramirez, and Yiming Qiu ZnCr2O4 S.-H. Lee, W. Ratcliff II, S.-W. Cheong, T. H. Kim, Q. Huang, and G. Gasparovic PHCC M. B. Stone, I. A. Zaliznyak, Daniel H. Reich PrxBi2-xRu2O7 J. van Duijn, K.H. Kim, N. Hur, D. T. Adroja, M. Adams, Q. Z. Huang, S.-W. Cheong, and T.G. Perring V2O3 Wei Bao, G. Aeppli, C.D. Frost, T. G. Pering, P. Metcalf, J. M. Honig

4. Destabilizing Static LRO Frustration: All spin pairs cannot simultaneously be in their lowest energy configuration Frustrated Weak connectivity: Order in one part of lattice does not constrain surroundings

5. Effective low dimensionality from frustration 1. Assume Neel order, derive spin wave dispersion relation 2. Calculate the reduction in staggered magnetization due to quantum fluctuations 3. If then Neel order is an inconsistent assumption diverges if on planes in Q-space Frustration + weak connectivity can produce local soft modes that destabilize Neel order

6. Renormalized Classical T/J H, P, x, 1/S…

7. Magnetism on a kagome’ Staircase c a b Ni3V2O8 • S=½ spinons above small gap • S=∞ No order or spin glass • Ising no phase transition • 3-state Potts model is critical at T=0 Coleman, Huse, Chandra, Sachdev…

8. Order from kagome’ critical state 8 (a) H║a 6 4 C’ LTI HTI P 2 C 0 8 (b) H║b 6 H(T) 4 C LTI HTI P 2 C’ 0 8 (c) H║c 6 4 C HTI P 2 C’ LTI 0 TCC’ TLC THL TPH 0 6 12 Temperature (K)

9. Non-collinear order from competition Anisotropy overpowers NNN interaction Spiral reduces Amplitude modulation Spine ANNNI model T<9 K T<6.5K T<2.1 K Kenzelmann et al. (2004)

10. From quasi-elastic to local resonance T=30 K T=1.5 K

11. Near Quantum Critical Renormalized Classical T/J ? H, P, x, 1/S…

12. Frustration and short range correlations

13. TN<T<|QCW| : Short range correlations

14. TN<T<|QCW| : Dynamic Short Range Order • Points of interest: • 2p/Qr0=1.4 • ⇒ nn. AFM correlations • No scattering at low Q • ⇒ satisfied tetrahedra S.-H. Lee et al. PRL (2000)

15. T<TN : Resonant mode and spin waves • Points of interest: • 2p/Qr0=1.4 • ⇒ nn. AFM correlations • No scattering at low Q • ⇒ satisfied tetrahedra • Resonance for ħw ≈ J • Low energy spin waves S.-H. Lee et al. PRL (2000)

16. Average form factor for AFM hexagons + ▬ + ▬ ▬ + Tchernyshyov et al. PRL (2001) S.-H. Lee et al. Nature (2002)

17. Sensitivity to impurities near quantum criticality TN Tf Ratcliff et al. PRB (2002)

18. Low T spectrum sensitive to bond disorder 5% Cd 0 0.5 1.0 1.5 2.0 2.5 Q (Å-1)

19. Near Quantum Critical Quantum Paramagnet ? T/J H, P, x, 1/S…

20. Singlet Ground state in PHCC J1=12.5 K a=0.6 c/cmax Daoud et al., PRB (1986).

21. 2D dispersion relation hw(meV) 1 0 l h 0 1

22. Neutrons can reveal frustration The first w -moment of scattering cross section equals “Fourier transform of bond energies” • bond energies are small if small • Positive terms correspond to “frustrated bonds” < × > J and/or S S + d r r d

23. Frustrated bonds in PHCC Green colored bonds increase ground state energy The corresponding interactions are frustrated

24. Near Quantum Critical T/J ? H, P, x, 1/S…

25. Colossal T-linear C(T) in PrxBi2-xRu2O7 K. H. Kim et al.

26. “Resilient” non-dispersive spectrum T=90 K J. Van Duijn et al. (2004) T=30 K ħw (meV) T=1.5 K Q (Å-1)

27. Properties of disordered two-level system Generalized susceptibility for two level system, D: Generalized susceptibility with distributed splitting, : How to derive the distribution function from “scattering law” How to derive specific heat from distribution function:

28. Identify Scaling form for S(w)

29. Colossal “g” from inhomogeneously split doublet • What is the role of frustration? • It allows high DOS without order far above percolation What do we learn from this? • Be aware of non-kramers doublets in alloys • There may be interesting magneto-elastic effects associated with frustrated non-kramers systems

30. Metal Insulator transition in V2O3 Hole doping Increase U/W Mott

31. Short Range order in Paramagnetic Insulator B.Z.

32. Spin wave dispersion Exchange constants 0.6 meV -22 meV -22 meV Bao et al. Unpublished

33. Orbital fluctuationsMagnetic SRO Orbital occupancy orderMagnetic order T>TC T<TC

34. Orbital frustration in V2O3? • An interesting possibility: • Bonds occupy kagome’ lattice • Ising model on kagome’ lattice • has no phase transition whence • the low TC • Orbital occupational order • eventually occurs because it • enables lower energy spin state

35. T=22 K Competing Interactions in URu2Si2? Wiebe et al. (2004) Broholm et al. (1991)

36. Effective low dimensionality of CeCu6 H.v. Lohneysen et al. (2000)

37. Conclusions • Frustration is a central aspect of SCES • Frustrated insulators display • Reduced TN with complex phase diagrams • Composite spin degrees of freedom • Magneto-elastic effects close to criticality • Hypersensitivity to quenched disorder • Singlet ground state phases are common when symmetry low • Metals with Frustrated magnetism • Large “g” from quenched disorder in frustrated non-kramers doublet systems • Orbital frustration may help to expose MIT in V2O3 • A possible role of frustration in U and Ce based HF systems