1. 10/24/01PPHMF-IV1 Spinons, Solitons, and Breathers in Quasi-one-dimensional Magnets Frustrated Magnetism & Heavy Fermions Collin Broholm Johns Hopkins University & NIST Center for Neutron Research SCES 2004 Karlsruhe, Germany 7/29/2004

2. SCES04 7/29/04 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. SCES04 7/29/04 Ni 3 V 2 O 8 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 ZnCr 2 O 4 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 Pr x Bi 2-x Ru 2 O 7 J. van Duijn, K.H. Kim, N. Hur, D. T. Adroja, M. Adams, Q. Z. Huang, S.-W. Cheong, and T.G. Perring V 2 O 3 Wei Bao, G. Aeppli, C.D. Frost, T. G. Pering, P. Metcalf, J. M. Honig Acknowledgements

4. SCES04 7/29/04 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. SCES04 7/29/04 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 Effective low dimensionality from frustration Frustration + weak connectivity can produce local soft modes that destabilize Neel order Frustration + weak connectivity can produce local soft modes that destabilize Neel order

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

7. SCES04 7/29/04 Magnetism on a kagome’ Staircase c a b — S=½ spinons above small gap — S=∞ No order or spin glass — Ising no phase transition — XY Critical at T=0 Ni 3 V 2 O 8

8. SCES04 7/29/04 Order from kagome’ critical state

9. SCES04 7/29/04 Non-collinear order from competition T<9 K T<6.5K T<2.1 K Spine ANNNI model Spiral reduces Amplitude modulation Anisotropy overpowers NNN interaction Kenzelmann et al. (2004)

10. SCES04 7/29/04 From quasi-elastic to local resonance T=30 K T=1.5 K

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

12. Frustration and short range correlations

13. SCES04 7/29/04 T N <T<|  CW | : Short range correlations

14. SCES04 7/29/04 T N <T<|  CW | : Dynamic Short Range Order S.-H. Lee et al. PRL (2000) Points of interest: 2  /Qr 0 =1.4 ⇒ nn. AFM correlations No scattering at low Q ⇒ satisfied tetrahedra

15. SCES04 7/29/04 T<T N : Resonant mode and spin waves S.-H. Lee et al. PRL (2000) Points of interest: 2  /Qr 0 =1.4 ⇒ nn. AFM correlations No scattering at low Q ⇒ satisfied tetrahedra Resonance for ħ  ≈ J Low energy spin waves

16. SCES04 7/29/04 Average form factor for AFM hexagons S.-H. Lee et al. Nature (2002) Tchernyshyov et al. PRL (2001) + + + + + + ▬ ▬ ▬ ▬ ▬ ▬

17. SCES04 7/29/04 Sensitivity to impurities near quantum criticality Ratcliff et al. PRB (2002) TNTN TfTf

18. SCES04 7/29/04 Low T spectrum sensitive to bond disorder Q (Å -1 ) 0 0.5 1.0 1.5 2.0 2.5 5% Cd

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

20. SCES04 7/29/04 Singlet Ground state in PHCC Daoud et al., PRB (1986). J 1 =12.5 K  =0.6 J 1 =12.5 K  =0.6  /  max

21. SCES04 7/29/04 2D dispersion relation   (meV) 0 1 0 1 h

22. SCES04 7/29/04 Neutrons can reveal frustration The first  -moment of scattering cross section equals “Fourier transform of bond energies”  bond energies are small if small  Positive terms correspond to “frustrated bonds”   drrd SSand/or J

23. SCES04 7/29/04 Frustrated bonds in PHCC Green colored bonds increase ground state energy The corresponding interactions are frustrated Green colored bonds increase ground state energy The corresponding interactions are frustrated

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

25. SCES04 7/29/04 Colossal T-linear C(T) in Pr x Bi 2-x Ru 2 O 7 K. H. Kim et al.

26. SCES04 7/29/04 “Resilient” non-dispersive spectrum T=1.5 K T=30 K T=90 K J. Van Duijn et al. (2004) ħ  meV  Q (Å -1 )

27. SCES04 7/29/04 Properties of disordered two-level system Generalized susceptibility for two level system,  : Generalized susceptibility with distributed splitting, : How to derive the distribution function from “scattering law” How to derive specific heat from distribution function:

28. SCES04 7/29/04 Identify Scaling form for S(  )

29. SCES04 7/29/04 Colossal “  ” 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 V 2 O 3 Hole doping Increase U/W Mott

31. SCES04 7/29/04 Short Range order in Paramagnetic Insulator B.Z.

32. SCES04 7/29/04 Spin wave dispersion Exchange constants 0.6 meV -22 meV Bao et al. Unpublished

33. Orbital occupancy order Magnetic order T<T C Orbital fluctuations Magnetic SRO T>T C

34. SCES04 7/29/04 Orbital frustration in V 2 O 3 ? An interesting possibility: Bonds occupy kagome’ lattice Ising model on kagome’ lattice has no phase transition whence the low T C Orbital occupational order eventually occurs because it enables lower energy spin state

35. SCES04 7/29/04 Competing Interactions in URu 2 Si 2 ? T=22 K Broholm et al. (1991) Wiebe et al. (2004)

36. SCES04 7/29/04 Effective low dimensionality of CeCu 6 H.v. Lohneysen et al. (2000)

37. SCES04 7/29/04 Conclusions  Frustration is a central aspect of SCES  Frustrated insulators display – Reduced T N 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 “  ” from quenched disorder in frustrated non-kramers doublet systems – Orbital frustration may help to expose MIT in V 2 O 3 – A possible role of frustration in U and Ce based HF systems