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Dilute anisotropic dipolar systems as random field Ising ferromagnets

Dilute anisotropic dipolar systems as random field Ising ferromagnets. Moshe Schechter. University of British Columbia. In collaboration with: Philip Stamp Nicolas Laflorencie. Discussions: Gabriel Aeppli. Transverse field Ising model. Interaction depends on dilution, FM or random.

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Dilute anisotropic dipolar systems as random field Ising ferromagnets

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  1. Dilute anisotropic dipolar systems as random field Ising ferromagnets Moshe Schechter University of British Columbia In collaboration with: Philip Stamp Nicolas Laflorencie Discussions: Gabriel Aeppli

  2. Transverse field Ising model Interaction depends on dilution, FM or random Quantum phase transitions Quantum annealing Quantum dynamics

  3. LiHoF - a model quantum magnet 4 Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996) S. Sachdev, Physics World 12, 33 (1999)

  4. Random field Ising model No FM realization DAFM - Constant field is random in staggered magnetization “trompe l’oeil critical behavior” - Field conjugate to order parameter Experiments, crackling noise - FM Away from criticality, applications - Quantum fluctuations Quantum dynamics, QPT - Verification of results near transition S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979)

  5. Outline • RF in anisotropic dipolar magnets • Consequences in FM and SG regimes • LiHo system – hyperfine interactions – transverse dipolar int.

  6. S -S Anisotropic dipolar systems Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction Single molecular magnets Rare-earth magnetic insulators

  7. S -S Anisotropic dipolar systems - TFIM Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction Single molecular magnets Rare-earth magnetic insulators

  8. QPT in dipolar magnets Thermal and quantum transitions MF of TFIM MF with hyperfine Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)

  9. LiHoY F x 1-x 4 Reich et al, PRB 42, 4631 (1990)

  10. S -S Dilution, transverse field – effective random longitudinal field M. S. and N. Laflorencie, PRL 97, 137204 (2006) M. S., PRB 77, 020401(R) (2008)

  11. S -S Offdiagonal dipolar terms M. S. and N. Laflorencie, PRL 97, 137204 (2006) M. S., PRB 77, 020401(R) (2008)

  12. S -S Offdiagonal dipolar terms symmetry symmetry M. S. and N. Laflorencie, PRL 97, 137204 (2006) M. S., PRB 77, 020401(R) (2008)

  13. S -S Offdiagonal dipolar terms symmetry symmetry M. S. and N. Laflorencie, PRL 97, 137204 (2006) M. S., PRB 77, 020401(R) (2008)

  14. Are the fields random? Square of energy gain vs. N, different dilutions Inset: Slope as Function of dilution M. S., PRB 77, 020401(R), (2008)

  15. S -S Ferromagnetic RFIM M. S., PRB 77, 020401(R) (2008)

  16. S -S Ferromagnetic RFIM M. S., PRB 77, 020401(R) (2008)

  17. S -S Ferromagnetic RFIM - Independently tunable random and transverse fields! M. S., PRB 77, 020401(R) (2008) - Classical RFIM despite applied transverse field M. S. and P. Stamp, PRL 95, 267208 (2005)

  18. RF in disordered systems • Transverse field, still , but no T. • Disordered systems: no pure Ising without T symmetry. No pure TFIM in field. • Anisotropic dipolar magnets: M. S. and P. Stamp, in preparation

  19. Experimental realization Sharp transition at high T, Rounding at low T (high transverse fields) Silevitch et al., Nature 448, 567 (2007)

  20. Random fields not specific to FM! Reich et al, PRB 42, 4631 (1990)

  21. Dilution: quantum spin-glass -Thermal vs. Quantum disorder -Cusp diminishes as T lowered Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)

  22. Spin glass – correlation length Flip a droplet – gain vs. cost: Lower critical dimension – infinity! Droplet size – Correlation length Imry and Ma, PRL 35, 1399 (1975) Fisher and Huse PRL 56, 1601 (1986); PRB 38, 386 (1988) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  23. quasi SG SG unstable to transverse field! Finite, transverse field dependent correlation length No SG-PM QPT in transversefield! M. S. and N. Laflorencie, PRL 97, 137204 (2006)

  24. Correlation length - experiment Domains of >10^3 spins Jonsson, Mathieu, Wernsdorfer, Tkachuk, Barbara, PRL 98, 256403 (2007)

  25. Remarks • Validity of droplet picture • Reduction of susceptibility in mean field - Jonnson, Takayama, Katori, Ito, PRB 71, 180412(R) (2005) - Young, Katzgraber, PRL 93, 207203 (2004) - Pirc, Tadic, Blinc, PRB 36, 8607 (1987) - Tabei, Gingras, Kao, Stasiak, Fortin, PRL 97, 237203 (2006)

  26. Hyperfine interaction: electro-nuclear Ising states Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)

  27. Hyperfine interaction: electro-nuclear Ising states Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, 267208 (2005) - N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)

  28. Hyperfine interaction: electro-nuclear Ising states Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, 267208 (2005) - N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)

  29. PM SG Experiment No off. dip. With off. dip. Enhanced transverse field – phase diagram Quantum disordering harder than thermal disordering Main reason – hyperfine interactions Off-diagonal dipolar terms in transverse field – also enhanced effective transverse field M.S. and P. Stamp, PRL 95, 267208 (2005)

  30. Re-entrance of crossover field Larger x – stronger reduction of c-o field by offdiagonal dipolar terms! PM X=0.167 X=0.045 SG Experiment No off. dip. With off. dip. • Ancona-Torres, Silevitch, Aeppli, Rosenbaum, PRL 101, 057201 (2008) • M.S. and P. Stamp, • PRB 78, 054438 (2008)

  31. S -S Significance of the hf in the LiHo

  32. Electro-nuclear entanglement entropy At electron and nuclear spin disentangle! However … M.S. and P. Stamp, PRB 78, 054438 (2008)

  33. Electro-nuclear entanglement entropy Ronnow et. Al. Science 308, 389 (2005) M.S. and P. Stamp, PRB 78, 054438 (2008)

  34. LiHo at 4.5% - Ghosh et al., Science 296, 2195 (2002) - Quilliam et al., arXiv:0808.1370

  35. LiHo at 4.5% - Theoretically – expect SG at any x (Stephen Aharony) - Experiments are above expected glass temperature (35 mK) - Efffective transverse field too low to explain spin liquid state - Narrowing of absorption spectrum at hyperfine energy Stephen and Aharony, J. Phys. C 14, 1605 (1981) M.S. and P. Stamp, PRB 78, 054438 (2008)

  36. Future research • Experiment: • Quantum and classical PT in FM RFIM • Hysteresis in the FM RFIM • Materials with • With • Pressure induced SG-PM QPT • Theory • Spin bath and QPT • Dynamics

  37. Conclusions • Dilution and transverse field induce random longitudinal field in Ising dipolar systems. • FM RFIM, no SG-PM QPT. • Disordered systems: Ising model is only realizable with time-reversal symmetry • LiHo – hyperfine, offdiagonal dipolar interactions dictate low-T physics

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