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Quantum phase transitions in anisotropic dipolar magnets

Quantum phase transitions in anisotropic dipolar magnets. Moshe Schechter. University of British Columbia. In collaboration with: Philip Stamp, Nicolas laflorencie. LiHoY F. x. 1-x. 4. 1. Transverse field Ising model:. LiHoY F. x. 1-x. 4. 1. Transverse field Ising model:.

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Quantum phase transitions in anisotropic dipolar magnets

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  1. Quantum phase transitions in anisotropic dipolar magnets Moshe Schechter University of British Columbia In collaboration with: Philip Stamp, Nicolas laflorencie

  2. LiHoY F x 1-x 4 1. Transverse field Ising model:

  3. LiHoY F x 1-x 4 1. Transverse field Ising model: 2. Dilution! Reich et al, PRB 42, 4631 (1990)

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

  5. Various dilutions Ghosh, Parthasarathy, Rosenbaum, Aeppli Science 296, 2195 (2002) Brooke, Bitko, Rosenbaum, Aeppli Science 284, 779 (1999) Ronnow et. Al. Science 308, 389 (2005) Giraud et. Al. PRL 87, 057203 (2001)

  6. LiHoF - a model quantum magnet 4 S. Sachdev, Physics World 12, 33 (1999)

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

  8. Fall and rise of QPT in dilute dipolar magnets • Hyperfine interactions and off-diagonal dipolar terms • No QPT in spin-glass regime • In FM regime can study classical and quantum phase transitions with controlled disorder and with coupling to spin bath

  9. S -S Anisotropic dipolar magnets Large spin, strong lattice anisotropy

  10. S -S Anisotropic dipolar magnets Large spin, strong lattice anisotropy Single molecular magnets Magnetic insulators

  11. S -S Anisotropic dipolar magnets - TFIM Large spin, strong lattice anisotropy

  12. Hyperfine interaction: electro-nuclear Ising states

  13. Hyperfine interaction: electro-nuclear Ising states Hyperfine spacing: 200 mK - M.S. and P. Stamp, PRL 95, 267208 (2005)

  14. Phase diagram – transverse hyperfine and dipolar interactions Splitting PM SG Experiment No off. dip. With off. dip. - M.S. and P. Stamp, PRL 95, 267208 (2005)

  15. S -S Anisotropic dipolar systems – offdiagonal terms symmetry symmetry

  16. S -S Anisotropic dipolar systems – offdiagonal terms symmetry symmetry M. S. and N. Laflorencie, PRL 97, 137204 (2006)

  17. Imry-Ma argument Ground state: (all spins up) Domain: (spins down) Energy cost Energy gain Spontaneous formation of domains Critical dimension: 2 (for Heisenberg interaction: 4) Y. Imry and S. K. Ma, PRL 35, 1399 (1975)

  18. Spin glass – correlation length Energy gain: Y. Imry and S. K. Ma, PRL 35, 1399 (1975) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  19. Spin glass – correlation length Energy gain: Energy cost: Y. Imry and S. K. Ma, PRL 35, 1399 (1975) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  20. Spin glass – correlation length Energy gain: Energy cost: Only extra sqrt of surface bonds are satisfied, can optimize boundary. Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  21. Spin glass – correlation length Energy gain: Energy cost: Only extra sqrt of surface bonds are satisfied, can optimize boundary. Flip a droplet – gain vs. cost: Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  22. Spin glass – correlation length Energy gain: Energy cost: Only extra sqrt of surface bonds are satisfied, can optimize boundary. Flip a droplet – gain vs. cost: Droplet size – Correlation length Fisher, Huse PRL 56, 1601 (86); PRB 38, 386 (88) M.S. and N. Laflorencie, PRL 97, 137204 (2006)

  23. quasi SG SG unstable to transverse field! Finite, transverse field dependent correlation length M. S. and N. Laflorencie, PRL 97, 137204 (2006)

  24. 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)

  25. Random fields not particular to SG! Reich et al, PRB 42, 4631 (1990)

  26. Interest in FM RFIM Diluted anti-ferromagnets: - Equivalence only near transition - No constant field in the staggered magnetization - Not FM - applications

  27. Interest in FM RFIM • Verifying interesting results on DAFM • Experimental techniques • Novel fundamental research (away from transition, conjugate field, quantum term) • Applications in ferromagnets, e.g. domain wall dynamics in random fields

  28. Are the fields random? Square of energy gain vs. N, different dilutions Inset: Slope as Function of dilution M. S., cond-mat/0611063

  29. S -S Random field and quantum term are independently tunable! M. S., cond-mat/0611063 M. S. and P. Stamp, PRL 95, 267208 (2005)

  30. S -S Ferromagnetic RFIM M. S., cond-mat/0611063 M. S. and P. Stamp, PRL 95, 267208 (2005)

  31. S -S Ferromagnetic RFIM - Independently tunable random and transverse fields! M. S., cond-mat/0611063 - Classical RFIM despite applied transverse field M. S. and P. Stamp, PRL 95, 267208 (2005)

  32. Realization of FM RFIM Sharp transition at high T, Rounding at low T (high transverse fields) Silevitch et al., Nature 448, 567 (2007)

  33. Conclusions • Strong hyperfine interactions in LiHo result in electro-nuclear Ising states. Dictates quantum dynamics and phase diagram in various dilutions • Ising model with tunable quantum and random effective fields can be realized in anisotropic dipolar systems • SG unstable to transverse field, no SG-PM QPT • First FM RFIM – implications to fundamental research and applications

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