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LiHo x Y 1-x F 4 : The road between solid state ion trap and quantum critical ferromagnet Gabriel Aeppli London Centre f

LiHo x Y 1-x F 4 : The road between solid state ion trap and quantum critical ferromagnet Gabriel Aeppli London Centre for Nanotechnology & UCL . TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A. Collaborators.

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LiHo x Y 1-x F 4 : The road between solid state ion trap and quantum critical ferromagnet Gabriel Aeppli London Centre f

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  1. LiHoxY1-xF4: The road between solid state ion trap and quantum critical ferromagnetGabriel AeppliLondon Centre for Nanotechnology & UCL TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

  2. Collaborators Andrew Fisher, Ché Gannarelli, Stephen Lynch, Edward Gryspeerdt, Marc Warner, Des McMorrow UCL Physics & Astronomy and London Centre for Nanotechnology Tom Rosenbaum, Dan Silevitch James Franck Institute and Dept of Physics, University of Chicago Sai Ghosh University of California at Merced Jens Jensen University of Copenhagen Henrik Ronnow EPFL

  3. Outline • Context • Introducing LiHoF4: • Structure, magnetism and single-ion physics • The new experiment: • Low-frequency dynamics while rotating the Ising moment out of the plane to create superpositions • Test of the adequacy of ion-pair models to describe these properties • Outlook and conclusions

  4. A=0.039 K Sharp nuclear levels at microwave frequencies (~10GHz) Hyperfine interaction with nuclear spins (I=7/2) Can be made manifest by ramping longitudinal (Ising) field in a very dilute system, and watching frequency-dependent tunnelling of magnetization mediated by nuclear spins (and residual dipolar interactions) Nuclear couplings produce line of avoided crossings in combined level scheme Giraud et al PRL 87 057203 (2001) and PRL 91 257204 (2003); x=0.1%

  5. Coupling, disorder and transverse fields Exchange is negligible because of the extreme localization of the electrons Ions coupled instead by pure magnetic dipole interaction (weak but precisely known): Ion j Ion i Note anisotropy of interaction In low-energy, 2-state limit for ordered material this becomes Magnitude of interaction is 0.214 K for r=a In pure material (x=1) mean fields lie along z, material behaves as a classical Ising magnet: FM couplings along c-axis, AFM in ab plane But…we expect non-classical behaviour to be obtained by introduction of transverse fields or by disorder

  6. c Ho Li F b a A three-dimensional quantum magnet - with decoherence due to spectatorsRealizing the transverse field Ising model, where can vary G – LiHoF4 • g=14 doublet • 9K gap to next state • dipolar coupled Toronto 2008

  7. c Ho Li F b a Realizing the transverse field Ising model, where can vary G – LiHoF4 • g=14 doublet • 9K gap to next state • dipolar coupled Toronto 2008

  8. c vs T for Ht=0 • D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), pp. 940-943, (1996) Toronto 2008

  9. Now impose transverse field … Toronto 2008

  10. Toronto 2008

  11. Toronto 2008

  12. 165Ho3+ J=8 and I=7/2 A=3.36meV Toronto 2008

  13. W=A<J>I ~ 140meV Toronto 2008

  14. Diverging c Toronto 2008

  15. Dynamics = • The Ising term  energy gap 2J • The G term does not commute with Need traveling wave solution: • Total energy of flip a Toronto 2008

  16. = • The Ising term  energy gap 2J • The G term does not commute with Need traveling wave solution: • Total energy of flip a Toronto 2008

  17. = • The Ising term  energy gap 2J • The G term does not commute with Need traveling wave solution: • Total energy of flip a Toronto 2008

  18. = • The Ising term  energy gap 2J • The G term does not commute with Need traveling wave solution: • Total energy of flip a Toronto 2008

  19. = • The Ising term  energy gap 2J • The G term does not commute with Need traveling wave solution: • Total energy of flip a Toronto 2008

  20. Spin Wave excitations inthe FM LiHoF4 Energy Transfer (meV) 1 1.5 2 Toronto 2008

  21. Spin Wave excitations inthe FM LiHoF4 Energy Transfer (meV) 1 1.5 2 Toronto 2008

  22. What happens near QPT? Toronto 2008

  23. H. Ronnow et al. Science (2005) Toronto 2008

  24. W=A<J>I ~ 140meV Toronto 2008

  25. wider significance • Connection to ‘decoherence’ problem in mesoscopic systems ‘best’ Electronic- TFI Toronto 2008

  26. d2s/dWdw=Sf|<f|S(Q)+|0>|2d(w-E0+Ef) where S(Q)+ =SmSm+expiq.rm Toronto 2008

  27. Where does spectral weight go & diverging correlation length appear? Ronnow et al, unpub (2006) Toronto 2008

  28. Introducing complexity via randomness & dipolar interaction … dipolar interaction between randomly placed spins leads to frustrationE=S1S2g2MB2[1-3(rz/r)2]/r3ferro for (rz/r)2 >1/3antiferro for (rz/r)2 <1/3 Toronto 2008

  29. c Ho Li F b a Experimental realization of Ising model in transverse fieldLiHoF4 • g=14 doublet • 9K gap to next state • dipolar coupled Toronto 2008

  30. b a Experimental realization of Ising model in transverse fieldLiHoF4 c Y • g=14 doublet • 9K gap to next state • dipolar coupled Ho Li F Toronto 2008

  31. b a Experimental realization of Ising model in transverse fieldLiHoF4 c Y • g=14 doublet • 9K gap to next state • dipolar coupled Ho Li F Toronto 2008

  32. What happens first? x=0.67 still ferromagnetic Tc=xTc(x=1) Toronto 2008

  33. x=0.44 also still ferromagnetic Toronto 2008

  34. Two effects: quantum mechanics + classical random fields Toronto 2008

  35. Strong random field effects near Ht=0 and T=TCMF  Thermal T-TC Transverse field   Toronto 2008

  36. Griffiths singularities at T=0.673K>TC+4mK All data collapse assuming Toronto 2008

  37. Quantum dominated Random-field dominated Toronto 2008

  38. Domain wall state pinned by random configurations of Y not much different from that at 300K in PdCo- What about domain wall dynamics? Y-A. Soh and G.A.,unpublished Toronto 2008

  39. How to see? • Measure small signal response M(t)=c’(w)hcos(wt)+c(w)”hsin(wt) where • c=c’+ic” is complex susceptibility • hcos(wt) is excitation Toronto 2008

  40. Experimental Setup G ~ Ht2 Toronto 2008

  41. The Spectral Response J.Brooke, T.F.Rosenbaum & G.A, Nature 413,610(2001) • Four parameters: • c(f) • fo • log slope • frolloff Toronto 2008

  42. Toronto 2008

  43. Domain Wall Tunneling w D Toronto 2008

  44. Evolution of themost mobileDomain Walls quantum tunneling thermal hopping Toronto 2008

  45. Domain Wall Parameters N 10 Toronto 2008

  46. What happens next? ? Toronto 2008

  47. 0.2 0.4 0.6 T(K) x=0.167 Spin glass Toronto 2008

  48. Toronto 2008

  49. f Re  / Im  ~  "~f-Glass transition when =0 Toronto 2008

  50. Revisited more recently (2008) with x=0.198% Ho Toronto 2008

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