1. 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.: AAA A AA A A AA A

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 LiHoF 4 : –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. 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% Sharp nuclear levels at microwave frequencies (~10GHz) Hyperfine interaction with nuclear spins (I=7/2) A=0.039 K

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): In low-energy, 2-state limit for ordered material this becomes 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 Ion i Ion j Note anisotropy of interaction Magnitude of interaction is 0.214 K for r=a But…we expect non-classical behaviour to be obtained by introduction of transverse fields or by disorder

6. Toronto 2008 A three-dimensional quantum magnet - with decoherence due to spectators Realizing the transverse field Ising model, where can vary  – LiHoF 4 c a b Ho Li F g=14 doublet 9K gap to next state dipolar coupled

7. Toronto 2008 c a b Ho Li F Realizing the transverse field Ising model, where can vary  – LiHoF 4 g=14 doublet 9K gap to next state dipolar coupled

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

9. Toronto 2008 Now impose transverse field …

10. Toronto 2008

12. 165 Ho 3+ J=8 and I=7/2 A=3.36  eV

13. Toronto 2008 W=A I ~ 140  eV

14. Toronto 2008 Diverging 

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

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

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

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

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

20. Toronto 2008 11.52 Energy Transfer (meV) Spin Wave excitations in the FM LiHoF 4

21. Toronto 2008 11.52 Energy Transfer (meV) Spin Wave excitations in the FM LiHoF 4

22. Toronto 2008 What happens near QPT?

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

24. Toronto 2008 W=A I ~ 140  eV

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

26. Toronto 2008    =  f | | 2  -E 0 +E f ) where S(Q) + =  m S m + expiq.r m

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

28. Toronto 2008 dipolar interaction between randomly placed spins leads to frustration E=S 1 S 2 g 2 M B 2 [1-3(r z /r) 2 ]/r 3 ferro for (r z /r) 2 >1/3 antiferro for (r z /r) 2 <1/3 Introducing complexity via randomness & dipolar interaction …

29. Toronto 2008 c a b Ho Li F Experimental realization of Ising model in transverse field LiHoF 4 g=14 doublet 9K gap to next state dipolar coupled

30. Toronto 2008 c a b Ho Li F Experimental realization of Ising model in transverse field LiHoF 4 g=14 doublet 9K gap to next state dipolar coupled Y

31. Toronto 2008 c a b Ho Li F Experimental realization of Ising model in transverse field LiHoF 4 g=14 doublet 9K gap to next state dipolar coupled Y

32. Toronto 2008 What happens first? T c =xT c (x=1) x=0.67 still ferromagnetic

33. Toronto 2008 x=0.44 also still ferromagnetic

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

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

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

37. Toronto 2008 Random-field dominated Quantum dominated

38. Toronto 2008 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

39. Toronto 2008 How to see? Measure small signal response M(t)=  ’(  )hcos(  t)+  ”hsin(  t) where  =  ’+i  ” is complex susceptibility hcos(  t) is excitation

40. Toronto 2008 Experimental Setup  ~ H t 2

41. Toronto 2008 The Spectral Response Four parameters: 1.  (f  ) 2. f o 3. log slope 4. f rolloff J.Brooke, T.F.Rosenbaum & G.A, Nature 413,610(2001)

42. Toronto 2008

43. Domain Wall Tunneling w 

44. Toronto 2008 Evolution of the most mobile Domain Walls thermal hopping quantum tunneling

45. Toronto 2008 Domain Wall Parameters N  10

46. Toronto 2008 What happens next? ?

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

48. Toronto 2008

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

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

51. Toronto 2008 Consistent with non-linear susceptibility

52. Toronto 2008

54. ?

56. Dynamic properties (I): the anti-glass and its relaxation Contrast behaviour of conventional glasses, where longer and longer tail of slow reponse develops below glass transition X=4.5%; Reichl et al PRL 59 1969 (1987), Ghosh et al Nature 425 48 (2003) Dilute system shows loss of low-frequency tail in dissipative (imaginary) part of response. Inference: fewer slow relaxations as temperature is lowered

57. Dynamic properties (II): hole-burning and addressing of excitations Cannot address individual ions spatially, but can excite in very narrow low-frequency windows. Absorption spectrum after “hole burning” Decay of oscillation amplitude with time Suggests low-frequency continuum is of oscillators, not just relaxation Ghost et al Science 216 2195 (2002)

58. Antiglass An RVB-like state analagous to Si:P (Bhatt- Lee)

60. But experiment seems to favour in-plane (AFM) pairs

61. Conclusions LiHoF 4 is just about the best imaginable solid-state ion trap Like its free-space counterparts, it has already enabled important demonstration experiments (though it lags behind in terms of level of control) Spectator degrees of freedom (nuclear spins) matter for quantum phase transitions Disordered ferromagnet displays both classical random field (at high T) and tuneable quantum tunneling effects (at low T and high H t ) Quantum glass phase Antiglass, entangled state Shape control of disordered ground state?

62. Post-2000 references H. M. Ronnow et al. Science 308, 392-395 (2005) D.M.Ancona-Torres et al. Phys. Rev. Lett. 101 057201 (2008) D. M. Silevitch et al. Phys. Rev. Lett. 99, 057203 (2007) D.M. Silevitch 448, p. 567-570 (2007) S.Ghosh et al. Nature 425, 48-51,(2003) & Science 296, pp. 2195-2198, (2002) J. Brooke et al., Nature 413, pp. 610 - 613 (2001)