Quantum effects in Magnetic Salts

1. Quantum effects in Magnetic Salts G. Aeppli (LCN) J. Brooke (NEC/UChicago/Lincoln Labs) T. F. Rosenbaum (UChicago) D. Bitko (UChicago) H. Ronnow (PSI/NEC) D. McMorrow (LCN) R. Parthasarathy (UChicago/Berkeley)

2. outline • Introduction – saltsquantum mechanicsclassical magnetism • RE fluoride magnet LiHoF4 – model quantum phase transition • 1d model magnets • 2d model magnets – Heisenberg & Hubbard models

4. Not magnetic, so need to look for a salt containing a simple magnetic ion…consult periodic table on Google

8. 4f76s2

9. EuO O Eu

10. From quantum mechanics • Electrons carry spin • Spin uncompensated for many ions in solids • e.g. Eu2+(f7,S=7/2), • but also Cu2+(d9,S=1/2), Ni2+ (d8,S=1), Fe2+ (d6,S=2)

11. put atoms together to make a ferromagnet-

12. Classical onset of magnetizationin a conventional transition metal alloy(PdCo)

13. Hysteresis

14. 3 mm Hysteresis comes from magnetic domain walls 300K Perpendicular recording medium

15. conventional paradigm for magnetism • Curie(FM) point Tc so that • for T<Tc, finite <Mo>=(1/N)S<Sj> • <Mo>=(Tc-T)b , x~|Tc-T|-n , c~|Tc-T|-g • for T<Tc, there are static magnetic domains, • from which most applications of magnetism are derived

16. + classical dynamics

17. Perring et al, Phys. Rev. Lett. 81 217201(2001)

18. What is special about ordinary ferromagnets? • [H,M]=0  order parameter is a conserved quantity  • classical FM eigenstates (Curie state | ½ ½ ½ … ½ >,| -½ -½ -½ … -½ > • & spin waves) are also quantum eigenstates •  no need to worry about quantum mechanics once spins exist

19. Do we ever need to worry about quantum mechanics for real magnets? need to examine cases where commutator does not vanish

20. Why should we ask? • Search for useable - scaleable, easily measurable - quantum • degrees of freedom, • e.g. for quantum computing • many hard problems (e.g. high-temperature superconductivity) • in condensed matter physics involve strongly fluctuating • quantum spins

21. Simplest quantum magnet Ising model in a transverse field: Quantum fluctuations matter for G  0: PM 1 Gc~kTc~J 0.5 FM 0 0.5 1

22. Plan of talk • Experimental realization of Ising model in transverse field • The simplest quantum critical point • Nuclear spin bath • Quantum mechanics with tunable mass • Possible applications

23. 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

24. c Ho 3+ Li+ F- b a Realizing the transverse field Ising model, where can vary G – LiHoF4 • g=14 doublet (J=8) • 9K gap to next state • dipolar coupled

27. Susceptibility • Real component diverges at FM ordering • Imaginary component shows dissipation

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

29. Now impose transverse field …

32. 165Ho3+ J=8 and I=7/2 A=3.36meV

33. W=A<J>I ~ 140meV

34. Diverging c

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

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

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

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

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

40. Spin Wave excitations inthe FM LiHoF4 Energy Transfer (meV) 1 1.5 2

41. Spin Wave excitations inthe FM LiHoF4 Energy Transfer (meV) 1 1.5 2

42. What happens near QPT?

43. H. Ronnow et al. Science 308, 392-395 (2005)

44. W=A<J>I ~ 140meV

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

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

48. summary • Electronic coherence limited by nuclear spins • QCP dynamics radically altered by simple ‘spectator’ degree of freedom • Nuclear spin bath ‘pulls back’ quantum system into classical regime

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