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Quantum effects in Magnetic Salts

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). outline. Introduction – salts  quantum mechanics classical magnetism

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Quantum effects in Magnetic Salts

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  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

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

  4. 4f76s2

  5. EuO O Eu

  6. 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)

  7. put atoms together to make a ferromagnet-

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

  9. Hysteresis

  10. 3 mm Hysteresis comes from magnetic domain walls 300K Perpendicular recording medium

  11. 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

  12. + classical dynamics

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

  14. 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

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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

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

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

  23. Now impose transverse field …

  24. 165Ho3+ J=8 and I=7/2 A=3.36meV

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

  26. Diverging c

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

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

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

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

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

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

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

  34. What happens near QPT?

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

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

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

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

  39. 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

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

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