Quantum effects in Magnetic Salts

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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)

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outline

• Introduction salts?quantum mechanics?classical
  magnetism
• RE fluoride magnet LiHoF4 model quantum phase
  transition
• 1d model magnets
• 2d model magnets Heisenberg Hubbard models

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Not magnetic, so need to look for a salt
containing a simple magnetic ionconsult
periodic table on Google
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4f76s2
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EuO
O
Eu
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From quantum mechanics

• Electrons carry spin
• Spin uncompensated for many ions in solids
• e.g. Eu2(f7,S7/2),
• but also Cu2(d9,S1/2), Ni2 (d8,S1), Fe2
  (d6,S2)

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put atoms together to make a ferromagnet-
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Classical onset of magnetizationin a
conventional transition metal alloy(PdCo)
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Hysteresis
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300K
Hysteresis comes from magnetic domain walls
Perpendicular recording medium
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conventional paradigm for magnetism

• Curie(FM) point Tc so that
• for TltTc, finite ltMogt(1/N)SltSjgt
• ltMogt(Tc-T)b , xTc-T-n , cTc-T-g
• for TltTc, there are static magnetic domains,
• from which most applications of magnetism are
  derived

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classical dynamics
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Perring et al, Phys. Rev. Lett. 81 217201(2001)
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What is special about ordinary ferromagnets?

• H,M0 ? order parameter is a conserved
  quantity ?
• classical FM eigenstates (Curie state ½ ½ ½ ½
  gt, -½ -½ -½ -½ gt
• spin waves) are also quantum eigenstates
• ? no need to worry about quantum mechanics once
  spins exist

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

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Simplest quantum magnet
Ising model in a transverse field
Quantum fluctuations matter for G ? 0
PM
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GckTcJ
0.5
FM
1
0
0.5
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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
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Realizing the transverse field Ising model, where
can vary G LiHoF4

• g14 doublet
• 9K gap to next state
• dipolar coupled

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Realizing the transverse field Ising model, where
can vary G LiHoF4

• g14 doublet (J8)
• 9K gap to next state
• dipolar coupled

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Susceptibility

• Real component diverges at FM ordering
• Imaginary component shows dissipation

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c vs T for Ht0

• D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev.
  Lett.77(5), pp. 940-943, (1996)

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Now impose transverse field
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165Ho3 J8 and I7/2 A3.36meV
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WAltJgtI 140meV
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Diverging c
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Magnetic Mass

a

• The Ising term ? energy gap 2J
• The G term does not commute with
• Need traveling wave solution
• Total energy of flip

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Magnetic Mass

a

• The Ising term ? energy gap 2J
• The G term does not commute with
• Need traveling wave solution
• Total energy of flip

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Magnetic Mass

a

• The Ising term ? energy gap 2J
• The G term does not commute with
• Need traveling wave solution
• Total energy of flip

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Magnetic Mass

a

• The Ising term ? energy gap 2J
• The G term does not commute with
• Need traveling wave solution
• Total energy of flip

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Magnetic Mass

a

• The Ising term ? energy gap 2J
• The G term does not commute with
• Need traveling wave solution
• Total energy of flip

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Spin Wave excitations inthe FM LiHoF4
Energy Transfer (meV)
1
1.5
2
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Spin Wave excitations inthe FM LiHoF4
Energy Transfer (meV)
1
1.5
2
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What happens near QPT?
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• H. Ronnow et al. Science 308, 392-395 (2005)

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WAltJgtI 140meV
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• d2s/dWdwSfltfS(Q)0gt2d(w-E0Ef) where
• S(Q) SmSmexpiq.rm

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

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wider significance

• Connection to decoherence problem in mesoscopic
  systems

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