Post on 01-Jan-2016
description
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
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 – saltsquantum mechanicsclassical magnetism
RE fluoride magnet LiHoF4 – model quantum phase transition
1d model magnets
2d model magnets – Heisenberg & Hubbard models
Not magnetic, so need to look for a salt containing a simple magnetic ion…
consult periodic table on Google
4f76s2
EuO
Eu
O
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)
put atoms together to make a ferromagnet-
Classical onset of magnetizationin a conventional transition metal
alloy(PdCo)
1.5x10-3
1.0
0.5
0.0
M (
emu)
400350300250200150T (K)
H=100G out of plane H=100G in plane
Hysteresis
3x10-3
2
1
0
-1
-2
-3
M (e
mu)
-4000 -2000 0 2000 4000H (G)
300 K 360 K
300K
Hysteresis comes from magnetic domain walls
Perpendicular recording medium 3 m
conventional paradigm for magnetism
Curie(FM) point Tc so that
for T<Tc, finite <Mo>=(1/N)<Sj>
<Mo>=(Tc-T)Tc-T|-Tc-T|-
for T<Tc, there are static magnetic domains,
from which most applications of magnetism are derived
+ classical dynamics
Dispersion relations:La2-2xSr1+2xMn2O7 (x=0.4)
[h 0 0]
0.0 0.1 0.2 0.3 0.4 0.5
En
erg
y (m
eV)
0
20
40
60
acousticopticPhonon
Perring et al, Phys. Rev. Lett. 81 217201(2001)
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
Do we ever need to worry about quantum mechanics for real magnets?
0],[
zz SHt
S
i
need to examine cases wherecommutator does not vanish
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
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
Simplest quantum magnet
c~kTc~J
N
i
xi
zj
zi
N
jijiJ
,,H
0],[
zz SHt
S
i
Ising model in atransverse field:
Quantumfluctuationsmatter for 0:
FM
PMc
cTT1
1
0 0.5
0.5
Plan of talk
Experimental realization of Ising model in transverse fieldThe simplest quantum critical pointNuclear spin bathQuantum mechanics with tunable massPossible applications
04/19/23
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Realizing the transverse field Ising model, where can vary –
LiHoF4
c
a
b
Ho
Li
F
•g=14 doublet•9K gap to next state•dipolar coupled
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c
a
b
Ho 3+
Li+
F-
Realizing the transverse field Ising model, where can vary –
LiHoF4
•g=14 doublet (J=8)•9K gap to next state•dipolar coupled
04/19/23
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04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
04/19/23
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Susceptibility
dh
dm
• Real component diverges at FM ordering
• Imaginary component shows dissipation
fiff
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vs T for Ht=0
•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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04/19/23
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04/19/23
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165Ho3+ J=8 and I=7/2 A=3.36eV
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W=A<J>I ~ 140eV
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Diverging
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Magnetic Mass
• The Ising term energy gap 2J
• The term does not commute with
Need traveling wave solution:
• Total energy of flip
N
i
xi
zj
zi
N
jijiJ
,,H
DW
DW =
mkk 222222 kaJE
2
2
2 am
a
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
Magnetic Mass
• The Ising term energy gap 2J
• The term does not commute with
Need traveling wave solution:
• Total energy of flip
N
i
xi
zj
zi
N
jijiJ
,,H
DW
DW =
mkk 222222 kaJE
2
2
2 am
a
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
Magnetic Mass
• The Ising term energy gap 2J
• The term does not commute with
Need traveling wave solution:
• Total energy of flip
N
i
xi
zj
zi
N
jijiJ
,,H
DW
DW =
mkk 222222 kaJE
2
2
2 am
a
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
Magnetic Mass
• The Ising term energy gap 2J
• The term does not commute with
Need traveling wave solution:
• Total energy of flip
N
i
xi
zj
zi
N
jijiJ
,,H
DW
DW =
mkk 222222 kaJE
2
2
2 am
a
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
Magnetic Mass
• The Ising term energy gap 2J
• The term does not commute with
Need traveling wave solution:
• Total energy of flip
N
i
xi
zj
zi
N
jijiJ
,,H
DW
DW =
mkk 222222 kaJE
2
2
2 am
a
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
1 1.5 2
Ene
rgy
Tra
nsfe
r (m
eV)
Spin Wave excitations inthe FM LiHoF4
0,0,ah
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
1 1.5 2
Ene
rgy
Tra
nsfe
r (m
eV)
Spin Wave excitations inthe FM LiHoF4
0,0,ah
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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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W=A<J>I ~ 140eV
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=f|<f|S(Q)+|0>|2-E0+Ef) where
S(Q)+ =mSm+expiq.rm
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Where does spectral weight go & diverging correlation length
appear?
Ronnow et al, unpub (2006)
04/19/23
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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
04/19/23
London Centre for NanotechnologyLondon Centre for Nanotechnology
wider significance
• Connection to ‘decoherence’ problem in mesoscopic systems
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