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Dilute anisotropic dipolar Dilute anisotropic dipolar systems as random field systems as random field
Ising ferromagnetsIsing ferromagnets
In collaboration with: Philip Stamp Nicolas Laflorencie
Moshe SchechterUniversity of British Columbia
Discussions: Gabriel Aeppli
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Transverse field Ising modelTransverse field Ising modelzj
ziij ijJ H
i
xi
Interaction depends on dilution, FM or random
Quantum phase transitionsQuantum annealingQuantum dynamics
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LiHoF - a model quantum LiHoF - a model quantum magnetmagnet4
S. Sachdev, Physics World 12, 33 (1999)Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)
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Random field Ising modelRandom field Ising modelzj
ziij ijJ H zii ih
DAFM - Constant field is random in staggered magnetization
- FM - Field conjugate to order parameter
- Quantum fluctuations- Verification of results near transition
“trompe l’oeil critical behavior”
Experiments, crackling noiseAway from criticality, applications
Quantum dynamics, QPT
S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979)
No FM realization
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OutlineOutline RF in anisotropic dipolar magnetsRF in anisotropic dipolar magnets
Consequences in FM and SG regimesConsequences in FM and SG regimes
LiHo system – hyperfine interactionsLiHo system – hyperfine interactions – – transverse dipolar int.transverse dipolar int.
i
xiz
jziij ijJ H zii ih
i
zitH )(
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Anisotropic dipolar systemsAnisotropic dipolar systems
zj
zi
ijjiJHIs
SSV jiij
ijHH cfD
iSD zi2
cfH
Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction
S0
-S
Rare-earth magnetic insulators
Single molecular magnets
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Anisotropic dipolar systems - Anisotropic dipolar systems - TFIMTFIM
i
xi
zj
zi
ijjiJ HIs
i
xiji
ijij SSSV HH cfD
iSD zi2
cfH
S0
-S
Single molecular magnets
Magnetic insulators, large spin, strong lattice anisotropy, dominant dipolar interaction
Rare-earth magnetic insulators
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QPT in dipolar magnetsQPT in dipolar magnets
Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)
Thermal and quantum transitions
MF of TFIM
MF with hyperfine
zj
ziij ijJ H
i
xi
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LiHoY FLiHoY Fx 1-x 4
Reich et al, PRB 42, 4631 (1990)
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Dilution, transverse field – Dilution, transverse field – effective random longitudinal effective random longitudinal
fieldfield
S0
-S
SSVSD zj
zi
ij
zzij
i
zi 2
DH
M. S. and N. Laflorencie, PRL 97, 137204 (2006)M. S., PRB 77, 020401(R) (2008)
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Offdiagonal dipolar termsOffdiagonal dipolar terms
S0
-S
SSVSD zj
zi
ij
zzij
i
zi 2
DH
SSV xi
zj
ij
zxij
M. S. and N. Laflorencie, PRL 97, 137204 (2006)M. S., PRB 77, 020401(R) (2008)
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Offdiagonal dipolar termsOffdiagonal dipolar terms
S0
-S
SSVSD zj
zi
ij
zzij
i
zi 2
DH
i
xiS SSV x
izj
ij
zxij
SS zz SS symmetry symmetry
M. S. and N. Laflorencie, PRL 97, 137204 (2006)M. S., PRB 77, 020401(R) (2008)
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Offdiagonal dipolar termsOffdiagonal dipolar terms
S0
-S
SSVSD zj
zi
ij
zzij
i
zi 2
DH
i
xiS SSV x
izj
ij
zxij
SS zz SS symmetry symmetry
i
SVEzjj
zxij
0
2)(
i
zxij
zj VSh
0
2
M. S. and N. Laflorencie, PRL 97, 137204 (2006)M. S., PRB 77, 020401(R) (2008)
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Are the fields random?Are the fields random?
Square of energy gain vs. N, different dilutions
Inset: Slope as Function of dilution
M. S., PRB 77, 020401(R), (2008)
i
zxij
zj VSh
0
2 x0
2 VSj
x1x
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Ferromagnetic RFIMFerromagnetic RFIM
S0
-S
M. S., PRB 77, 020401(R) (2008)
SSVSD jiij
iji
zi
2
DH
i
xiS
i
ziSth )(||
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Ferromagnetic RFIMFerromagnetic RFIMi
xiz
jziij ijJ H zii ih
i
zitH )(
S0
-S
M. S., PRB 77, 020401(R) (2008)
SSVSD jiij
iji
zi
2
DH
i
xiS
i
ziSth )(||
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Ferromagnetic RFIMFerromagnetic RFIM
S0
-S
M. S. and P. Stamp, PRL 95, 267208 (2005)M. S., PRB 77, 020401(R) (2008)
SSVSD jiij
iji
zi
2
DH
i
xiS
i
ziSth )(||
i
xiz
jziij ijJ H zii ih
i
zitH )(
S2h
1x
- Independently tunable random and transverse fields!- Classical RFIM despite applied transverse field
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RF in disordered systemsRF in disordered systems
Transverse field, still , but no T. Transverse field, still , but no T. Disordered systems: no pure Ising Disordered systems: no pure Ising
without T symmetry. No pure TFIM in without T symmetry. No pure TFIM in field.field.
Anisotropic dipolar magnets:Anisotropic dipolar magnets:
M. S. and P. Stamp, in preparation
0
2 VSh jzj x
zj
ziij ijJ H
i
xi
Z2
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Experimental realizationExperimental realization
Silevitch et al., Nature 448, 567 (2007)
Sharp transition at high T, Rounding at low T (high transverse fields)
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Random fields not specific to Random fields not specific to FM!FM!
Reich et al, PRB 42, 4631 (1990)
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Dilution: quantum spin-glassDilution: quantum spin-glass
-Thermal vs. Quantum disorder-Thermal vs. Quantum disorder-Cusp diminishes as T lowered-Cusp diminishes as T lowered
Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)
VTc
Vc
VTc
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Spin glass – correlation lengthSpin glass – correlation length
LVSLVS 2
0
2/32
Flip a droplet –
gain vs. cost:
M.S. and N. Laflorencie, PRL 97, 137204 (2006)
Fisher and Huse PRL 56, 1601 (1986); PRB 38, 386 (1988)
2/2/)1( dd Lower critical dimension – infinity!
i
zxij
zj VSh
0
2 X0
2 VSj
Droplet size –
Correlation length)2/3/(1)/(
0
Imry and Ma, PRL 35, 1399 (1975)
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SG unstable to transverse SG unstable to transverse field!field!
Finite, transverse field dependent correlation length
SG
quasi
M. S. and N. Laflorencie, PRL 97, 137204 (2006)
No SG-PM QPT in transverse field!
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Correlation length - Correlation length - experimentexperiment
Jonsson, Mathieu, Wernsdorfer, Tkachuk, Barbara, PRL 98, 256403 (2007)
Domains of >10^3 spins
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RemarksRemarks Validity of droplet pictureValidity of droplet picture Reduction of susceptibility in mean Reduction of susceptibility in mean
fieldfield
- Tabei, Gingras, Kao, Stasiak, Fortin, PRL 97, 237203 (2006)
- Young, Katzgraber, PRL 93, 207203 (2004)
- Jonnson, Takayama, Katori, Ito, PRB 71, 180412(R) (2005)
- Pirc, Tadic, Blinc, PRB 36, 8607 (1987)
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Hyperfine interaction: electro-Hyperfine interaction: electro-nuclear Ising statesnuclear Ising states
K100 i
xiji
ijij SSSV HH cfLH
i
xi
zj
zi
ijjiJ HIs
2
Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)(1993)
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Hyperfine interaction: electro-Hyperfine interaction: electro-nuclear Ising statesnuclear Ising states
ccS z2221
~
27,a 2
7,a
27,b 2
7,b
K100
K4.12 A
Hyperfine spacing: 200 mK
SJJ zeff
~2
i
xiji
ijij SSSV HH cfLH
)( SISIASIA iiii
iJzi
i
ziJ
- M.S. and P. Stamp, PRL 95, 267208 (2005)
2/7I
- N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)
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Hyperfine interaction: electro-Hyperfine interaction: electro-nuclear Ising statesnuclear Ising states
27,a 2
7,a
27,b
27,b
K100
K4.12 A
Hyperfine spacing: 200 mK
i
xiji
ijij SSSV HH cfLH
)( SISIASIA iiii
iJzi
i
ziJ
- M.S. and P. Stamp, PRL 95, 267208 (2005)
2/7I
- N. Prokof’ev and P. Stamp, Rep. Prog. Phys. 63, 669 (2000)
eff
J eff
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Enhanced transverse field – Enhanced transverse field – phase diagramphase diagram
eff
SG
PM
No off. dip.
With off. dip.
Experiment
V||V||
M.S. and P. Stamp, PRL 95, 267208 (2005)
Quantum disordering harder than thermal disordering
Main reason – hyperfine interactions
Off-diagonal dipolar terms in transverse field – also enhanced effective transverse field
i
SVE
zjj
zxij
0
2)(
i
zxij
zj VSh
0
2
Page 30
Re-entrance of crossover Re-entrance of crossover fieldfield
SG
PM
No off. dip.
With off. dip.
Experiment
V||V||
Larger x – stronger reduction of c-o field by offdiagonal dipolar terms!
-M.S. and P. Stamp, PRB 78, 054438 (2008)
- Ancona-Torres, Silevitch, Aeppli, Rosenbaum, PRL 101, 057201 (2008)
X=0.167X=0.045
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Significance of the hf in the Significance of the hf in the LiHoLiHo
27,a 2
7,a
S0
-S
S2h
1x
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Electro-nuclear entanglement Electro-nuclear entanglement entropyentropy
M.S. and P. Stamp, PRB 78, 054438 (2008)
At electron and nuclear spin disentangle!
T2H t
However …
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Electro-nuclear entanglement Electro-nuclear entanglement entropyentropy
M.S. and P. Stamp, PRB 78, 054438 (2008)Ronnow et. Al. Science 308, 389 (2005)
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LiHo at 4.5%LiHo at 4.5%
- Quilliam et al., arXiv:0808.1370- Ghosh et al., Science 296, 2195 (2002)
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LiHo at 4.5%LiHo at 4.5%
M.S. and P. Stamp, PRB 78, 054438 (2008)
- Experiments are above expected glass temperature (35 mK)
- Narrowing of absorption spectrum at hyperfine energy
- Efffective transverse field too low to explain spin liquid state
- Theoretically – expect SG at any x (Stephen Aharony)
Stephen and Aharony, J. Phys. C 14, 1605 (1981)
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Future researchFuture research Experiment:Experiment:
Quantum and classical PT in FM RFIMQuantum and classical PT in FM RFIM Hysteresis in the FM RFIMHysteresis in the FM RFIM Materials withMaterials with
With With Pressure induced SG-PM QPT Pressure induced SG-PM QPT
TheoryTheory Spin bath and QPTSpin bath and QPT DynamicsDynamics
0VA
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ConclusionsConclusions Dilution and transverse field induce Dilution and transverse field induce
random longitudinal field in Ising random longitudinal field in Ising dipolar systems.dipolar systems.
FM RFIM, no SG-PM QPT.FM RFIM, no SG-PM QPT. Disordered systems: Ising model is only Disordered systems: Ising model is only
realizable with time-reversal symmetryrealizable with time-reversal symmetry LiHo – hyperfine, offdiagonal dipolar LiHo – hyperfine, offdiagonal dipolar
interactions dictate low-T physicsinteractions dictate low-T physics