Dilute anisotropic dipolar systems as random field Ising ferromagnets In collaboration with: Philip...
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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 Schechter
University of British Columbia
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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 noise
Away 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.
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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
SVE
zjj
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
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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)
S2h
SSVSD jiij
iji
zi
2
DH
i
xiS
i
ziSth )(||
i
xiz
jziij
ijJ H zii
ih i
zitH )(
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 Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)(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)
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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
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Hyperfine interaction: electro-Hyperfine interaction: electro-nuclear Ising statesnuclear Ising states
ccS z2221
~
27,a
27,a
27,b
27,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
27,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
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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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ConclusionsConclusions
Ising model with tunable quantum and Ising model with tunable quantum and random effective fields can be realized in random effective fields can be realized in anisotropic dipolar systemsanisotropic dipolar systems
FM RFIM – implications to fundamental FM RFIM – implications to fundamental research and applicationsresearch and applications
Quasi-SG, no SG-PM QPT in Ising magnetsQuasi-SG, no SG-PM QPT in Ising magnets 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