order and disorder in dilute dipolar magnets moshe schechter (bgu) helmut katzgraber (texas a&m)...
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![Page 1: Order and disorder in dilute dipolar magnets Moshe Schechter (BGU) Helmut Katzgraber (Texas A&M) Juan Carlos Andresen (KTH, Sweden) Creighton Thomas (Google)](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649f575503460f94c7c298/html5/thumbnails/1.jpg)
Order and disorder in dilute dipolar magnets
Moshe Schechter (BGU)
Helmut Katzgraber (Texas A&M)
Juan Carlos Andresen (KTH, Sweden)
Creighton Thomas (Google)
Vadim Oganesyan (CUNY)
Nicolas Laflorencie (Toulouse)
Philip Stamp (UBC)
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Introduction
zj
ziij
ijJ H
1 .Moderate dilutions: Competing interactions with FM mean – disordering by random fields different
from simple mechanism, different from Imry-Ma
2 .Extreme dilution in dipolar Ising – is there SG phase?
Relation to experiments in LiHoxY1-xF4
Dilute dipolar Ising model
J. C. Andresen, C. Thomas, H. Katzgraber, M. S., PRL 111, 177202 (2013)
J. C. Andresen, H. Katzgraber, V. Oganesyan, M. S., PRX 4, 041016 (2014)
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Outline
• Standard Imry-Ma
• LiHo - competing interactions and random fields
• Experimental results
• Disordering of FM with competing interactions
Competing interactions:
Dipolar glass in dilute regime:
• Overview
• Results
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RFIM and Imry Ma
zj
ziij
J H
Flip a droplet
Energy gain:
Energy cost:
Large droplets flip – FM phase disordered!
Lower critical dimension - two
Imry and Ma, PRL 35, 1399 (1975)
12/ dd
1dJL2/dhL
d≤2 : infinitesimal random field, large FM domains
zii
ih
d>2 : disordering at h≈J, single spins reorient
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Competing interactionszj
ziij
ijJ H
σ – standard deviation. Mean=1
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Competing interactionszj
ziij
ijJ H
σ – standard deviation. Mean=1
zii
ih
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Competing interactionszj
ziij
ijJ H
σ – standard deviation. Mean=1
FM d>2
FM d≤2C.I. d=3
hcJ≈0?
mechanismSingle spins
FM domains
?
zii
ih
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Competing interactionszj
ziij
ijJ H
σ – standard deviation. Mean=1
FM d>2
FM d≤2C.I. d=3
hcJ≈0?
mechanismSingle spins
FM domains
?
zii
ih
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LiHoF4 - Dipolar Ising model
zj
zi
ijjiJHIs
SSV jiij
ijHH cfD
iSD zi2
cfH
S0
-S
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LiHoF4 with hyperfine interactions
iSD zi2
cfH
S0
-S
LiHo
27,a
27,a
Hyperfine spacing: 200 mK
K100
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LiHoxY1-xF4 - Continuous dilution
LiHoxY1-xF4
zj
ziij
ijJ H
σ – standard deviation. Mean=1
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LiHoF4 - Transverse field Ising model
i
xi
zj
zi
ijjiJ HIs
i
xiji
ijij SHSSV xcfD HH
iSD zi2
cfH
S0
-S
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QPT 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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Ferromagnetic RFIM
S -S
M. S. and N. Laflorencie, PRL 97, 137204 (2006)
M. S., PRB 77, 020401(R) (2008)
SSVSD jiij
iji
zi
2
DH
i
xix SH
i
ziSth )(||
i
xiz
jziij
ijJ H zii
ih i
zitH )(
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Ferromagnetic RFIM
S -S
SSVSD jiij
iji
zi
2
DH
i
xix SH
i
ziSth )(||
i
xiz
jziij
ijJ H zii
ih i
zitH )(
j
zxij
xBzi V
HSh
0
2
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Ferromagnetic RFIM
S0
-S
H xS2
Hh x
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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xBzi V
HSh
0
2
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Imry Ma for SG – correlation length
2/2/)1( dd
Flip a droplet –
gain vs. cost:
Fisher and Huse PRL 56, 1601 (1986); PRB 38, 386 (1988)
Lower critical dimension – infinity!
Droplet size –
Correlation length
Imry and Ma, PRL 35, 1399 (1975)
)2/3/(1)/( hJ
JLhL 2/3
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Dilution: quantum spin-glass
-Thermal vs. Quantum disorder-Cusp diminishes as T lowered
Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)
VTc
Vc
VTc
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SG unstable to transverse field !
Finite, transverse field dependent correlation length
SG
quasi
M. S. and N. Laflorencie, PRL 97, 137204 (2006)
Young, Katzgraber, PRL 93, 207203 (2004)
i
zxij
xBzj V
HSh
0
2
)2/3/(1)/(0
xBH
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Disordering of FM at x=0.44
Silevitch et al., Nature 448, 567 (2007)
Sharp transition at high T, Rounding at low T (high transverse fields)
Decrease of critical Temperature with random Field (roughly) linear
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FM and SG phases in random field
)3/()2/3()3/()2/3()]([ Jxxhcc
FMSGcEExxhJhh )()/(/ )2/3/(2/332/3
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FM and SG phases in random field
)()/( )2/3/(2/3cxxhJh
)3/()2/3()3/()2/3()]([ Jxxhcc
Disordering of the FM phase in 3D by finite, yet SMALL random field Jh
c
Disordered phase: SG domains of size )2/3/(1)/( hJ
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Finite temperature
Sharp transition at high T, Rounding at low T (high transverse fields)
Decrease of critical Temperature with random Field (roughly) linear
)2/3/(1)/( hJSilevitch et al., Nature 448, 567 (2007)Andresen et. al., PRL 111, 177202 (2013)
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Finite temperature
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Finite temperature
T>0.3K : FM to PM transition
Andresen et. al., PRL 111, 177202 (2013)
T<0.3K : Intermediate frozen QSG phase
Silevitch et al., Nature 448, 567 (2007)
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Finite temperature“Standard”PM Glassy
domains
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Conclusions 1• Generalized Imry-Ma: 3D FM with competing
interactions – disordering at small random field• Disordered phase: spin glass domains with typical
size depending on random field• At low temperatures disordered phase is frozen,
explains rounding off of the susceptibility cusp• Critical temperature linear with field down to small
fields
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Dilute Dipolar Glass
Reich et al, PRB 42, 4631 (1990)
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Dilute Dipolar Glass
Ghosh, Parthasarathy, Rosenbaum, Aeppli Science 296, 2195 (2002)
Quilliam, Meng, Kycia,
PRB 85, 184415 (2012)
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Dilute Dipolar Glass
Experiment: Anti-glass? Spin liquid?
Analytics
• Mean field theory (Stephen and Aharony): Tc linear in x• Fluctuations are large, could dominate• RG ineffective
Numerical
• Fluctuations increase with dilution• Snider and Yu, Biltmo and Henelius – no glass phase • Tam and Gingras – Glass phase down to 6.25%
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Finite size scaling
J. C. Andresen, H. Katzgraber, V. Oganesyan, M. S., PRX 4, 041016 (2014)
• Parallel tempering Monte Carlo
• Combine single spin flip with cluster renormalization algorithm
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Strong fluctuations
Algorithm: 1. cluster all spins with
Algorithm efficiency concentration independent!! Size limited by Ewald sums
.
for all n until left only with pairs.2. Repeat for
3. Sweep spins, flip: single spin - 75%, random cluster – 25%
Strong fluctuations coming from nearby spins do not effect thermodynamic transition, nor efficiency of algorithm
Cluster strongly interacting spins, standard MC for resulting entities
Can not use one method for strongly interacting and typical spins.
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Tc linear in dipole concentration
Tc=ax; a=0.59(1)
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LiHoxY1-xF4 - phase diagram
1 .FM-SG boundary at x=0.3. No significant reentrant SG regime
2 .SG phase down to x=0, with linear Tc
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Dilute dipolar glass - broad distribution of random fields
Assume: 1n;00 Jh -Random field dictated by rare events of nearest neighbor impurities.
-Interactions are dictated by typical strength.
1/ 00 nJh
Typical random field:)2/3/(1)/( hJ
)2/3/(12/1 )/( hJn
)2/3(2/1)/( hJ00 / Jhn
M.S. and P. Stamp, EPL 88, 66002 (2009)
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Conclusions 2• Dilute dipolar Ising spins order at any small
concentration with Tc linear in concentration• Induced random field – non trivial dependence of
domain size on concentration
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Dipolar glasses – scaling with dilution
Interaction allows diliution – expect scaling ),( 00 nhnJf