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

Transverse field Ising modelTransverse field Ising modelzj

ziij ijJ H

i

xi

Interaction depends on dilution, FM or random

Quantum phase transitionsQuantum annealingQuantum dynamics

LiHoF - a model quantum LiHoF - a model quantum magnetmagnet4

S. Sachdev, Physics World 12, 33 (1999)Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996)

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

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 )(

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

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

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

LiHoY FLiHoY Fx 1-x 4

Reich et al, PRB 42, 4631 (1990)

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)

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)

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)

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)

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

Ferromagnetic RFIMFerromagnetic RFIM

S0

-S

M. S., PRB 77, 020401(R) (2008)

SSVSD jiij

iji

zi

2

DH

i

xiS

i

ziSth )(||

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 )(||

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

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

Experimental realizationExperimental realization

Silevitch et al., Nature 448, 567 (2007)

Sharp transition at high T, Rounding at low T (high transverse fields)

Random fields not specific to Random fields not specific to FM!FM!

Reich et al, PRB 42, 4631 (1990)

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

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)

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!

Correlation length - Correlation length - experimentexperiment

Jonsson, Mathieu, Wernsdorfer, Tkachuk, Barbara, PRL 98, 256403 (2007)

Domains of >10^3 spins

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)

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)

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)

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

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

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

Significance of the hf in the Significance of the hf in the LiHoLiHo

27,a 2

7,a

S0

-S

S2h

1x

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 …

Electro-nuclear entanglement Electro-nuclear entanglement entropyentropy

M.S. and P. Stamp, PRB 78, 054438 (2008)Ronnow et. Al. Science 308, 389 (2005)

LiHo at 4.5%LiHo at 4.5%

- Quilliam et al., arXiv:0808.1370- Ghosh et al., Science 296, 2195 (2002)

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)

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

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