dilute anisotropic dipolar systems as random field ising ferromagnets in collaboration with: philip...

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

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

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.

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


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


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., 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

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)

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

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 Wu, Bitko, Rosenbaum, Aeppli, PRL 71, 1919 (1993)(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


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


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)


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

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

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

dilute anisotropic dipolar systems as random field ising ferromagnets in collaboration with: philip...

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