LiHoxY1-xF4: The road between solid state ion trap and quantum critical ferromagnet

Gabriel AeppliLondon Centre for Nanotechnology & UCL

Collaborators

Andrew Fisher, Ché Gannarelli, Stephen Lynch, Edward Gryspeerdt, Marc Warner, Des McMorrow

UCL Physics & Astronomy and London Centre for Nanotechnology

Tom Rosenbaum, Dan Silevitch

James Franck Institute and Dept of Physics, University of Chicago

Sai Ghosh

University of California at Merced

Jens Jensen

University of Copenhagen

Henrik Ronnow

EPFL

Outline

• Context• Introducing LiHoF4:

– Structure, magnetism and single-ion physics

• The new experiment:– Low-frequency dynamics while rotating the Ising moment out of the

plane to create superpositions– Test of the adequacy of ion-pair models to describe these

properties

• Outlook and conclusions

Can be made manifest by ramping longitudinal (Ising) field in a very dilute system, and watching frequency-dependent tunnelling of magnetization mediated by nuclear spins (and residual dipolar interactions)

Nuclear couplings produce line of avoided crossings in combined level scheme

Giraud et al PRL 87 057203 (2001) and PRL 91 257204 (2003); x=0.1%

Sharp nuclear levels at microwave frequencies (~10GHz)

Hyperfine interaction with nuclear spins (I=7/2)

A=0.039 K

Coupling, disorder and transverse fieldsExchange is negligible because of the extreme localization of the electrons

Ions coupled instead by pure magnetic dipole interaction (weak but precisely known):

In low-energy, 2-state limit for ordered material this becomes

H e®dipolar = 1

2

Pi j Ve®

i j _zi _z

j

Hdipolar =_ 04_

(gL _ B )2

2

Pi j

P_ º L

_ ºi j J

_i ^J º

j

In pure material (x=1) mean fields lie along z, material behaves as a classical Ising magnet: FM couplings along c-axis, AFM in ab plane

L_ ºi j ´

±_ º

jr i j j2¡ 3r

_i j r

ºi j

jr i j j5 / 1¡ 3cosµi µj

r i j

Ion i

Ion j

µiµj

Note anisotropy of interaction

Magnitude of interaction is 0.214 K for r=a

But…we expect non-classical behaviour to be obtained by introduction of transverse fields or by disorder

Toronto 2008

A three-dimensional quantum magnet - with decoherence due to spectators

Realizing the transverse field Ising model, where can vary – LiHoF4

A three-dimensional quantum magnet - with decoherence due to spectators

Realizing the transverse field Ising model, where can vary – LiHoF4

c

a

b

Ho

Li

F

•g=14 doublet•9K gap to next state•dipolar coupled

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c

a

b

Ho

Li

F

Realizing the transverse field Ising model, where can vary – LiHoF4

•g=14 doublet•9K gap to next state•dipolar coupled

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vs T for Ht=0 vs T for Ht=0

•D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), pp. 940-943, (1996)

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Now impose transverse field …Now impose transverse field …

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165Ho3+ J=8 and I=7/2 A=3.36eV

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W=A<J>I ~ 140eV

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Diverging Diverging

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• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

∑∑ −−=N

i

xi

zj

zi

N

jijiJ σσσ

,,H

DWΨ

DWΨ =

∗= mkk 222hε222 kaJE +=

2

2

2 am

=∗ h

a

DynamicsDynamics

Toronto 2008

• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

∑∑ −−=N

i

xi

zj

zi

N

jijiJ σσσ

,,H

DWΨ

DWΨ =

∗= mkk 222hε222 kaJE +=

2

2

2 am

=∗ h

a

Toronto 2008

• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

∑∑ −−=N

i

xi

zj

zi

N

jijiJ σσσ

,,H

DWΨ

DWΨ =

∗= mkk 222hε222 kaJE +=

2

2

2 am

=∗ h

a

Toronto 2008

• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

∑∑ −−=N

i

xi

zj

zi

N

jijiJ σσσ

,,H

DWΨ

DWΨ =

∗= mkk 222hε222 kaJE +=

2

2

2 am

=∗ h

a

Toronto 2008

• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

∑∑ −−=N

i

xi

zj

zi

N

jijiJ σσσ

,,H

DWΨ

DWΨ =

∗= mkk 222hε222 kaJE +=

2

2

2 am

=∗ h

a

Toronto 2008

1 1.5 2

Ene

rgy

Tra

nsfe

r (m

eV)

Spin Wave excitations inthe FM LiHoF4

Spin Wave excitations inthe FM LiHoF4

⎟⎠

⎞⎜⎝

⎛0,0,

ahπ

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1 1.5 2

Ene

rgy

Tra

nsfe

r (m

eV)

Spin Wave excitations inthe FM LiHoF4

Spin Wave excitations inthe FM LiHoF4

⎟⎠

⎞⎜⎝

⎛0,0,

ahπ

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What happens near QPT?

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•H. Ronnow et al. Science (2005)

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W=A<J>I ~ 140eV

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wider significancewider significance

• Connection to ‘decoherence’ problem in mesoscopic systems

‘best’ Electronic-TFI

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=f|<f|S(Q)+|0>|2-E0+Ef) where

S(Q)+ =mSm+expiq.rm

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Where does spectral weight go & diverging correlation length appear?

Where does spectral weight go & diverging correlation length appear?

Ronnow et al, unpub (2006)

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dipolar interaction between randomly placed spins leads to frustration

E=S1S2g2MB2[1-3(rz/r)2]/r3

ferro for (rz/r)2 >1/3antiferro for (rz/r)2 <1/3

Introducing complexity via randomness& dipolar interaction …

Toronto 2008

c

a

b

Ho

Li

F

Experimental realization of Ising model in transverse field

LiHoF4

•g=14 doublet•9K gap to next state•dipolar coupled

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c

a

b

Ho

Li

F

Experimental realization of Ising model in transverse field

LiHoF4

•g=14 doublet•9K gap to next state•dipolar coupled

Y

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c

a

b

Ho

Li

F

Experimental realization of Ising model in transverse field

LiHoF4

•g=14 doublet•9K gap to next state•dipolar coupled

Y

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What happens first?What happens first?

Tc=xTc(x=1)

x=0.67

stillferromagnetic

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x=0.44

also stillferromagnetic

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Two effects: quantum mechanics + classical random fields

Two effects: quantum mechanics + classical random fields

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Strong random field effects near Ht=0 and T=TCMFStrong random field effects near Ht=0 and T=TCMF

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Thermal T-TC

Transverse field

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Griffiths singularities at T=0.673K>TC+4mKGriffiths singularities at T=0.673K>TC+4mK

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All data collapse assuming

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Random-field dominatedQuantum dominated

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Domain wall state pinned by random configurations of Y not much different from that at 300K in PdCo-

What about domainwall dynamics?

Y-A. Soh and G.A.,unpublished

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How to see?How to see?

• Measure small signal response

M(t)=’()hcos(t)+”hsin(t)

where • =’+i” is complex susceptibility• hcos(t) is excitation

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Experimental SetupExperimental Setup

~ Ht2

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The Spectral ResponseThe Spectral Response

Four parameters:1. (f)

2. fo3. log slope4. frolloff

J.Brooke, T.F.Rosenbaum & G.A, Nature 413,610(2001)

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Domain Wall TunnelingDomain Wall Tunneling

w

⎟⎟⎠

⎞⎜⎜⎝

⎛− BE

Mw

2

2exp~

h

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Evolution of themost mobile

Domain Walls

Evolution of themost mobile

Domain Walls

( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−=

2

22expexp

hm

wTFf oo

thermal hopping

quantum tunneling

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Domain Wall ParametersDomain Wall Parameters

( )iaN

Γ+Γ⋅=

⋅=

2

2

spinDW

2

mNm

h

N 10

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What happens next?What happens next?

?

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0.2 0.4 0.6T(K)

x=0.167Spin glass

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f Re / Im ~ "~f-

Glass transition when =0

f Re / Im ~ "~f-

Glass transition when =0

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Revisited more recently (2008) with x=0.198% Ho Revisited more recently (2008) with x=0.198% Ho

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Consistent with non-linear susceptibilityConsistent with non-linear susceptibility

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?

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Dynamic properties (I): the anti-glass and its relaxation

Contrast behaviour of conventional glasses, where longer and longer tail of slow reponse develops below glass transition

X=4.5%; Reichl et al PRL 59 1969 (1987), Ghosh et al Nature 425 48 (2003)

Dilute system shows loss of low-frequency tail in dissipative (imaginary) part of response.

Inference: fewer slow relaxations as temperature is lowered

Dynamic properties (II): hole-burning and addressing of excitations

Cannot address individual ions spatially, but can excite in very narrow low-frequency windows.

Absorption spectrum after “hole burning” Decay of oscillation amplitude with time

Suggests low-frequency continuum is of oscillators, not just relaxation

Ghost et al Science 216 2195 (2002)

AntiglassAn RVB-like

state analagous to Si:P (Bhatt-Lee)

But experiment seems to favour in-plane (AFM) pairs

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Conclusions

• LiHoF4 is just about the best imaginable solid-state ion trap• Like its free-space counterparts, it has already enabled important

demonstration experiments (though it lags behind in terms of level of control)

• Spectator degrees of freedom (nuclear spins) matter for quantum phase transitions

• Disordered ferromagnet displays both classical random field (at high T) and tuneable quantum tunneling effects (at low T and high Ht )

• Quantum glass phase• Antiglass, entangled state • Shape control of disordered ground state?

Post-2000 references

• H. M. Ronnow et al. Science 308, 392-395 (2005)• D.M.Ancona-Torres et al. Phys. Rev. Lett. 101 057201

(2008) • D. M. Silevitch et al. Phys. Rev. Lett. 99, 057203 (2007)• D.M. Silevitch 448, p. 567-570 (2007)• S.Ghosh et al. Nature 425, 48-51,(2003) & Science

296, pp. 2195-2198, (2002)• J. Brooke et al., Nature 413, pp. 610 - 613 (2001)