LiHo x Y 1-x F 4 : The road between solid state ion trap and quantum critical ferromagnet Gabriel Aeppli London Centre for Nanotechnology & UCL
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
Toronto 2008
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
Toronto 2008
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)
Toronto 2008
Now impose transverse field …Now impose transverse field …
Toronto 2008
Toronto 2008
Toronto 2008
165Ho3+ J=8 and I=7/2 A=3.36eV
Toronto 2008
W=A<J>I ~ 140eV
Toronto 2008
Diverging Diverging
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
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
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
Toronto 2008
What happens near QPT?
Toronto 2008
•H. Ronnow et al. Science (2005)
Toronto 2008
W=A<J>I ~ 140eV
Toronto 2008
wider significancewider significance
• Connection to ‘decoherence’ problem in mesoscopic systems
‘best’ Electronic-TFI
Toronto 2008
=f|<f|S(Q)+|0>|2-E0+Ef) where
S(Q)+ =mSm+expiq.rm
Toronto 2008
Where does spectral weight go & diverging correlation length appear?
Where does spectral weight go & diverging correlation length appear?
Ronnow et al, unpub (2006)
Toronto 2008
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
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
Y
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
Y
Toronto 2008
What happens first?What happens first?
Tc=xTc(x=1)
x=0.67
stillferromagnetic
Toronto 2008
x=0.44
also stillferromagnetic
Toronto 2008
Two effects: quantum mechanics + classical random fields
Two effects: quantum mechanics + classical random fields
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Toronto 2008
Strong random field effects near Ht=0 and T=TCMFStrong random field effects near Ht=0 and T=TCMF
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Thermal T-TC
Transverse field
Toronto 2008
Griffiths singularities at T=0.673K>TC+4mKGriffiths singularities at T=0.673K>TC+4mK
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
All data collapse assuming
Toronto 2008
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Random-field dominatedQuantum dominated
Toronto 2008
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
Toronto 2008
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
Toronto 2008
Experimental SetupExperimental Setup
~ Ht2
Toronto 2008
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)
Toronto 2008
Toronto 2008
Domain Wall TunnelingDomain Wall Tunneling
w
⎟⎟⎠
⎞⎜⎜⎝
⎛− BE
Mw
2
2exp~
h
Toronto 2008
Evolution of themost mobile
Domain Walls
Evolution of themost mobile
Domain Walls
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛−+−=
2
22expexp
hm
wTFf oo
thermal hopping
quantum tunneling
Toronto 2008
Domain Wall ParametersDomain Wall Parameters
( )iaN
Γ+Γ⋅=
⋅=
2
2
spinDW
2
mNm
h
N 10
Toronto 2008
What happens next?What happens next?
?
Toronto 2008
0.2 0.4 0.6T(K)
x=0.167Spin glass
Toronto 2008
Toronto 2008
f Re / Im ~ "~f-
Glass transition when =0
f Re / Im ~ "~f-
Glass transition when =0
Toronto 2008
Revisited more recently (2008) with x=0.198% Ho Revisited more recently (2008) with x=0.198% Ho
Toronto 2008
Consistent with non-linear susceptibilityConsistent with non-linear susceptibility
Toronto 2008
Toronto 2008
Toronto 2008
?
Toronto 2008
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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)