Transcript Chasing down coherent magnetic excitations in solids

LiHoxY1-xF4: The road between
solid state ion trap and quantum
critical ferromagnet
Gabriel Aeppli
London 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
Sharp nuclear levels at microwave
frequencies (~10GHz)
Hyperfine
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)
interaction with
nuclear spins
(I=7/2)
A=0.039 K
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%
Coupling, disorder and transverse fields
µj
Exchange is negligible because of the extreme
localization of the electrons
µi
Ions coupled instead by pure magnetic dipole
interaction (weak but precisely known):
H^ dipolar =
L ¹i j º
¹ º
´
±
¹ 0 (gL ¹ B ) 2
4¼
2
j r i j j ¡ 3r ¹i j
jr i j j5
2
r ºi j
P
P
ij
¹º
L ¹i j º J^i¹ J^jº
2
Ion i
/ 1 ¡ 3cosµi µj
In low-energy, 2-state limit for ordered material this
P
becomes
1
e® z z
^ e®
H dipolar =
rij
ij
Vi j ¾
^i ¾
^j
Ion j
Note anisotropy
of interaction
Magnitude of interaction is
0.214 K for r=a
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
But…we expect non-classical behaviour to be obtained by introduction of
transverse fields or by disorder
A three-dimensional quantum magnet - with
decoherence due to spectators
Realizing the transverse field Ising model, where
can vary G – LiHoF4
c
Ho
Li
F
b
a
Toronto 2008
•g=14 doublet
•9K gap to next state
•dipolar coupled
Realizing the transverse field Ising model, where
can vary G – LiHoF4
c
Ho
Li
F
b
a
Toronto 2008
•g=14 doublet
•9K gap to next state
•dipolar coupled
c 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 …
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165Ho3+
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J=8 and I=7/2
A=3.36meV
W=A<J>I
~ 140meV
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Diverging c
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Dynamics
DW
=
N
N
i, j
i
H   J i , j  iz  zj  G ix
• The Ising term energy gap 2J
• The G term does not commute with
DW
Need traveling wave solution:
• Total energy of flip
 k  2k 2 2m
E  2 J  Ga 2 k 2
2

m 

Toronto 2008
a
2Ga 2
DW
=
N
N
i, j
i
H   J i , j  iz  zj  G ix
• The Ising term energy gap 2J
• The G term does not commute with
DW
Need traveling wave solution:
• Total energy of flip
 k  2k 2 2m
E  2 J  Ga 2 k 2
2

m 

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a
2Ga 2
DW
=
N
N
i, j
i
H   J i , j  iz  zj  G ix
• The Ising term energy gap 2J
• The G term does not commute with
DW
Need traveling wave solution:
• Total energy of flip
 k  2k 2 2m
E  2 J  Ga 2 k 2
2

m 

Toronto 2008
a
2Ga 2
DW
=
N
N
i, j
i
H   J i , j  iz  zj  G ix
• The Ising term energy gap 2J
• The G term does not commute with
DW
Need traveling wave solution:
• Total energy of flip
 k  2k 2 2m
E  2 J  Ga 2 k 2
2

m 

Toronto 2008
a
2Ga 2
DW
=
N
N
i, j
i
H   J i , j  iz  zj  G ix
• The Ising term energy gap 2J
• The G term does not commute with
DW
Need traveling wave solution:
• Total energy of flip
 k  2k 2 2m
E  2 J  Ga 2 k 2
2

m 

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a
2Ga 2
Energy Transfer (meV)
Spin Wave excitations in
the FM LiHoF4
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1
1.5
 

h
,
0
,
0


a


2
Energy Transfer (meV)
Spin Wave excitations in
the FM LiHoF4
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1
1.5
 

h
,
0
,
0


a


2
What happens near QPT?
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•H. Ronnow et al.
Science (2005)
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W=A<J>I
~ 140meV
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wider significance
•
Connection to ‘decoherence’ problem in mesoscopic systems
‘best’
ElectronicTFI
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d2/dWdw=Sf|<f|S(Q)+|0>|2d(w-E0+Ef) where
S(Q)+ =SmSm+expiq.rm
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Where does spectral weight go & diverging correlation length
appear?
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Ronnow et al, unpub (2006)
Introducing complexity via randomness
& dipolar interaction …
dipolar interaction between randomly
placed spins leads to frustration
E=S1S2g2MB2[1-3(rz/r)2]/r3
ferro for (rz/r)2 >1/3
antiferro for (rz/r)2 <1/3
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Experimental realization of Ising model in
transverse field
LiHoF4
c
Ho
Li
F
b
a
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•g=14 doublet
•9K gap to next state
•dipolar coupled
Experimental realization of Ising model in
transverse field
LiHoF4
c
Y
Ho
Li
F
b
a
Toronto 2008
•g=14 doublet
•9K gap to next state
•dipolar coupled
Experimental realization of Ising model in
transverse field
LiHoF4
c
Y
Ho
Li
F
b
a
Toronto 2008
•g=14 doublet
•9K gap to next state
•dipolar coupled
What happens first?
x=0.67
still
ferromagnetic
Tc=xTc(x=1)
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x=0.44
also still
ferromagnetic
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Two effects: quantum mechanics + classical random
fields
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Strong random field effects near Ht=0 and T=TCMF
/d
Thermal
cT-TC
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
/d/2
Toronto 2008
Transverse field
cG/d
Griffiths singularities at T=0.673K>TC+4mK
All data collapse assuming
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Toronto 2008
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Quantum dominated
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Random-field dominated
Domain wall state pinned by random configurations of
Y not much different from that at 300K in PdCo-
What about
domain
wall dynamics?
Y-A. Soh and G.A.,unpublished
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How to see?
• Measure small signal response
M(t)=c’(w)hcos(wt)+c(w)”hsin(wt)
where
• c=c’+ic” is complex susceptibility
• hcos(wt) is excitation
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Experimental Setup
G ~ Ht2
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J.Brooke, T.F.Rosenbaum & G.A, Nature 413,610(2001)
The Spectral Response
Four parameters:
1. c(f)
2. fo
3.
4.
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log slope
frolloff
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Domain Wall Tunneling


2M

~ exp  w
E
B 
2



w
D
Toronto 2008
Evolution of the
most mobile
Domain Walls
quantum tunneling
thermal hopping



2mG

f  Fo exp( D G T )  exp  2wo
D G 
2




Toronto 2008
Domain Wall Parameters
m DW  N  m spin
2
N 2
2a (G  Gi )
N 10
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What happens next?
?
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x=0.167
Spin glass
0.2
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0.4 0.6
T(K)
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/f Re c / Im c ~ 
c "~f-
Glass transition when =0
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Revisited more recently (2008) with x=0.198% Ho
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Consistent with non-linear susceptibility
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?
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Dynamic properties (I): the anti-glass and its
relaxation
Dilute system shows loss of low-frequency tail in dissipative
(imaginary) part of response.
Inference: fewer slow relaxations as temperature is lowered
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)
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
Ghost et al
Science 216
2195 (2002)
Suggests low-frequency continuum is of oscillators, not just relaxation
Antiglass
An RVB-like
state
analagous to
Si:P (BhattLee)
But experiment seems to favour in-plane
(AFM) pairs
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (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)