electron coherence in the presence of magnetic impurities felicien schopfer wilfried rabaud crtbt...
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Electron coherence in the presence of magnetic impurities
Felicien Schopfer
Wilfried Rabaud
CRTBT
Laurent SaminadayarC.B.
Grenoble, France
The - problem
Mohanthy and Webb PRL 1997
theory: T - experiment: saturates at low T !
Does Fermi Liquid theory describe the ground state of a metal ?
K()
The - problem
Theory: experiment:but K()
Pothier et al. PRL 1997
The - problem
Akimoto et al. PRL 2003
Experimental data seem to diagree with Fermi Liquid theory
spin polarized 3He
Fermi liquidtheory
• Dephasing rate ~ quasiparticle inelastic rate i
1 ~
1
~ (kBT) p finite T
~ 0 T=0• phase space crunches to zero at T=0
• A disordered metal in low dimensions is still a Fermi liquid
Quasi-1D Disordered Conductors
Thigh at phonon - electron 3T
T lowat electron - electron 3/2T 1
Altshuler, Aronov, Khlemnitskii (82)
Ground state of an electron gas
• available phase space of final states for scattering
decoherence
e- - phonone- - magnetic impurities
(two level systems)(ext RF)
...
e- - e-
0K 1K 4K 300K
e- - magnetic impurity
e- -e- e- - phonon
How to measure the decoherence time
Via weak localisation
A
B
O
ij
jii
ii
iAB AAAAw2
2
In general 0ij
ji AA due to disorder average,but NOT for time reversed paths
2
121
2
2
2
10 4Re2 AAAAAw for time reversed paths
electron is « localised » at point O « weak localisation »
leads to quantum corrections of transport properties (R/R~ 10-3)
< l
t -tr r’
|A1+A2|2 = |A1|2 + |A2|2 + 2 Re (A1*A2) = cos (2 e/ħ )
Localization (return probability) is modified by applied flux.
Aharonov-Bohm phase acquired by the loops:
. .
1 1 2 2A A A Ai i
B Area B Areae e
Applied magnetic flux
Weak localisation in external magnetic field
Weak localisation near zero field
Grain boundaries
Quenched impurities
Flux
|A|2
R
Magnetic field
Weak localization
wll = D
quasi 1D conductor
w
l
Weak localisation
R/R
*10-4
-2000 0 2000-0.8
-0.6
-0.4
-0.2
0
0.2
690 mK2.10 - 5
B (G)
theory (Hikami et al. )
l m for very pure samples
example: quasi 1D gold wire
Kondo effect
spin flip scattering
e-
purely elastic !!
energy scale
Kondo effect
R/R0
T (K)
Fe/Cu
0.05% Fe
0.1% Fe
0.2% Fe
T << TK :
non magnetic ground state « spin singlet »
single impurity model (q, S)
coupling of magnetic impurity with conduction electrons
screening
of charge q spin S
Kondo-cloud
T= 0: unitary limit: complete screening of magnetic impurity spin
Kondo effect
T
R unitary limit
TK TTK
T
For T « TK Fermi liquid theory should be valid again (s=1/2)
Nozières 1974
log
Ground state of Kondo system
2D films
Bergmann et al. PRB 89
T 1/2
T 2
Nozières 74’
TK
low temperature behaviour is NOT described by Fermi liquid theory
Kondo system Au/Fe
Laborde 71’
well known Kondo system
easy to use for nanolithography
no surface oxidationTmeasure < TK < phonon
0.2
ncm
/ppm
TK
Experimental set-up
eV < kBT
sample
Tmin = 5mK
RF filtering
-60
-50
-40
-30
-20
-10
0
0 5 10 15 20
thermocoax 30cm 1.54K S21
Att
énu
ati
on
[d
B]
f [GHz]
Att
én
ua
tion
(d
B)
f (GHz)
30 cm-420 dB at 20 GHz
Thermocoax®
Iinj = 2 nA
Weak localisation signal: V 10-4 V
Electrical resistivity
3352
3353
3354
3355
6982
6986
6990
6994
10 100 1000
60 ppm
15ppm
T (mK)
(n
cm) (n
cm
)
B=0T
3 contributions: weak loc + e-e interaction + magnetic impurities
T ln(T/TK)
maximum is due to magnetic impurities
2.5
3
3.5
4
4.5
5
5.5
6
6.5
1 10 100 1000
-2000 -1000 0 1000 2000-4
-2
0
2
4
6
20 mK
75 mK
160 mK
590 mK
900 mK
2.10 - 4
Weak localisation
-2000 0 2000-0.8
-0.6
-0.4
-0.2
0
0.2
690 mK2.10 - 5
lI (nA)
l
m
B (G) B (G)
R/R
*10
-4
R/R
*10
-4
25 mK
0.01
0.1
1
0.1
1
10
10 100 1000
60 ppm
15 ppm
(ns
) (ns)
T (mK)
Three distinct temperature regimes
T-2/3
T-3
TK
phase coherence time
(AAK)
0
0.2
0.4
0.6
0.8
1
0 200 400 600
Au6, Mohanthy et al.Au_MSUAg_SaclayAu/Fe_Grenoble
1/
(ns
-1)
T (mK)
0
20
40
60
80
100
120
0 200 400 600 800
15ppm
60 ppm
T(mK)1/
(
ns-1)
Linear variation of with T is an experimental fact !
0
1
2
3
4
5
6
3351
3352
3353
3354
3355
10 100 1000
15 ppm
0.1
1
10
10 100 1000
T (mK)T (mK)
(
ns
)
(
ns)
(ncm
)
TK
new regime
saturation at LT
maximum in (T)
T- variation of (T) and (T) are correlated
versus (T)
Resistance maximum
Au/Fe Cu/Mn
maximum in R(T) is a signature of a spin glass formation
Laborde 71’
Kondo effect : RKKY interactions :
screening of impurity spin via the conduction electrons
TK
T << TK : unitary limit
complete screening of the magnetic impurity spin
Fermi liquid theory should apply
between the impurity spins via the conduction electrons
Tfreeze
T < Tf :
leads to magnetic ordering at Tf
random spin configuration destroys phase coherence
Competition between screening of magnetic impurities and spin glass formation
0.01
0.1
1
10
10 100 1000 104
magneticnonscatteringspinmeasure
111
1/non-magnetic
theoretical expectations (AAK)
T (mK)
1/
(ns
-1)
measure1
1/spin-scattering
allows to extract spin scattering rate
0
0.05
0.1
0.15
0.2
3356
3356
3356
3357
3358
3358
3359
10 100 1000
15 ppm
1/ s
(n
s-1)
(ncm
)
T (mK)
TK
Spin scattering rate s
constant spin scattering rate in spin glass regime
onset of RKKY interactions
0.1
1
10
100
0.05
0.1
0.15
0.2
10 100 1000
1/ s
(n
s-1) 1/
s (ns -1
)
T (mK)
T1/2
Spin scattering rate s
T 1/2
T 2
Nozières 74’
Bergmann PRB 89’Schopfer et al., PRL 03
Conclusions
when working with metals which « almost » always contain magnetic impurities, one has to worry about 2 energy scales :
TK and Tf
leads to saturation of
way out of this dilemma:
cleaner materials (semi conductors)
measurements in high magnetic field
even in the presence of very diluted magnetic impurities, RKKY interactions are important