Transcript Electron Cherence in the presence of magnetic impurities

CRTBT
Grenoble, France
Electron coherence in the
presence of magnetic impurities
Felicien Schopfer
Wilfried Rabaud
Laurent Saminadayar
C.B.
The tf - problem
Mohanthy and Webb
PRL 1997
theory:
tf  T -a
experiment:
tf
saturates at low T !
The tf - problem
Pothier et al. PRL 1997
Theory:
K(e)  e2
but
experiment:
K(e)
 e3/2
Does Fermi Liquid theory describe the ground state of a metal ?
The tf - problem
spin polarized 3He
Fermi liquid
theory
Akimoto et al. PRL 2003
Experimental data seem to diagree with Fermi Liquid theory
Ground state of an electron gas
• A disordered metal in low dimensions is still a Fermi liquid
• Dephasing rate ~ quasiparticle inelastic rate
• available phase space of final states for scattering
• phase space crunches to zero at T=0
1
tf
~
1
ti
1/t ~ (kBT) p
~
0
finite T
T=0
Quasi-1D Disordered Conductors
1
 T 2/3
t
f
 T3
electron - electron
at low T
electron - phonon
at high T
Altshuler, Aronov, Khlemnitskii (82)
decoherence
e-
-
e-
e- - magnetic impurities
e- - phonon
(two level systems)
(ext RF)
...
e- - magnetic impurity
e- -e-
0K
e- - phonon
1K
4K
300K
How to measure the decoherence time
< lf
Via weak localisation
B
wAB 
A
2
i
i
  Ai   Ai Aj
2
i
ij
A
O
 AA
In general
i
ij
j
0
due to disorder average,
but NOT for time reversed paths
w0  A1  A2  2 Re A1 A2  4 A1
2
2
2
for time reversed paths
electron is « localised » at point O
« weak localisation »
leads to quantum corrections of transport properties (DR/R~ 10-3)
Weak localisation in external magnetic field
Aharonov-Bohm phase acquired by the loops:

r
A1  A1e


i
B. Area
A2  A2e
i
B. Area
|A1+A2|2 = |A1|2 + |A2|2 + 2 Re (A1*A2)
= cos (2 e/ħ F)
r’
t  -t
Applied magnetic flux F
Localization (return probability) is modified
by applied flux.
Weak localisation near zero field
quasi 1D conductor
w
Grain boundaries
Quenched impurities
l
|A|2
Flux
DR
wlf
Weak localization
lf = D t f
Magnetic field
Weak localisation
theory (Hikami et al. )
example: quasi 1D gold wire
0.2
DR/R*10-4
0
-0.2
-0.4
2.10
-5
690 mK
-0.6
-0.8
-2000
0
2000
B (G)
lf
 mm for very pure samples
Kondo effect
espin flip scattering
purely elastic !!
energy scale
Kondo effect
single impurity model (q, S)
R/R0
Fe/Cu
coupling of magnetic impurity with
conduction electrons
0.2% Fe
T << TK :
screening
of charge q
spin S
0.1% Fe
Kondo-cloud
0.05% Fe
non magnetic ground state « spin singlet »
T= 0: unitary limit: complete screening of magnetic impurity spin
T (K)
Kondo effect
R
tf
unitary limit
TK
log T
Ta
TK
T
For T « TK Fermi liquid theory should be valid again (s=1/2)
Nozières 1974
Ground state of Kondo system
2D films
TK
T 1/2
T2
Nozières 74’
Bergmann et al. PRB 89
low temperature behaviour is NOT described by Fermi liquid theory
Kondo system Au/Fe
0.2 nWcm/ppm
Laborde 71’
TK
well known Kondo system
easy to use for nanolithography
no surface oxidation
Tmeasure < TK < phonon
Experimental set-up
RF filtering
thermocoa x 30cm 1.54K S21
0
30 cm
-420 dB at 20 GHz
Atténuation [dB]
(dB)
Atténuation
-10
eV < kBT
-20
-30
-40
-50
Thermocoax®
-60
0
10
ff (GHz)
[GHz]
sample
Tmin = 5mK
5
Iinj = 2 nA
Weak localisation signal: DV  10-4 mV
15
20
Electrical resistivity
B=0T
60 ppm
3355
6994
3354
6986
3353
15ppm
r (nWcm)
r (nWcm)
6990
6982
3352
10
100
1000
T (mK)
3 contributions:
weak loc
+ e-e interaction
a
T
+ magnetic impurities
ln(T/TK)
maximum is due to magnetic impurities
Weak localisation
6
0.2
4
0
DR/R *10-4
590 mK
160 mK
2
75 mK
20 mK
0
2.10
-4
-2
-4
-2000
-1000
0
1000
-0.2
-0.4
2.10
-5
-0.8
2000
-2000
6
25 mK
5.5
5
4.5
4
3.5
3
2.5
0
B (G)
6.5
lf
690 mK
-0.6
B (G)
lf (mm)
DR/R *10-4
900 mK
1
10
100
I (nA)
1000
2000
phase coherence time tf
T-2/3 (AAK)
15 ppm
0.1
T-3
10
1
TK
0.01
0.1
60 ppm
10
100
1000
T (mK)
Three distinct temperature regimes
tf (ns)
tf (ns)
1
1
Au6, Mohanthy et al.
Au_MSU
Ag_Saclay
Au/Fe_Grenoble 15ppm
120
100
0.6
1/tf (ns-1)
1/tf (ns -1)
0.8
0.4
80
60
40
20
0.2
0
0
60 ppm
200
400
T(mK)
0
0
200
400
600
T (mK)
Linear variation of tf with T is an experimental fact !
600
800
tf versus r(T)
maximum in r(T)
3355
6
saturation at LT
5
new regime
tf (ns)
tf (ns)
3354
4
3353
3
2
1
3352
1
TK
0.1
10
100
T (mK)
3351
1000
0
10
100
1000
T (mK)
T- variation of
r(T) and tf(T) are correlated
r (nWcm)
10
15 ppm
Resistance maximum
Au/Fe
Cu/Mn
Laborde 71’
maximum in R(T) is a signature of a spin glass formation
Kondo effect :
RKKY interactions :
screening of impurity spin via
the conduction electrons
between the impurity spins via
the conduction electrons
TK
Tfreeze
T << TK : unitary limit
complete screening of the
magnetic impurity spin
Fermi liquid theory should apply
T < Tf :
leads to magnetic ordering at Tf
random spin configuration
destroys phase coherence
Competition between screening of magnetic impurities
and spin glass formation
1
tf
measure

1
t spin scattering

1
t non magnetic
1/tf (ns-1)
10
1/tspin-scattering
1 tf
measure
1
0.1
1/tnon-magnetic
theoretical expectations
(AAK)
0.01
10
100
1000
T (mK)
allows to extract spin scattering rate
104
Spin scattering rate ts
0.2
3359
TK
15 ppm
3358
3358
0.1
3357
3356
0.05
3356
constant spin scattering
rate in spin glass regime
0
3356
10
100
1000
T (mK)
onset of RKKY interactions
r (nWcm)
1/ts (ns-1)
0.15
Spin scattering rate ts
Bergmann PRB 89’
100
0.2
10
0.15
1
0.1
1/ts (ns-1)
1/ts (ns-1)
Schopfer et al., PRL 03
T 1/2
T2
Nozières 74’
T1/2
0.1
0.05
10
100
T (mK)
1000
Conclusions
even in the presence of very diluted magnetic impurities, RKKY
interactions are important
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 tf
way out of this dilemma:
cleaner materials (semi conductors)
measurements in high magnetic field