Electron coherence in the presence of magnetic impurities

1
Electron coherence in the presence of magnetic
impurities
Grenoble, France

• Felicien Schopfer
• Wilfried Rabaud

Laurent Saminadayar C.B.
2
The tf - problem
Mohanthy and Webb PRL 1997
tf
tf ? T -a
experiment
saturates at low T !
theory
3
The tf - problem
Pothier et al. PRL 1997
K(e) ? e2
K(e) ? e3/2
experiment
Theory
but
Does Fermi Liquid theory describe the ground
state of a metal ?
4
The tf - problem
spin polarized 3He
Akimoto et al. PRL 2003
Experimental data seem to diagree with Fermi
Liquid theory
5
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

1/t (kBT) p finite T 0
T0

• phase space crunches to zero at T0

Quasi-1D Disordered Conductors
Altshuler, Aronov, Khlemnitskii (82)
6
decoherence
e- - magnetic impurities
e- - phonon
e- - e-
(two level systems) (ext RF) ...
e- - magnetic impurity
e- -e-
e- - phonon
1K
4K
300K
0K
7
How to measure the decoherence time
lt lf
Via weak localisation
In general
due to disorder average, but NOT for time
reversed paths
for time reversed paths
electron is localised at point O weak
localisation
leads to quantum corrections of transport
properties (DR/R 10-3)
8
Weak localisation in external magnetic field
Aharonov-Bohm phase acquired by the loops
?
?
?
A1A22 A12 A22 2 Re (A1A2)
cos (2 e/h F)
Localization (return probability) is modified by
applied flux.
Applied magnetic flux F
9
Weak localisation near zero field
quasi 1D conductor
w
l
DR
Weak localization
lf
wlf
Magnetic field
10
Weak localisation
theory
(Hikami et al. )
example quasi 1D gold wire
DR/R10-4
B (G)
? mm for very pure samples
11
Kondo effect
e-
spin flip scattering
purely elastic !!
energy scale
12
Kondo effect
single impurity model (q, S)
R/R0
Fe/Cu
coupling of magnetic impurity with conduction
electrons
0.2 Fe
T ltlt TK
screening
of charge q
spin S
0.1 Fe
Kondo-cloud
0.05 Fe
T (K)
non magnetic ground state spin singlet
T 0 unitary limit complete screening of
magnetic impurity spin
13
Kondo effect
tf
T a
TK
T
log
For T TK Fermi liquid theory should be valid
again (s1/2)
Nozières 1974
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Ground state of Kondo system
2D films
TK
Bergmann et al. PRB 89
low temperature behaviour is NOT described by
Fermi liquid theory
15
Kondo system Au/Fe
Laborde 71
0.2 nWcm/ppm
TK
well known Kondo system
easy to use for nanolithography
no surface oxidation
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Experimental set-up
RF filtering
-420 dB at 20 GHz
eV lt kBT
Thermocoax
sample
Iinj 2 nA
Tmin 5mK
Weak localisation signal DV ? 10-4 mV
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Electrical resistivity
B0T
r (nWcm)
r (nWcm)
T (mK)
weak loc e-e interaction magnetic
impurities
3 contributions
a
T
ln(T/TK)
maximum is due to magnetic impurities
18
Weak localisation
DR/R 10-4
DR/R 10-4
B (G)
B (G)
25 mK
lf (mm)
I (nA)
19
phase coherence time tf
(AAK)
T-2/3
tf (ns)
tf (ns)
T-3
TK
T (mK)
Three distinct temperature regimes
20
15ppm
1/tf (ns-1)
60 ppm
T(mK)
Linear variation of tf with T is an experimental
fact !
21
tf versus r(T)
maximum in r(T)
saturation at LT
new regime
tf (ns)
r (nWcm)
tf (ns)
TK
T (mK)
T (mK)
T- variation of r(T) and tf(T) are correlated
22
Resistance maximum
Laborde 71
maximum in R(T) is a signature of a spin glass
formation
23
Kondo effect
RKKY interactions
between the impurity spins via the conduction
electrons
screening of impurity spin via the conduction
electrons
TK
Tfreeze
T ltlt TK
T lt Tf
unitary limit
complete screening of the magnetic impurity spin
leads to magnetic ordering at Tf
random spin configuration destroys phase coherence
Fermi liquid theory should apply
Competition between screening of magnetic
impurities and spin glass formation
24
1/tf (ns-1)
1/tnon-magnetic theoretical expectations (AAK)
1/tspin-scattering
T (mK)
allows to extract spin scattering rate
25
Spin scattering rate ts
TK
15 ppm
1/ts (ns-1)
r (nWcm)
constant spin scattering rate in spin glass regime
T (mK)
onset of RKKY interactions
26
Spin scattering rate ts
Schopfer et al., PRL 03
Bergmann PRB 89
1/ts (ns-1)
1/ts (ns-1)
T 1/2
T 2
Nozières 74
T1/2
T (mK)
27
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