1. Electron coherence 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.

2. The tf - problem tf  T -a tf theory: experiment: saturates at low T !
Mohanthy and Webb
PRL 1997
tf  T -a tf
theory:
experiment:
saturates at low T !

3. The tf - problem
Pothier et al. PRL 1997
K(e)  e2
K(e)  e3/2
Theory:
but
experiment:
Does Fermi Liquid theory describe the ground state of a metal ?

4. The tf - problem spin polarized 3He
Fermi liquid
theory
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
~ T=0
phase space crunches to zero at T=0
Quasi-1D Disordered Conductors
Altshuler, Aronov, Khlemnitskii (82)

6. decoherence e- - magnetic impurities e- - phonon e- - e- ... 0K 1K 4K
(two level systems)
(ext RF)
...
e- - magnetic impurity
e- -e-
e- - phonon 0K 1K 4K
300K

7. How to measure the decoherence time
< lf
Via weak localisation A B O
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:
t  -t r r’   
|A1+A2|2 = |A1|2 + |A2|2 + 2 Re (A1*A2)
= cos (2 e/ħ F)
Localization (return probability) is modified by applied flux.
Applied magnetic flux F

9. Weak localisation near zero field
quasi 1D conductor w
Grain boundaries
Quenched impurities l
Flux
|A|2 DR
Weak localization
lf =
wlf
Magnetic field

10. lf Weak localisation  mm for very pure samples theory
(Hikami et al. )
example: quasi 1D gold wire
DR/R*10-4
B (G) lf
 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
coupling of magnetic impurity with conduction electrons
Fe/Cu
0.2% Fe
T << 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 R TK TK T T T a unitary limit log
For T « TK Fermi liquid theory should be valid again (s=1/2)
Nozières 1974

14. Ground state of Kondo system
2D films
T 1/2
T 2
Nozières 74’ TK
Bergmann et al. PRB 89
low temperature behaviour is NOT described by Fermi liquid theory

15. Kondo system Au/Fe 0.2 nWcm/ppm TK well known Kondo system
Laborde 71’
0.2 nWcm/ppm TK
well known Kondo system
easy to use for nanolithography
Tmeasure < TK < phonon
no surface oxidation

16. Experimental set-up RF filtering -420 dB at 20 GHz eV < kBT sample
Atténuation (dB)
f (GHz)
30 cm
-420 dB at 20 GHz
eV < kBT
Thermocoax®
sample
Tmin = 5mK
Iinj = 2 nA
Weak localisation signal: DV  10-4 mV

17. Electrical resistivity
B=0T
r (nWcm)
r (nWcm)
T (mK)
3 contributions:
weak loc e-e interaction magnetic impurities a T
ln(T/TK)
maximum is due to magnetic impurities

18. lf Weak localisation lf (mm) DR/R *10-4 DR/R *10-4 B (G) B (G) 25 mK
I (nA)

19. phase coherence time tf
(AAK)
tf (ns)
tf (ns)
T-3 TK
T (mK)
Three distinct temperature regimes

20. 1/tf (ns -1) 15ppm 1/tf (ns-1) 60 ppm T(mK) T (mK)
Linear variation of tf with T is an experimental fact !

21. tf versus r(T) tf (ns) r (nWcm)
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 Au/Fe Cu/Mn
Laborde 71’
maximum in R(T) is a signature of a spin glass formation

23. TK Tfreeze 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
T < Tf :
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. allows to extract spin scattering rate
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 tsTK
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 TK and Tf leads to saturation of tf
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