Electron coherence in the presence of magnetic impurities Felicien Schopfer Wilfried Rabaud CRTBT Laurent Saminadayar C.B. Grenoble, France.

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