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