1. GDR-Physique Quantique Mésoscopique, 8-11 Décembre 2008
Microscopic Origin of CPP-GMR…
SPIN ACCUMULATION
& SPIN DIFFUSION
Henri JAFFRES
Unité Mixte de Physique CNRS/Thales et Université Paris Sud 11
a terrific example of how fundamental research can lead to cutting-edge technology, which in turn feeds back into fundamental research -- in this case, possibly enabling future breakthroughs in nanotechnology and quantum computing.
GDR-Physique Quantique Mésoscopique, 8-11 Décembre 2008

2. Spin-polarized transport in 3d Ferromagnet
*) two current model by Mott M
Ex: Co
Transport du courant en parallèle pa un canal d’ ⓔ de spin  et un canal de spin 
Résistivité dans chaque canal proportionnelle au nombre de transition sd EF s d
*) Equivalent resistor scheme
*) Bulk spin asymetry coefficient

3. CPP-GMR & SPIN ACCUMULATION
NANOWIRES : Co Co
H(kG)
(NiFe50Å)/Cu40Å)
(Co100Å/Cu50Å)
Piraux et al.; Appl. Phys. Lett. 65, 2484 (1994)
Blondel et al.; Appl. Phys. Lett. 65, 3019 (1994)
First measurements of CPP-GMR in 2-D multilayers, see Schroeder, Bass, Pratt (MSU)
For a review see Barthélémy et al., Handbook of Magn. Mat., vol.12, edt by K.J.Buschow , Elsevier(1999)

4. CPP-GMR & SERIES RESISTANCE MODEL
P configuration
AP configuration M NM M M NM M  
CONDITIONS :
thickness << Spin Diff. Length lsf
&
Spin relaxation negligible in Cu   r R
R  = (r+R)/2
R  = (R+r)/2
R  = r r r
SPIN ACC. R R
Current spin polarization
R  = R
GMR as a probe of the current spin polarization
T. Valet - A. Fert, PRB (1993)

5. IN MAGNETIC MULTILAYER
SPIN ACCUMULATION
IN MAGNETIC MULTILAYER s s d d

6. Ferromagnet ( ex: Fe, Co ) current Spin Polarization
Interface FM/NM : mécanisme d’injection de spins
Spin Polarization
ex: Co = 0.46
Mott, Proc. Roy. Soc. 156, 368 (1936)
Campbell-Fert, Ferrom. mater, vol.3, 717 (1982)
Ferromagnet ( ex: Fe, Co )
Non magnetic
( ex: Cu, GaAs )
zone of spin accumulation
Splitting of  and  Fermi levels 
current Spin Polarization
diffusive spin current
Van Son, PRL 58 (1987)

7. Good conductivity matching for metals
Injection métal magnétique  métal non magnétique FM NM
T. Valet, A. Fert, PRB 1993
number of spin flips in F
accum. spins in FM
accum. spins in NM
number of spin flips in NM
Good conductivity matching for metals

8. Profile n(x) of carrier density
DIFFUSIVE CURRENT
Profile n(x) of carrier density Jl
n(x)
current J ? Jr
: mean free path z
Diffusion constant

9. (related to band filling)
DIFFUSION CURRENT
carrier density
Fermi level
density of states EF
EF,0=equilibrium
chemical potential
(related to band filling)
EF=c

10. DRIFT CURRENT Ohm’s law
Drift current JE in the presence of an electric field E
*) average velocity acquired by a particle between 2 successive diffusions
Momentum relaxation time :
Displacement of the Fermi surface
drift velocity
Electrical potential
Ohm’s law

11. ELECTROCHEMICAL POTENTIAL
relaxation term
phenomenological

12. DIFFUSION Vs. BROWNIAN MOTION ( E=0 )
Diffusion equation S
*) EXPLORATION RADIUS
 mean free path
*) NUMBER OF SURFACE ‘S’ CROSSINGS

13. SPIN ACCUMULATION & SPIN CURRENT
p ,  (mean free path)
sf, lsf
(spin diffusion length)
t=0
lsf

14. CHEMICAL vs. ELECTRICAL POTENTIALSd d eV
zone of spin accumulation Co Cu

15. LINK BETWEEN SPIN CURRENT
& SPIN ACCUMULATION

16. SPIN ACCUMULATION & SPIN CURRENT
diffusive spin current FM NM
Interface
z=0
Current
polarization
continuity of
spin current Co Cu
= spin-polarized current at the interface

17. SIMPLE SCHEME FOR MAGNETORESISTANCEFM
Interface
z=0 NM
potential drop at
the interface

18. Positive MR CONTACT RESISTANCE Vs. SPIN ACCUMULATION SPIN ASSYMETRY
Paramagnetic
electrodes
SPIN ASSYMETRY
FERROM. RESISTIVITY
 FERROM. SPIN DIFF. LENGTH
 CHARACTERISTIC RESISTANCE

19. EFFETS DE BULK + INTERFACEFM NM

20. CPP-GMR & SPIN ACCUMULATION
NANOWIRES : Co Co
H(kG)
(NiFe50Å)/Cu40Å)
(Co100Å/Cu50Å)
Piraux et al.; Appl. Phys. Lett. 65, 2484 (1994)
Blondel et al.; Appl. Phys. Lett. 65, 3019 (1994)
First measurements of CPP-GMR in 2-D multilayers, see Schroeder, Bass, Pratt (MSU)
For a review see Barthélémy et al., Handbook of Magn. Mat., vol.12, edt by K.J.Buschow , Elsevier(1999)

21. CPP-GMR & SERIES RESISTANCE MODEL
P configuration
AP configuration M NM M M NM M  
CONDITIONS :
thickness << Spin Diff. Length lsf
&
Spin relaxation negligible in Cu   r R
R  = (r+R)/2
R  = (R+r)/2
R  = r r r
SPIN ACC. R R
Current spin polarization
R  = R
GMR as a probe of the current spin polarization
T.Valet - A. Fert, PRB (1993)

22. SPIN-SWITCH : DETECTION ELECTRIQUE D’UNE ACCUMULATION DE SPINS
Principle : Johnson and Silsbee, PRL 55, 1790 (1985) ; PRB 37, 5312 (1988)
Experiments : Jedema et al., Nature 410, 345 (2001)
A. Fert & al., J. Phys. D : Appl. Phys 35, 2443 (2002) ; J.-M. George PRB (2003)
spin injection into Cu (N) through a first magnetic electrode
magnetic third contact
 100 nm

23. Good conductivity matching for metalsFM NM
T. Valet, A. Fert, PRB 1993
accum. spins in FM
accum. spins in NM
number of spin flips in F
number of spin flips in NM
Good conductivity matching for metals

24. discontinuity of EF,  and EF,  at interface = (1 ) rb j,
Rashba PRB 62,R16267 (2000); Fert-Jaffres PRB 64, (2001)
discontinuity of EF,  and EF,  at interface = (1 ) rb j,
large interface resistance  large discontinuity of EF 
number of spin flip in F 
number of spin flip in SC
 Increase of the spin diffusive current in the semiconductor

25. CASE OF MULTILAYERS accumulation vector at left accumulation vector
Co  Cu
Co  Cu
accumulation vector at left
accumulation vector
at right
propagation matrix
transfer matrix
interface matrix

27. Ferromagnet ( ex: Fe, Co ) current Spin Polarization
Interface FM/NM : mécanisme d’injection de spins
Spin Polarization
ex: Co = 0.46
Mott, Proc. Roy. Soc. 156, 368 (1936)
Campbell-Fert, Ferrom. mater, vol.3, 717 (1982)
Ferromagnet ( ex: Fe, Co )
Non magnetic
( ex: Cu, GaAs )
zone of spin accumulation
Splitting of  and  Fermi levels 
current Spin Polarization
diffusive spin current
Van Son, PRL 58 (1987)

28. FM NM
T. Valet, A. Fert, PRB 1993

29. discontinuity of EF,  and EF,  at interface = (1 ) rb j,
Rashba PRB 62,R16267 (2000); Fert-Jaffres PRB 64, (2001)
discontinuity of EF,  and EF,  at interface = (1 ) rb j,
large interface resistance  large discontinuity of EF 
number of spin flip in F 
number of spin flip in SC
 Increase of the spin diffusive current in the semiconductor

30. Magnetic tunnel junction : Spin-dependent Interface resistanceFM I SC
Tunnel junction =
Spin-Dependent interface resistance
 P : polarisation

31. SPIN INJECTION : MICROSCOPIC MODEL OF DIFFUSION
current polarization ? NO
YES FM SC ? FM  SC FM SC FM  d
Sink
Sink 
Probe ? ?
resistive interface ( T )
Current polarization :
Current polarization :

32. Spin Accumulation Vs. Spin CurrentFM I SC

33. EFFETS DE BULK + INTERFACEFM NM

34. EFFETS DE BULK + INTERFACEFM NM

35. + - CoFe MgO AlGaAs(n) GaAs AlGaAs(p) Spin LED
Coll., LPCNO TOULOUSE (X. Marie)

36. Electrical spin injection & optical detection
Polarisation-resolved Electroluminescence experiments 1 3 s+
s - H s- s+ s- s+
Measure of the circular polarization(Pc)
Determine the current spin-polarization injected in the Quantum well
I+ - I-
I+ + I-
Pc (EL) =
« Injection and detection of a spin-polarized current in a light-emitting diode », R. Fiederling et al., Nature 402, 787 (1999)

37. Zhu et al., Phys. Rev. Lett. 87, 016601 (2001)
INJECTION INTO (Al)GaAs THROUGH A SCHOTTKY BARRIER : DETECTION BY ELECTROLUMINESCENCE MEASUREMENTS
TG=10°C
Hanbicki et al., Appl. Phys. Lett. 80, 1240 (2002)
Zhu et al., Phys. Rev. Lett. 87, (2001)
Ploog, J. Appl. Phys., 91 (10), 7256 (2002)
TG=50°C

38. INJECTION INTO GaAs THROUGH AN OXIDE BARRIER (Al2O3)
V.F. Mostnyi, V.I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) 1
SZ  2.5%  Pelec. >10 %
P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol.42, L502 (2003)
SZ  8%  Pelec. >24 %
sputtering
MBE
100 nm
Oblique Hanle Effect (OHE)

39. INJECTION INTO GaAs THROUGH AN OXIDE BARRIER (Al2O3)
V.F. Mostnyi, V.I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) 1
SZ  2.5%  Pelec. >10 %
P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol.42, L502 (2003)
SZ  8%  Pelec. >24 %
sputtering
MBE
100 nm
Oblique Hanle Effect (OHE)

40. OPTICAL DETECTION OF SPIN ACCUMULATION IN GaAs

41. Injection électrique et détection optique de spina)
Croissance
T° ambiante b)
Croissance
300° C
Circular polarization Vs. perpendicular magnetic field
Y. Lu et al., Appl. Phys. Lett. 93, (2008)

42. Measurement of t(T) et ts (T) et F(T) by Time-Resoloved PL experiments
 Lifetime and S spin relaxation time
PC = F*Ps
Ps is the spin-polarization of electrons injected in the QW
F(T) = 1
1+(T)/ S(T))

43. Mg0 thickness dependence on spin-injection yield
Sample
Thickness (nm) A
1.4 B2
2.6 C
4.3
The EL Spin-polarization increases
With MgO thickness B2 A C

44. MR vs. characteristic times…
‘Courant de spin de rétrodiffusion’
injection
détection

46. HANLE EFFECT = DEPOLARIZATION BY SPIN PRECESSION AROUND A TRANSVERSE MAGNETIC FIELD

50. Hanle effect

51. A SINGLE CONTACT EXPERIMENT……
n  51018 cm-3
n  21019 cm-3 w L 2 1 W M I
GaAs Co
Al2O3 H
Coll. LPN Marcoussis (A. Lemaitre)

52. VARIATION OF THE CONTACT RESISTANCE ……
( NO WEAK LOCALIZATION EFFECT ! )

53. Electrical measurements…B C a b

54. Electrical measurements…B C a b
Kerr effect…

56. Resume : MR Vs. INTERFACIAL RESISTANCE (CPP GEOMETRY)
A. Fert, H. Jaffrès. Phys. Rev. B, 64, (2001) FM SC d
NO SPIN INJECTION +
NO SPIN DETECTION
INJECTION & DETECTION