Models in spintronics (Part I) OUTLINE : Spin-dependent transport - - PowerPoint PPT Presentation

SLIDE 1

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Models in spintronics (Part I)

OUTLINE : Spin-dependent transport in metallic magnetic multilayers

• Introduction to spin-electronics
• Spin-dependent scattering in magnetic metal
• Current-in-plane Giant Magnetoresistance
• Modelling transport in CIP spin-valves
• Current-perpendicular-to-plane Giant Magnetoresistance
• Spin accumulation, spin current, 3D generalization.

SLIDE 2

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Magnetic field (kG)

~ 80%

Fe/Cr multilayers

P P AP

R R R GMR  

Fert et al, PRL (1988), Nobel Prize 2007

Birth of spin electronics : Giant magnetoresistance (1988)

Antiferromagnetically coupled multilayers

I V

Current-in-plane

I

I I V

I

Current-perpendicular-to-plane

Two limit geometries of measurement:

SLIDE 3

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara B.Dieny et al, Phys.Rev.B.(1991)+patent US5206590 (1991).

Low field GMR: Spin-valves

1 2 3 4

R/R (%)

• 1

1

M (10

• 3 emu)

200 400 600 800

H(Oe)

• 200

1 2 3 4

R/R (%) H(Oe)

20 40

• 20
• 40

(c) (b) (a) Non magnetic spacer

Buffer layer

Soft ferromagnetic layer

substrate

Ferromagnetic pinned layer Antiferromagnetic pinning layer

Ta 50Å NiFe 70Å Cu 22Å NiFe 40Å FeMn 90Å

IBM Almaden Ultrasensitive magnetic field sensors (MR heads) Spin engineering

SLIDE 4

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Benefit of GMR in magnetic recording

GMR spin-valve heads from 1998 to 2004

SLIDE 5

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Two current model (Mott 1930) for transport in magnetic metals Sources of spin flip: magnons and spin-orbit scattering

      

                  

1

1 1

As long as spin-flip is negligible, current can be considered as carried in parallel by two categories of electrons: spin  and spin  (parallel and antiparallel to quantization axis) Negligible spin-flip often crude approximation (spin diffusion length in NiFe~4.5nm, 30% spin memory loss at Co/Cu interfaces)

SLIDE 6

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

D(EF) = D(EF)

Most of transport properties are determined by DOS at Fermi energy Spin-dependent density of state at Fermi energy

D (E) E D (E) E s (E) s(E) E E

Spin dependent transport in magnetic metals (1)

Band structure of 3d transition metals

Non-magnetic Cu : Magnetic Ni :

D(EF)  D(EF)

D (E) D (E) s (E) s(E)

In transition metals, partially filled bands which participate to conduction are s and d bands

SLIDE 7

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

m*(d) >> m*(s) J mostly carried by s electrons in transition metals Scattering of electrons determined by DOS at EF :

Fermi Golden rule :

Spin dependent transport in magnetic metals (2) Spin-dependent scattering rates in magnetic transition metals Example:

) (

2 F f E

D f W i    P

nm nm

Co Co

1 ; 10  

 

 

D(E) E D(E) s(E) s(E)

s s d s s d

Most efficient scattering channel

SLIDE 8

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Co/Cu minority electrons : parallel magnetic configuration Co/Cu minority electrons : parallel magnetic configuration Co/Cu majority electrons : parallel magnetic configuration

Co Co Cu Cu

(a) (b)

Co/Cu minority electrons : antiparallel magnetic configuration Co/Cu majority electrons : antiparallel magnetic configuration

z x U(x,z) (d) (c)

Parallel magnetic configuration Potential experienced by conduction electrons in magnetic metallic multilayers Antiparallel magnetic configuration

• Lattice potential modulation due to difference between Fermi energy and

bottom of conduction band (reflection, refraction)

• Spin-dependent scattering on impurities, interfaces or grain boundaries

(Dominant effect in GMR)

SLIDE 9

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Simple model of Giant Magnetoresistance

Parallel config

       

Equivalent resistances :

Antiparallel config

 ap             

2

  1  1    

2

   

Key role of scattering contrast 

Fe Fe Cr Fe Fe Cr

 

   

       2

P

 

2

 

    AP

SLIDE 10

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current-in-plane transport (semi-classical Boltzman theory of GMR) Approach initiated by Camley and Barnas, PRL, 63, 664 (1989) Gas of independent particles described by distribution f(r, v, t), submitted to force field F (=-eE for electrons in electrical field E). Time evolution of the distribution described by Boltzman equation:

t t+dt

Equilibrium function conserved in a volume element drdv along a flow line. In presence of scattering,

              

scattering F

dt df dt df dt df

f a f v t f a v f a v f a v f v z f v y f v x f t f dt df

v r z z y y x x z y x F

                                     



. . . . . . . .

with

F a m   

Balance between acceleration due to force and relaxation due to scattering

E

SLIDE 11

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

In stationary regime,

   t f

In single relaxation time approximation ()

 

 f f dt df

scatt

         f m F f v t f dt df dt df

v r scatt F

                       



. .

Where f0 is the equilibrium distribution (Fermi Dirac for electrons).

 

 . . f f f m E e f v

v r

          



Boltzmann equation for electron gas in electrical field E:

SLIDE 12

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current transport in bulk metals

     

v r g v r f v r f       , , ,  

Fermi-Dirac Perturbation due to electric field

I V

x

I

 

 . . f f f m E e f v

v r

          



 

1 exp 1 ,            T k v r f

B F

   

E

  f

r 



Spatially homogeneous transport

x x x

v f m eE v g    ) ( 

kx ky kz In k-space, shift in Fermi surface by

k



x

eE k    

SLIDE 13

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current transport in bulk metals (cont’d) Current density:

v d v g v e j

x 3

) (



  E E E m ne j    1

2

  

Well-known expression of conductivity in Drude model n=density of conduction electrons n~1/atom in noble metals such as Cu, Ag, Au n~0.6/atom in metals such as Ni, Co, Fe

m ne  

2



SLIDE 14

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Material (ferro) Measured resistivity 4K/300K Ni80Fe20

a

10-15.cm 22-25 Ni66Fe13Co2

1 b

9-13.cm 20-23 Coa,d 4.1-6.45.cm 12-16 Co90Fe10

h

6-9.cm 13-18 Co50Fe50

h

7-10.cm 15-20 Material Measured resistivity 4K/300K Cua 0.5-0.7.cm 3-5 Agf 1.cm 7 Aug 2.cm 8 Pt50Mn50

e

160.cm 180 Ni80Cr20

e

140.cm 140 Ruc 9.5-11.cm 14-20

Typical resistivity of sputtered metals Thermal variation of resistivity due to phonon scattering and magnon scattering (in magnetic metals)

SLIDE 15

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

     

x z z

v v f mv eE v v z g z v z g       , , 

F

v   

= elastic mean free path  

                   

  z x

v z A f v eE v z g     exp 1 ,

General solution :

Integration constants determined from boundary conditions

Modeling current transport in metallic thin films

I V

x

I

E

     

v r g v r f v r f       , , ,  

 

 . . f f f m E e f v

v r

          



Due to scattering at outer surfaces, the perturbation g is no longer homogeneous: g(z) +(-) refer to electrons traveling towards z>0 (z<0) z

SLIDE 16

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

   

sup sup

z Rg z g

 



Boundary conditions for a thin film : Proba of specular reflection R Proba of diffuse reflection 1-R

 



 v d z v g v e j(z)

z x 3

,



Current density:

 

    d t A t A z j                           

 



exp exp 2 1 ) (

1 2

t=layer thickness, = cosine of electron incidence

zsup zinf  

sup

z g

 

sup

z g

Proba R Proba 1-R

   

inf inf

z Rg z g

 



 

inf

z g

 

inf

z g 

Two boundary conditions, two unknowns A+, A-, solvable problem

SLIDE 17

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

1

G G G  

t t m v ne G

F 2

   

Same conductance as in bulk

 

                                           

 



       t A t A d G exp 1 exp 1 1 4 3

1 2 1

G1 contains all finite size effects. Characteristic length in current-in-plane transport=elastic mfp

j(z)

Assuming diffuse surface scatt

Modeling current transport in metallic thin films (cont’d)

Fuchs-Sondheimer approximate expressions:

t for 8 3 1

2

            t ne mvF

   

t for 423 . / ln 1 3 4

2

              t t ne mvF

thickness

SLIDE 18

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Models in spintronics (Part I)

OUTLINE : Spin-dependent transport in metallic magnetic multilayers

• Introduction to spin-electronics
• Spin-dependent scattering in magnetic metal
• Current-in-plane Giant Magnetoresistance
• Modelling CIP Giant Magnetoresistance
• Current-perpendicular-to-plane Giant Magnetoresistance
• Spin accumulation, spin current, 3D generalization.

SLIDE 19

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current in plane GMR in metallic multilayers

Same as for thin films but separately considering spin and spin  electrons and solving the Boltzmann equation within each layer with appropriate boundary conditions.

I V

CIP

I

Layer i Layer i+1 Interface i

Proba Ti



• f

transmission Proba Ri



• f reflexion

Proba 1-Ri

-Ti 

• f diffusion

         

 

, 1 , , 1 i i i i i

g R g T g

        

 

, , 1 , i i i i i

g R g T g

• Bulk spin-dependent scattering

described by spin dependent mfp 

• Interfacial scattering described by spin

dependent R and T

SLIDE 20

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

1

G G G  

 

   

 

N i i i N i i F i i i

t m v t n e G

, 1 , 1 2

/

  

 

Same conductance as if all layers were connected in parallel

 

                                               

  



        

      i i i i i i i i i

t A t A d G exp 1 exp 1 1 4 3

, , , 1 2 1

G1 contains all finite size effects and is responsible for GIP GMR. To obtain the GMR, G1 is calculated in parallel and antiparallel configurations.

In AP configuration, and are inverted in every other layer.

CIP GMR comes from second order effect in conductivity (in contrast to CPP GMR) Characteristic lengths in CIP GMR are the elastic mean-free paths

Modeling current in plane GMR in metallic multilayers

  

T , R , 

  

T , R , 

SLIDE 21

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Example of calculated CIP curves For a NiFe tNiFe/Cu 2nm/NiFe tNiFe Sandwich. R=coeff of specular reflection at lateral edges Absolute change of sheet conductance most intrinsic measure of CIP GMR

9 . , 12 , 8 . , 7

/ /

    

    Cu NiFe Cu NiFe Cu NiFe NiFe

T T nm nm nm   

F/Cu25Å/NiFe50Å/FeMn100Å

5 10 50 100 150 200 250 300

tF (nm)

p = 1

R/Rp (%)

p = 0 0.05 0.1 0.15 0.2 0.25 0.3 p = 1

G (-1)

p = 0 0.001 0.002 0.003 p = 1

G (-1)

p = 0

(Å)

B.Dieny JMMM (1994)

Influence of feromagnetic layer thickness on GMR in spin-valves

R=0 R=0 R=0 R=1 R=1 R=1

SLIDE 22

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

1 2 3 4 5 R/R (%) 10 20 30 40 50 tF (nm)

F tF/Cu 2.5nm/NiFe 5nm/FeMn 10nm, with F=Ni80Fe20, Co and Fe (Dieny, 1991).

1 2 3 4 5 10 20 30 40 50

tF (nm) R/R p (%)

Co NiFe Fe

F tF/Cu 2.5nm/NiFe5nm/FeMn 10nm

. 30 . , 70 . , 5 . 4 , 5 . 4 , 30 . , 95 . , 9 . , 9 , 30 . , 85 . , 7 . , 7

/ / / / / /

           

            Cu Fe Cu Fe Fe Fe Cu Co Cu Co Co Co Cu NiFe Cu NiFe NiFe NiFe

T T nm nm T T nm nm T T nm nm      

Influence of nature of ferro materials on GMR in spin-valves

SLIDE 23

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

NiFe 3nm/Cu tCu/NiFe 3nm

5 10 15 20 50 100 150

tF (nm)

p = 1

R/R p (%)

p = 0

tCu

Semi-classical theory Experiments

NiFe50Å/NM tNM /NiFe50Å/FeMn100Å

B.Dieny JMMM (1994)

Influence of non-magnetic spacer layer thickness on GMR in spin-valves

Two effects as tNM increases:

• Reduced number of electrons travelling from one ferro layer to the other
• Increasing shunting of the current in the spacer layer

SLIDE 24

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

<j>=2.107A/cm² Local current density and magnetic field due to current in a CIP spin-valve

 

     

   

d t A t A z j

i i i i i i i

                            

  



exp exp 2 1 ) (

, , , 1 2

Local current density (u.a) Magnetic field due to sense current (Oe) Local current density (u.a) Magnetic field due to sense current (Oe)

J

Oersted field due to sense current in a CIP spin-valves

cst dz z j z B

z

 



' ) ' ( ) ( 

Oe field plays an important role in the bias of spin-valve heads

SLIDE 25

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Fly height 10nm, disk rotating at 5000 to 10000 rpm.

substrate reader writer MR shield 1 shield 2 Planar coil

100nm

1m

Fly height 10nm, disk rotating at 5000 to 10000 rpm.

substrate reader writer MR shield 1 shield 2 Planar coil

100nm

1m

Vertical head with CIP MR reader

Free Pinned Field to be measured

J

SLIDE 26

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Linear response of spin-valves MR heads

Energy terms influencing the orientation

• f free layer magnetization:
• Zeeman coupling to H, to coupling field

through Cu spacer and to Oersted field:

) sin( ). (

1



J SV

H H H M E    

• Uniaxial and shape anisotropy

) ²( cos ). (

2



s

NM K E   

• Dipolar coupling with pinned layer

) sin( .

1



dip

H M E 

Minimizing energy yields linear in H. Since R varies as linear R(H)

) sin( ) sin( .

2 1

  M M  

   

   

             

2 1 1

2 1 NM K H H H H M R R R H R

dip I SV P AP P

SLIDE 27

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara 5 10 15 20 25

• 1000 -800
• 600
• 400
• 200

200 400 600 800 1000 H (Oe) GMR (%)

Experimental optimization of spin-valves GMR amplitude significantly improved by increasing specular reflection at boundaries of active part of the spin-valve //(pinned/spacer/free)//

NiFeCr/PtMn 120Å/ CoFe 15Å /Ru 7Å/CoFe 5Å/NOL/CoFe 15Å /Cu 20Å/CoFe10Å/NiFe 20Å /NOL

Spin-valves greatly optimized in 1994-2003 for HDD MR heads but replaced in 2004 by TMR heads soft pinned

SLIDE 28

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Conclusion on CIP GMR : CIP GMR well modeled by semi-classical Boltzmann theory. Local conductivity can only vary on length scale of the order of the elastic mean free path. Quantum mechanical theory of CIP transport were proposed to properly take into account the quantum confinement/reflection/refraction effects induced by lattice potential modulation. Predictions of oscillations in conductivity and GMR versus thickness but hardly seen in experiments due to interfacial roughness CIP GMR amplitude up to 20% in specular spin-valves. Spin-valves were used in MR heads of hard disk drives from 1998 to 2004. Later on, they were replaced by Tunnel MR heads.

SLIDE 29

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Models in spintronics (Part I)

OUTLINE : Spin-dependent transport in metallic magnetic multilayers

• Introduction to spin-electronics
• Spin-dependent scattering in magnetic metal
• Current-in-plane Giant Magnetoresistance
• Modelling CIP Giant Magnetoresistance
• Current-perpendicular-to-plane Giant Magnetoresistance
• Spin accumulation, spin current, 3D generalization.

SLIDE 30

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

I I V

I

Current Perpendicular to Plane GMR

Much more difficult to measure, Either on macroscopic samples (0.1mm diameter) with superconducting leads (R~ . thickness / area ~ 10)

• r on patterned microscopic pillars of area <m² (R~ a few Ohms)

SLIDE 31

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

F Ft 



 NM F

AR

/

F Ft 



F Ft 



 NM F

AR

/

F Ft 



 NM F

AR

/  NM F

AR

/

NM NMt



NM NMt

 (a) Parallel magnetic configuration :

F Ft 



 NM F

AR

/

F Ft 



F Ft 



 NM F

AR

/

F Ft 



 NM F

AR

/  NM F

AR

/

NM NMt



NM NMt

 (b) Antiparallel magnetic configuration :

Without spin-filp, serial resistance network can be used for CPP transport Serial resistance model for CPP-GMR CPP transport through F/NM/F sandwich described by:

SLIDE 32

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Serial resistance model for CPP-GMR:

CPP GMR of (Co tCo/Cu tCu) 2 multilayers

Parallel magnetic configuration :

Spin up channel Spin down channel



Cot Co



Cut Cu



Cot Co



Cot Co



Cut Cu



Cut Cu



Cot Co



Cut Cu

Antiparallel magnetic configuration :

Spin up channel Spin down channel



Cot Co



Cut Cu



Cot Co



Cot Co



Cut Cu



Cut Cu



Cot Co



Cut Cu

CIP GMR cannot be described by a parallel resistance network only

(no change of R between parallel and antiparallel magnetic configuration)

CPP GMR can be « qualitatively » described by a serial resistance network

(without spin-flip, i.e. no mixing between up and down channels)

Parallel resistance model for CIP-GMR:

CIP GMR of (Co tCo/Cu tCu) 2 multilayers

Parallel configuration :



Cot Co

Cut Cu 

Cot Co



Cot Co

Cut Cu Cut Cu 

Cot Co

Cut Cu

Antiparallel configuration :

Co Co t

/





Cu Cu t

/ 

Co Co t

/





Cu Cu t

/ 

Co Co t

/





Cu Cu t

/ 

Cu Cu t

/ 

Co Co t

/





SLIDE 33

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Spin accumulation – spin relaxation in CPP geometry z



J



J

  2

1 J  

 

2 1 J  

lSF lSF F1 F2 e flow e flow

In F1: Different scattering rates for spin  and spin  electrons  different spin  and spin  currents. Larger scattering rates for spin  : J >>J far from the interface. In F2: Larger scattering rates for spin  : J >>J far from the interface. Majority of incoming spin electrons, majority of outgoing spin electrons Building up of a spinaccumulation around the interface balanced in steady state by spin-relaxation

Valet and Fert theory of CPP-GMR (Phys.Rev.B48, 7099(1993))

SLIDE 34

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Starting point : Valet and Fert theory of CPP-GMR (Phys.Rev.B48, 7099(1993))

lSF lSF 

J l e

F SF F *

 

z z



J



J

  2

1 J  

 

2 1 J  

lSF lSF

Spin-relaxation at F/F interface:

Spin relaxation :

2

2 SF l z J e

   

  



   

Spin-dependent current driven by

z e J   

  

  1

 : spin-dependent chemical potential

  

Generalization of Ohm law In homogeneous material, =F-e

lSF=spin-diffusion length (~5nm in NiFe, ~20nm in Co))

SLIDE 35

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Interfacial boundary conditions

   

1 ) ( 1 ) ( 1       



i i i i

z J z J

     

1 ) ( ) ( 1 1 ) ( 1 ) ( 1             

 

i i i i i i i

z J r z z  

(if no interfacial spin-flip is considered) (Ohm law at interfaces)

Note: Interfacial spin memory loss can be introduced by :

   

1 ) ( 1 ) ( 1       



i i i i

z J z J 

30% memory loss as at Co/Cu interface yields =0.7

SLIDE 36

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Input microscopic transport parameters to describe macroscopic CPP properties : Within each layer :

• The measured resistivity .
• The scattering asymmetry .
• The spin diffusion length lsf.

At each interface :

• The measured interfacial area*resistance product
• The interfacial scattering asymmetry .

 

 

 

2 * 1

) ( 1 * 2                 

      measured

 

 

 

2

1 * ) ( 1 * 2         

     

r r r r r r r r

measured

measured

r

SLIDE 37

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Material Measured resistivity 4K/ 300K  Bulk scattering asymmetry lSF Cu 0.5-0.7.cm 3-5 500nm 50-200nm Au 2.cm 8 35nm 25nm Ni80Fe20 10-15 22-25 0.73-0.76 0.70 5.5 4.5 Ni66Fe13Co21 9-13 20-23 0.82 0.75 5.5 4.5 Co 4.1-6.45 12-16 0.27 – 0.38 0.22-0.35 60 25 Co90Fe10 6-9 13-18 0.6 0.55 55 20 Co50Fe50 7-10 15-20 0.6 0.62 50 15 Pt50Mn50 160 180 1 1 Ru 9.5-11 14-20 14 12

Examples of bulk parameters

SLIDE 38

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Examples of interfacial parameters

Material Measured R.A interfacial resistance  Interfacial scattering assymetry Co/Cu 0.21m.m2 0.21-0.6 0.77 0.7 Co90Fe10/Cu 0.25-0.7 0.25-0.7 0.77 0.7 Co50Fe50/Cu 0.45-1 0.45-1 0.77 0.7 NiFe/Cu 0.255 0.25 0.7 0.63 NiFe/Co 0.04 0.04 0.7 0.7 Co/Ru 0.48 0.4

• 0.2
• 0.2

Co/Ag 0.16 0.16 0.85 0.80

SLIDE 39

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Spin relaxation :

2

2 SF l z J e

   

  



   

Spin-dependent currents :

z e J   

  

  1

( generalized Ohm law in the bulk of the layer)



                   

sf sf

l z B l z A exp exp  Diffusion equation diffusion for spin accumulation 

2 2 2 SF

l z       

Solution within each layer: A, B integration constants determined from interfacial boundary conditions Diffusion equation of spin-accumulation               z e grad J   



1 1

Drift due to electrical field Diffusion due to local spin accumulation

SLIDE 40

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

 

    



   



 

i i i i i i

l d i i i i i i l d i i i i i i i i i i i N i i CPP

e l r e B J e l r e A J r d R

   

                                       

 

1 1 1 1 1 1 1 1 1 1 1

* * 1 2

Final expression of CPP resistance for any multilayered structures (N layers) : Where :

i i i i i i

J J B A B A ˆ ˆ

1 1

                 

 



        

BB i BA i AB i AA i i

     ˆ

        

BJ i AJ i i

J   ˆ

i i

l d i i i i i i i AA i

e l r l l           

  * * 1 * 1

1    

i i

l d i i i i i i i AB i

e l r l l

  

          

* * 1 * 1

1    

i i

l d i i i i i i i BA i

e l r l l           

  * * 1 * 1

1    

i i

l d i i i i i i i BB i

e l r l l

  

          

* * 1 * 1

1    

   

 

i i i i i AJ i

l r

i i

         

 



1 1 * *

1

2 1

   

 

i i i i i BJ i

l r

i i

         

 



1 1 * *

1

2 1

with : and with :

SLIDE 41

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

1 2 3 4 5 10 15 20 25 30

R/R (%) Free layer thickness (nm)

Ni80Fe 20 lSF NiFe =4.5nm Fe 50Co50 l SF FeCo =15nm (c)

Comparison of NiFe and FeCo free layer : influence of lSF

Smooth maximum in CPP GMR versus tF

Free layer : NiFe/FeCo

• r FeCo only

t

F .cm m.m²

nm nm Data from Headway Technologies

Phenomenologically, R  1-exp(-tF/lSF F) and R/R  [1-exp(-tF/lSF F]/(tF+cst)

SLIDE 42

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

0.5 1 1.5 2 2.5 3 10 20 30 40 50

R/R (%)

Cu lSF Cu=50nm Au lSF Au=10nm

Comparison of Cu and Au spacer layers : influence of lSF Spacer layer thickness (nm) Phenomenologically, decrease of R as exp(-tspacer/lSF spacer) and R/R as exp(-tspacer/lSF spacer)/(tspacer+cst)

Data from Headway Technologies

SLIDE 43

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Current confined paths (CCP) GMR

K.Nagasaka et al, JAP89 (2001), 6943 H.Fukazawa et al, IEEE Trans.Mag.40 (2004), 2236

Current crowding effects in low RA MTJ Spin transfer oscillators in point-contact geometry

See for instance: J.Chen et al, JAP91(2002), 8783. S.Kaka et al, Nat.Lett.437, 389 (2005) F.B.Mancoff et al, Nat.Lett.437, 393 (2005)

Inhomogeneous current distributions in numerous experimental situations… Metallic CPP heads

Shield 1 Shield 2

J

20nm

… almost all models of spin-dependent transport assume uniform current

Generalization of spin-dependent transport to any geometry (colinear magnetization)

SLIDE 44

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

             

 

z e grad J    1 Extending Valet-fert theory at 3D in colinear geometry              

 

z e grad J    1   

B

m  

energy

DOS

Out-of-equilibrium magnetization

   

z m e grad J J J

B el

        

     

      

Electrical current:

With

 

   



1

 

   



1 z m e grad J

B el

          2 2

3D expression of electron current:

m e J

B e

            2 2

SLIDE 45

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

     

                            

     

z m e grad e J J e J

B s

       1 1

Spin current:

z m e grad e J

B s

              

2

2 2

: Spin current

z m e grad e J

B m

             

2

2 2

: Moment current 3D expression of moment current:

m e e J

B m

                

2

2 2

In colinear magnetization Jm is a vector

SLIDE 46

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Transport equations:



e

J div

 

1 l 2

2 2 sf

   m Jm    div

Diffusion of charge (with conservation of charge) Diffusion of spin (without spin conservation due to spin-torque and spin- relaxation

lSF=spin-diffusion length

m e J

B e

            2 2 m e e J

B m

                

2

2 2

2 Unknowns: 2 Unknowns:

z

m 

2

2 SF l z J e

   

  



   

derived from Valet/Fert: 2 Equations: 2 Equations:

1 diffusion of e + 1 diffusion of m

Can be solved in complex geometry with a finite element solver

SLIDE 47

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

200nm

in

Cu Cu

out

20nm

2D CPP pillar with extended electrodes Je

+2.03·10-5

Co3/Cu2/Co3nm

10 times higher current density at corners than in center of CPP- GMR stack

Mapping of charge current

Charge current amplitude

SLIDE 48

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

my

+2.14·10-4

• 2.14·10-4

( Jm,yx, Jm,yy)

Mapping of y-spin current x y z

2D CPP pillar with extended electrodes

Parallel Antiparallel

Large excess

• f  e

Large excess

• f  e

Cu Co/Cu/Co Cu Cu Co/Cu/Co Cu Very large excess of  e Weak excess of  e Large in- plane spin- current

SLIDE 49

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Conclusion on CPP transport

• Serial resistance model can be used at lowest order of approximation to

describe CPP transport. However, does not take into account spin-flip.

• With spin-flip, spin accumulation and spin-relaxation play an important

role in CPP transport.

• Semi-classical theory of transport describes CPP transport fairly well.

CPP macroscopic transport properties (R, R/R) can be calculated from microscopic transport parameters (, lSF, r)

• In complex geometry, charge and spin current can have very different

behavior. Two contributions to j: drift along electrical field and diffusion along gradient of spin accumulation.

SLIDE 50

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

SLIDE 51

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

f TR k V

B Johnson

  4

I R V .   

Signal : To maximize the SNR in MR heads, the power dissipated in the head must be as large as possible compatible with reasonable heating and electromigration Noise : Signal/Noise :

f T k power R R V V SNR

B Johnson

           4

Signal/noise ration in CIP MR heads <j>~4.107A/cm² used in heads with CIP-GMR~15%