Dieny « Models in Spintronics » 2009 European School on Magnetism, Timisoara Birth of Spin Electronics : Giant Magnetoresistance (1988)

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.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Birth of spin electronics : Giant magnetoresistance (1988)

Fe/Cr multilayers Fert et al, PRL (1988), Nobel Prize 2007 Two limit geometries of measurement: I

~ 80% V

I Current-in-plane

V Magnetic field (kG) I I

Current-perpendicular-to-plane

R  R GMR  AP P Antiferromagnetically coupled multilayers RP

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Low field GMR: Spin-valves ) (a)

emu 1 3

Antiferromagnetic - FeMn 90Å pinning layer 0 M (10 M NiFe 40Å Ferromagnetic -1 pinned layer Cu 22Å Non magnetic spacer 4 (b) 3 NiFe 70Å Soft ferromagnetic layer 2 R/R (%) R/R Ta 50Å Buffer layer  1

0 -200 0 200 400 600 800 substrate H(Oe) 4 (c) IBM Almaden 3

Ultrasensitive magnetic field sensors (MR heads) (%) R/R Spin engineering  1

B.Dieny et al, Phys.Rev.B.(1991)+patent US5206590 (1991). 0 -40 -20 0 20 40 H(Oe) 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

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Two current model (Mott 1930) for transport in magnetic metals

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)

1  1 1                    

Sources of spin flip: magnons and spin-orbit scattering

Negligible spin-flip often crude approximation (spin diffusion length in NiFe~4.5nm, 30% spin memory loss at Co/Cu interfaces)

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

Spin dependent transport in magnetic metals (1)

Band structure of 3d transition metals In transition metals, partially filled bands which participate to conduction are s and d bands

Non-magnetic Cu : Magnetic Ni :

E E

s(E) s (E) s(E) s (E)

D (E) D (E) D (E) D (E)

E E

D(EF) = D(EF) D(EF)  D(EF) Most of transport properties are determined by DOS at Fermi energy Spin-dependent density of state at Fermi energy

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Spin dependent transport in magnetic metals (2) m*(d) >> m*(s) J mostly carried by s electrons in transition metals

Scattering of electrons determined by DOS at EF : E s (E) s (E)  2   Fermi Golden rule : P   iW f  D f (EF )

D(E) D(E) s s d

s s d Most efficient scattering channel

Spin-dependent scattering rates in magnetic transition metals

Example: Co  10nm;Co  1nm

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Potential experienced by conduction electrons in magnetic metallic multilayers

Parallel magnetic configuration Antiparallel magnetic configuration

Co/Cu majority electrons : antiparallel magnetic configuration Co/Cu majority electrons : parallel magnetic configuration Co Cu Co Cu (c) (a)

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

U(x,z) (b) (d) x

z •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)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Simple model of Giant Magnetoresistance

Parallel config Antiparallel config

Fe Cr Fe Fe Cr Fe

2        1 2          ap       1 Equivalent resistances :

              Key role of 2     scattering contrast          P  AP      2

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: Equilibrium function conserved in a volume element drdv along a flow line. df  df   df  t+dt In presence of scattering,        0 dt dt dt t  F  scattering E Balance between acceleration due to force and relaxation due to scattering  df  f f f f f f f     .vx  .vy  .vz  .ax  .ay  .az  dt F t x y z vx vy vz    f      v.  f  a. f with ma  F t r v

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara      df   df  f  F        v.r f  .v f  dt F  dt scatt t m f In stationary regime,  0 t  df    f  f 0  In single relaxation time approximation ()     dt scatt  Where f0 is the equilibrium distribution (Fermi Dirac for electrons).

Boltzmann equation for electron gas in electrical field E:      eE  f  f 0 v.  f  . f    r m v 

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current transport in bulk metals I       f r,v  f r,v g r,v 0 V Fermi-Dirac Perturbation due to electric field   1 f r,v  0      I exp F  1  k T    B  E   0   eE   f  f  v.  f  . f  x r v  m  Spatially homogeneous transport  r f  0

kz eEx f0 g(vx )  m vx

In k-space, shift in Fermi surface by kx k  k  eEx ky

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current transport in bulk metals (cont’d)

Current density:  j  e v g(v)d 3v  x ne2 1 j  E  E  E m  ne2   m

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

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Typical resistivity of sputtered metals

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

Cua 0.5-0.7.cm a Ni80Fe20 10-15.cm 3-5 22-25 Agf 1.cm

7 Ni66Fe13Co2 9-13.cm g b 20-23 Au 2.cm 1 8 Coa,d 4.1-6.45.cm e Pt50Mn50 160.cm 12-16 180 h Co90Fe10 6-9.cm e Ni80Cr20 140.cm 13-18 140 h Co50Fe50 7-10.cm Ruc 9.5-11.cm 15-20 14-20 Thermal variation of resistivity due to phonon scattering and magnon scattering (in magnetic metals)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current transport in metallic thin films I       f r,v  f r,v g r,v 0 z   V   eE   f  f 0  v.  f  . f  I r m v  E x Due to scattering at outer surfaces, the perturbation g is no longer homogeneous: g(z) gz,v g z,v eE f 0 v   z vz mvz vx    = elastic mean free path v Integration constants determined F from boundary conditions General solution :    f0  z g z,v  eE v 1 A exp   x     v    z  +(-) refer to electrons traveling towards z>0 (z<0)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Boundary conditions for a thin film :

zsup g z  Rg z  g zsup  g zsup   sup  sup

g zinf   Rg zinf  g zinf  g  zinf  zinf Proba R Proba 1-R Proba of specular reflection R Proba of diffuse reflection 1-R

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

Current density: j(z)  e v g v , z d 3v  x  z  1    t   t  j(z)  1  2 2  A exp   A exp  d          0       

t=layer thickness, = cosine of electron incidence

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current transport in metallic thin films (cont’d)

G  G0  G1 thickness ne2 G0  t   t Same conductance as in bulk vF m 3 1     t    t  G  d 1  2  A 1 exp   A 1 exp  1             4 0         

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

Fuchs-Sondheimer approximate expressions: mv  1 3    F    for   t j(z) ne2   8t 

4mv  1    F   for   t 2   Assuming diffuse surface scatt 3ne  tln / t 0.423

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.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current in plane GMR in metallic multilayers I Same as for thin films but separately considering spin and spin  V electrons and solving the Boltzmann equation within each layer with appropriate boundary conditions. I •Bulk spin-dependent scattering CIP described by spin dependent mfp   Proba Ti of •Interfacial scattering described by spin transmission dependent R and T Layer i+1

Interface i      Layer i  g  T g  R g Proba Ri of reflexion i1, i i, i i1, g   T  g   R g    i, i i1, i i, Proba 1-Ri -Ti of diffusion

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Modeling current in plane GMR in metallic multilayers

G  G0  G1

N   N 2 i ni ti  Same conductance as if all layers G0  e   ti / i were connected in parallel i1, vF mi i1,

 1      3i 2     ti    ti   G1  d1  Ai, 1 exp   Ai, 1 exp  4           i ,i 0    i    i 

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,  , R , T and  , R , T 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

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Influence of feromagnetic layer thickness on GMR in spin-valves

0.3 Example of calculated CIP curves 0.25 For a NiFe tNiFe/Cu 2nm/NiFe tNiFe

) 0.2

-1 Sandwich.

 0.15 R=1p = 1 R=coeff of specular reflection at lateral edges

G( 0.1 p = 0 NiFe NiFe R=0   7nm,  .8nm, 0.05   Cu 0   12nm, R=1 p = 1 NiFe / Cu NiFe / Cu

) 0.003 T  T  0.9 -1 

0.002 Absolute change of sheet conductance G (

 p = 0 most intrinsic measure of CIP GMR R=0 0.001 F/Cu25Å/NiFe50Å/FeMn100Å 0

p = 1 R=1 10 (%) p

R/R 5 

p = 0 R=0 B.Dieny 0 0 50 100 150 200 250 300 JMMM (1994) t (nm) F (Å)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Influence of nature of ferro materials on GMR in spin-valves

5 5

4 4 Co

3 (%) 3 p NiFe

R/R (%) R/R 2

 2 R/R Fe  1 1

0 0 0 10 20 30 40 50 0 10 20 30 40 50 t (nm) F t (nm) F

F tF/Cu 2.5nm/NiFe 5nm/FeMn 10nm, F tF/Cu 2.5nm/NiFe5nm/FeMn 10nm with F=Ni80Fe20, Co and Fe (Dieny, 1991).     NiFe  7nm,NiFe  0.7nm,TNiFe / Cu  0.85,TNiFe / Cu  0.30,     Co  9nm,Co  0.9nm,TCo / Cu  0.95,TCo / Cu  0.30,     Fe  4.5nm,Fe  4.5nm,TFe / Cu  0.70,TFe / Cu  0.30.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Influence of non-magnetic spacer layer thickness on GMR in spin-valves

NiFe 3nm/Cu tCu/NiFe 3nm NiFe50Å/NM tNM /NiFe50Å/FeMn100Å 20

p = 1

15 (%) p 10 R/R

 5

p = 0 0 0 50 100 150 t (nm) tCuF Semi-classical theory Experiments B.Dieny JMMM (1994)

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

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Local current density and magnetic field due to current in a CIP spin-valve

1    t   t  j(z)  1  2 2  A exp i   A exp i  d    i,    i,    ,i 0   i    i  

Oersted field due to sense current )

in a CIP spin-valves Oe ( ) u.a ( current density sense current J to due field Local Local

z Magnetic B(z)  0 j(z')dz'  cst 0 =2.107A/cm² Oe field plays an important role in the bias of spin-valve heads

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Vertical head with CIP MR reader

reader writer

1m Planar coil 1 2

Pinned MR shield shield substrate Free

J Fly height 10nm, 100nm Field to be measured disk rotating at 5000 to 10000 rpm.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Linear response of spin-valves MR heads Energy terms influencing the orientation of free layer magnetization:

•Zeeman coupling to H, to coupling field through Cu spacer and to Oersted field:

E  M1(H  H SV  H J ).sin() •Uniaxial and shape anisotropy 2 E  (K  NM s ).cos ²() •Dipolar coupling with pinned layer

E  M1H dip .sin() Minimizing energy yields sin() linear in H.  

Since R varies as M1.M 2  sin() linear R(H)

 M1H  H SV  H I  H dip  RH   RP  RAP  RP 1 2   2K  NM1  

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Experimental optimization of spin-valves

Spin-valves greatly optimized in 1994-2003 for HDD MR heads but replaced in 2004 by TMR heads NiFeCr/PtMn 120Å/ CoFe 15Å /Ru 7Å/CoFe 5Å/NOL/CoFe 15Å /Cu 20Å/CoFe10Å/NiFe 20Å /NOL

pinned soft 25

GMR (%) GMR 10

0 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 H (Oe) GMR amplitude significantly improved by increasing specular reflection at boundaries of active part of the spin-valve //(pinned/spacer/free)//

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.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Models in spintronics (Part I)

OUTLINE :

Spin-dependent transport in metallic magnetic multilayers

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Current Perpendicular to Plane GMR

I I

Much more difficult to measure, Either on macroscopic samples (0.1mm diameter) with superconducting leads (R~ . thickness / area ~ 10) or on patterned microscopic pillars of area <m² (R~ a few Ohms)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Serial resistance model for CPP-GMR

Without spin-filp, serial resistance network can be used for CPP transport

CPP transport through F/NM/F sandwich described by: (a) Parallel magnetic configuration :

   t   F tF ARF / NM NM NM ARF / NM F tF    t   F tF ARF / NM NM NM ARF / NM F tF

(b) Antiparallel magnetic configuration :

   t   F tF ARF / NM NM NM ARF / NM F tF    t   F tF ARF / NM NM NM ARF / NM F tF

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Serial resistance model for CPP-GMR: Parallel resistance model for CIP-GMR:

CPP GMR of (Co tCo/Cu tCu) 2 multilayers CIP GMR of (Co tCo/Cu tCu) 2 multilayers Parallel magnetic configuration :

 t  t   Parallel configuration : Antiparallel configuration : Co Co Cu Cu  Cot Co  Cut Cu

  Cot /CotCo Spin up channel  / t Spin down channel CuCut Cu Cu  CoCot/ CotCo   t    t  Cot Co Cu Cu  Cot Co  Cut Cu CuCu Cu/ tCu

 Antiparallel magnetic configuration : CoCo/t tCoCo   CuCut Cu/ tCu  t  t  t  Co Co Cu Cu Co Co  Cut Cu  CoCot/ CotCo

CuCut Cu/ tCu Spin up channel Spin down channel CIP GMR cannot be described  t  t   t by a parallel resistance network only Co Co Cu Cu  Cot Co Cu Cu (no change of R between parallel and antiparallel magnetic configuration) CPP GMR can be « qualitatively » described by a serial resistance network B.Dieny « Models(without in spintronics » spin-flip, i.e. no 2009 mixing European between School up on and Magnetism, down channels) Timisoara Spin accumulation – spin relaxation in CPP geometry F1 F2

J J 1   e flow 2 e flow

J 1   2 J lSF lSF Valet and Fert theory of CPP-GMR (Phys.Rev.B48, z 7099(1993)) 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

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)) Spin-relaxation at F/F interface:  : spin-dependent chemical potential In homogeneous material, = -e F J J 1    2 Spin-dependent current driven by  J 1   1  2 J l l J   SF SF e z Generalization of Ohm law z

* F Spin relaxation : e F lSF J J        e  2 z 2lSF

lSF=spin-diffusion length (~5nm in NiFe, ~20nm in Co)) lSF lSF B.Dieny « Models in spintronics » 2009 Europeanz School on Magnetism, Timisoara Interfacial boundary conditions

() () () () i1 zi1  i zi1   ri1 Ji zi1  (Ohm law at interfaces)

() () (if no interfacial spin-flip is considered) Ji1 zi1   Ji zi1 

Note: Interfacial spin memory loss can be introduced by :

() () Ji1 zi1    Ji zi1 

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

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 .   2 *1 ()  -The scattering asymmetry .         * 1  2  measured    -The spin diffusion length lsf.   At each interface :

-The measured interfacial area*resistance product rmeasured -The interfacial scattering asymmetry .

r  2r *1 () 

rr 2 rmeasured   r *1  r  r

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Examples of bulk parameters

Material Measured  lSF resistivity 4K/ Bulk 300K scattering asymmetry Cu 0.5-0.7.cm 0 500nm 3-5 0 50-200nm Au 2.cm 0 35nm 8 0 25nm

Ni80Fe20 10-15 0.73-0.76 5.5 22-25 0.70 4.5

Ni66Fe13Co21 9-13 0.82 5.5 20-23 0.75 4.5 Co 4.1-6.45 0.27 – 0.38 60 12-16 0.22-0.35 25

Co90Fe10 6-9 0.6 55 13-18 0.55 20

Co50Fe50 7-10 0.6 50 15-20 0.62 15

Pt50Mn50 160 0 1 180 0 1 Ru 9.5-11 0 14 B.Dieny 14-20« Models in spintronics »0 2009 European12 School on Magnetism, Timisoara Examples of interfacial parameters

Material Measured R.A  interfacial Interfacial resistance scattering assymetry Co/Cu 0.21m.m2 0.77 0.21-0.6 0.7

Co90Fe10/Cu 0.25-0.7 0.77 0.25-0.7 0.7

Co50Fe50/Cu 0.45-1 0.77 0.45-1 0.7 NiFe/Cu 0.255 0.7 0.25 0.63 NiFe/Co 0.04 0.7 0.04 0.7 Co/Ru 0.48 -0.2 0.4 -0.2 Co/Ag 0.16 0.85 0.16 0.80

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Diffusion equation of spin-accumulation

1  Spin-dependent currents : J  ( generalized Ohm law in the bulk of the layer) e z J    Spin relaxation : e  2 z 2lSF  2   Diffusion equation diffusion for spin accumulation   z 2 l 2 Solution within each layer: SF  z   z    Aexp   B exp       lsf   lsf  A, B integration constants determined from interfacial boundary conditions

1  1     J   grad     e z  Drift due to Diffusion due electrical field to local spin accumulation

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Final expression of CPP resistance for any multilayered structures (N layers) :

N 2 * * RCPP  1 i i di  ri 1 i 1 i  i1 d  r 1  i 1 i i  i  li  Ai 1 i 1 e  e  J  ili  d  r 1   i 1 i i  i  li  Bi 1 i 1 e  e J  ili 

 A   A    AA  AB  Where :  i1   ˆ  i   JJˆ with : ˆ   i i    i   i i  BA BB  Bi1 Bi i i   d       * l r  i  AA  1 i1 i1  i e li i  * *   i li i li  d   * l r   i  AB  1 i1 i1  i e li i  * *    AJ   i li i li  and Jˆ   i  with : d i  BJ    * l r  i  i  BA  i1 i1 i  li i  1  e  * *  BJ 1 * *  i li i li    r      l     d i  i i i i1 i1 i1 i  *  i 2 BB  i1li1 ri  l   1  e i AJ 1 * * i * *  B.Dieny « Modelsi in spintronics » r  i 2009 i European  Schoolli1 on Magnetism,i1   Timisoarai   i li i li  2 i i1 Comparison of NiFe and FeCo free layer : influence of lSF

.cm m.m² nm nm Free layer : F NiFe/FeCo or FeCo only t

4 Ni Fe l =4.5nm Smooth maximum in CPP GMR versus tF 80 20 SF NiFe

3 Phenomenologically, R  1-exp(-tF/lSF F) 2 and Fe Co l =15nm 50 50 SF FeCo R/R(%) R/R  [1-exp(-tF/lSF F]/(tF+cst) 

(c) Data from Headway Technologies 0 0 5 10 15 20 25 30 Free layer thicknessB.Dieny (nm) « Models in spintronics » 2009 European School on Magnetism, Timisoara Comparison of Cu and Au spacer layers : influence of lSF 3

2.5 Cu 2 l =50nm SF Cu

1.5 R/R (%)  1

0.5 Au l =10nm SF Au 0 0 10 20 30 40 50

Spacer layer thickness (nm) Data from Headway Technologies

Phenomenologically, decrease of R as exp(-tspacer/lSF spacer) and R/R as exp(-tspacer/lSF spacer)/(tspacer+cst)

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Generalization of spin-dependent transport to any geometry (colinear magnetization)

Inhomogeneous current distributions in numerous experimental situations…

Current confined paths (CCP) GMR Current crowding effects in low RA MTJ

See for instance: J.Chen et al, K.Nagasaka et al, JAP89 (2001), 6943 JAP91(2002), 8783. H.Fukazawa et al, IEEE Trans.Mag.40 (2004), 2236

Spin transfer oscillators in point-contact geometry Metallic CPP heads

J Shield 1 Shield 2 Shield

S.Kaka et al, Nat.Lett.437, 389 (2005) F.B.Mancoff et al, Nat.Lett.437, 393 (2005) 20nm … almost all models of spin-dependent transport assume uniform current

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Extending Valet-fert theory at 3D in colinear geometry

 1   Out-of-equilibrium magnetization J    grad        e z  m    1     J    grad   B    e z  energy   DOS

Electrical current:

     m Jel  J  J      grad  eB z

With    1      1   2 m J  2 grad  el e  z B    2 J  2   m 3D expression of electron current: e eB

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

 1  1      m J s   J  J         grad    e   e  eB z  2 2 m   : Spin current J s   grad  2  e  e B z

 2 B  2 m J m   grad  : Moment current  e  e2 z     2 B  2 3D expression of moment current: J m     m  e  e2

In colinear magnetization Jm is a vector

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara    2 J e  2   m eB 2 Unknowns:  m    z  2 B  2 J m     m  e  e2

Transport equations:

Diffusion of charge (with divJe  0 conservation of charge)

2 2 divJm  2 1  m  0 Diffusion of spin (without  lsf spin conservation due to spin-torque and spin- J    derived from Valet/Fert: e  relaxation z 2l 2 SF lSF=spin-diffusion length 2 Equations: 1 diffusion of e + 1 diffusion of m Can be solved in complex geometry with a finite element solver

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara in 2D CPP pillar with extended electrodes out

Cu Cu Mapping of charge current +2.03·10-5 200nm

Je Charge current amplitude current Charge

10 times higher current density at corners than in center of CPP- Co3/Cu2/Co3nm GMR stack

20nm B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara 2D CPP pillar with extended electrodes

y Mapping of y-spin current ( Jm,yx, Jm,yy) x z Cu Co/Cu/Co Cu Cu Co/Cu/Co Cu Very large excess of  e +2.14·10-4 Large Large excess excess of  e of  e Large in- plane spin- current my

Weak excess of  e -2.14·10-4 Parallel Antiparallel

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.

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara Signal/noise ration in CIP MR heads

Signal : V  R.I

Noise : VJohnson  4k BTRf

V  R  power Signal/Noise : SNR     VJohnson  R  4k BTf

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

~4.107A/cm² used in heads with CIP-GMR~15%

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