[PPT] - Mairbek Chshiev European School on Magnetism Spintronics PowerPoint Presentation

SLIDE 1

Mairbek Chshiev

European School on Magnetism

SLIDE 2

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

GMR & TMR Spin Transfer Torques (STT) Spin Hall Effect (SHE) Rashba Effect

Spin-orbit phenomena -> Spin orbitronics

Interlayer Exchange (IEC) Spin Filtering (SF) Magneto crystalline anisotropy

Conventional spintronics

Dzyaloshinskii- Moriya (DMI) Spin-orbit Torques (SOT)

Spin valves Alloys (BiCu, IrCu…) Single & double barrier MTJs AFM metals AFM insulators Frustrated magnets Rutiles Heusler alloys Graphene Garnets (Y3Fe5O12) Layered structures (Pt/Co/AlOx, Ta/CoFe/MgO Interfaces perovskites Domain walls

… …

Ferrites (CoFe2O4)

This lecture:

Tunnel magnetoresistance (TMR) Spin transfer torques (STT)

Quantum origin of spin transfer torque
Description of spin currents and spin transfer torques
Free electron model
Tight-binding model
Voltage dependence of STT
symmetric MTJs
asymmetric MTJs

Interlayer exchange coupling …

Spintronics

SLIDE 3

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

) (k

n



|| 

k

 F

E

 F

E

Fe M’

M

H 

magnetization acts on current

Spintronics

Huge TMR in crystalline MTJ if:

Good epitaxial fit between FM and I(SC)
Evanescent states in I(SC) with the same

Bloch state symmetry

High symmetry Bloch state (1) for one of two e-

spin states in FM electrodes (“half-metallic”-like)

dxy dxz, dyz px, py

1 in MgO

dz

2

pz s

The 1st Brillouin zone with high symmetry k-points

TMR~600% Fe|MgO|Fe (Tohoku,2008)

Tunnel (TMR) magnetoresistance:

W. H. Butler et al, PRB (2001)

Bloch state symmetry based Spin Filtering (SF)

SLIDE 4

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

M’

M

H 

TMR~600% Fe|MgO|Fe (Tohoku,2008)

Spintronics

Huge TMR in crystalline MTJ if:

Good epitaxial fit between FM and I(SC)
Evanescent states in I(SC) with the same

Bloch state symmetry

High symmetry Bloch state (1) for one of two e-

spin states in FM electrodes (“half-metallic”-like)

The 1st Brillouin zone with high symmetry k-points

5 10 15 20 25

e

20

e

16

e

12

e

8

e

4

Fe  Fe  MgO

layer



  

Bloch state symmetry based Spin Filtering (SF)

W. H. Butler et al, PRB (2001)

IEEE Trans. Mag., 41 (2005) 2645

Sci. Technol. Adv. Mater. 9 (2008) 014106

magnetization acts on current

Tunnel (TMR) magnetoresistance:

W. H. Butler et al, PRB (2001)

SLIDE 5

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

M’ M

j 

ref free

) (H R 

Field (Oe)

) ( j R 

Current (mA)

Spin Transfer Torque (STT):

current acts on magnetization

R(H)

Sensors “1” “0”

(Rhigh)

Freescale 4Mbit

(Rlow)

MRAM

Memories RF components

Cu PtMn Cu

CoFe CoFe

MgO

(Pt/Co)

J

Si

Logic MTJs Logics

Functional devices

GMR, TMR, STT

M’ M

H 

P P AP

R R R   TMR

Spintronics

Tunnel (TMR) magnetoresistance:

magnetization acts on current

SLIDE 6

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spintronics

Giant

magnetoresistance (GMR) metallic nanostructures Keldysh formalism Tight

binding model

Kubo formalism Free electron model Ab

initio

(DFT )

Calculation techniques

Tunnel

m agnetoresistance

(TMR )

amorphous and crystalline , single and double barrier tunnel junctions

Spin transfer

torque (STT), exchange coupling (IEC), anisotropy

Spin filtering

Spin Hall Effect (SHE) alloys

Materials for spintronics

amorphous and crystalline tunnel junctions crystalline magnetic tunnel junctions chalcogenides , rutiles , spinels , Heusler alloys, Graphene , frustrated magnets

Computational Materials Science Condensed Matter Theory

+ Boltzmann approach (drift

diffusion)

Quantum transport theory and electronic structure of materials for spintronics

SLIDE 7

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

   

 

R L R L parallel

D D D D J

   

 

R L R L el antiparall

D D D D J 300K

P>0 (~50%) in Fe, Co  R/R~40 - 70% with alumina barriers at low T

Julliere 1975 -> Moodera 1995

R/R~ 15%  P+0.26

H 

Fe Co AlOx Different coercive fields For Co, Fe

) ( ) ( ) ( ) (

) ( ) ( ) ( ) ( ) ( F R L F R L F R L F R L R L

E D E D E D E D P

   

  

R L R L P

P P P P R R TMR     1 2

Moodera et al, PRL 74, 3273 (1995)

Parallel configuration Antiparallel configuration

Miyazaki

SLIDE 8

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Julliere’s model is insufficient! Stearns’ polarization

 Stearns first explanation in this way

) ( ) ( ) ( ) (

) ( ) ( ) ( ) ( ) ( F R L F R L F R L F R L R L

E D E D E D E D P

   

   )

) ( ) ( ) ( ) ( ) (    

  

R L R L R L R L R L

k k k k P

M. B. Stearns, JMMM 5, 1062 (1977)

   

Not overall density of states important but specific bands at the Fermi level and their properties

SLIDE 9

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

1.5
1
0.5

0.5 1 1.5

2
1.5
1
0.5

0.5 1 1.5 2 2.5 3

Energy, Wave Function

y

Energy

1.5
1
0.5

0.5 1 1.5

2
1.5
1
0.5

0.5 1 1.5 2 2.5 3

Energy, Wave Function

y

Energy

Matching Boundary Conditions (4 linear equations with 4 unknowns) allows the solution for the transmission probability.

y=0 y=a

y y

Be Ae

 



 y ikR

te

y ik y ik

L L

re e





Free electron model for tunneling (no spin)

Boundary conditions : continuity of |Y> and its derivative

 

t transmission amplitude EF at equal potential

SLIDE 10

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

 

a R L a R R L L R L a R L a R L R L R L

e T T e k k k k T k k e k k T e k k k k a k k k k T

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2

) ( 4 ) ( 4 : as written be can that this Note ) )( ( 16 : 1 t enough tha thick is system When ) )( ( 4 ) 2 cosh( ) )( ( 8 : y probabilit

n

Transmissi

   

             

  

       >>         



Free electron model for tunneling (no spin)

Depends on barrier thickness + height
k=kF
Given by transmission probabilities L, R

T=|t|²

=T(k//)

 

E

T h e V I G

F

|| 2

e Conductanc for Formula Landauer ) (

   

             

  

       >>         



||

k

SLIDE 11

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

U

EF



E

  

E

Slonczewski (1989) Delocalized electrons contribute most to the current (sp states)

Localized states don’t (d states)  free electron tunneling

) )( ( 16

2 2 ' 2 2 2 ' 2 '

  

     

  



k k e k k T

a

Spin  and spin  channels conduct in parallel (two current model):

   

    G G G G G G

el Antiparall Parallel

and

 

   

2 2 2 2 2 2 2 2

16            

      

k k k k k k e G G

a el antiparall Parallel

   



Tunnel magnetoresistance

² 2

1 2 P P G G G G G

parallel el antiparall Parallel Parallel

    

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

        F F F F F F F F

k k k k k k k k P

2 2

 

Slonczewski model for tunneling (with spin)

Depends on properties of FM and barrier!
Bandstructure details are important!

for simplicity L=R material Slonczewski Polarisation

SLIDE 12

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Case of high barrier:

 

>>

F F

k k , 

>   

    F F F F

k k k k P

Free electrons:

k mk E DOS  

2 2

) (  

   

   D D D D P

Back to Julliere formula With P defined via DOS

In Julliere’s model, only the polarization within the magnetic electrodes influences the TMR. In Slonczewski’s model, the barrier height also plays a role.

² 2

1 2 P P G G R R

Parallel el Antiparall

    

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

        F F F F F F F F

k k k k k k k k P

2 2

 

2 || 2

) ( 2 k E U m       Slonczewski model for tunneling (with spin)

Electrons with highest velocity give strongest contribution to tunneling

SLIDE 13

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

     

                      

                   

  

R R R R R L L L L L R L R L R L R L R L R L R L R L AP AP P

T T T T P T T T T P P P P P T T T T T T T T T T T T T T T T T T T T T where 1 2 TMR TMR

Jullière model

a R L a

e T T k k e k k T

2 ' 2 2 ' 2 2 2 ' 2 '

) )( ( 16

        

  

 

    ) ( 4 ; ) ( 4

2 2 ' 2 2

   

     

   

R R R L L L

k k T k k T

Generalized model for tunneling (with spin)

Generalization: Write TMR in terms of the transmission probability

Provides defintion that can be generalized to complex bandstructures

U

EF



E



E

SLIDE 14

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z=0 z=a V1 V0 V2

V e

a z / V V(z) 

Voltage dependence of tunnel current

SLIDE 15

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

            >>



E U L D k k e k k T e

L L 2 2 2 2 2 1 2 2 1 2 2

2 exp ) )( ( 16 : 1 t enough tha thick is system When    

 

But what if the barrier is not rectangular???

          



2 1

) ( 2 exp : ion approximat WKB use We

z z

E z U dz D T 

de Broglie wavelength is much smaller than (z2-z1)
U(z) should vary slowly over (z2-z1)

z

p /   

 Simmons model based on WKB is usually used to estimate potential barrier height and width

Voltage dependence of tunnel current

Slonczewski

SLIDE 16

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

1

1 ik z

re k



2

2 ik z

te k

  

 dz z dz z

Be Ae

) ( ) (  

1

1 ik z

e k

z=0 z=a V1 V0 V2

V e

V 2

2 2 || 2 2 2

e m k k k

E

   

) ( 2

2 2 2

V E m k E   

2 || 2 1 1

k k k

E 



) ( 2

1 2 1

V E m k E    ) ( V 2 ) (

2 2 || 2

z e m k z       ) ( 2

2

E V m    

a z / V V(z) 

 

 

  

|| || ||)

, V , ( ) V ( ) ( 2 dk k k E T e E f E f dE h e j 

     

2 2 2 2 1 2 2 1 2 2 2 2 1 2 2 1 ||

) ( ) ( ) ( ) ( 4 ) ( 2 cosh ) ( ) ( ) ( ) ( 8 ) V, , ( k a k a k k dz z k a k a k k k E T

a

              



        

Current density:

voltage dependence appears

eq first up j

 I(V)

Voltage dependence tunnel current

SLIDE 17

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

 

 

  

|| || ||)

, V , ( ) V ( ) ( 2 dk k k E T e E f E f dE h e j 

Current density:

 I(V)

Fermi Dirac, gives window ~V I/V=G = conductance =Integral of T

Note 1) increase of G with V since more states available for tunneling 2) For symmetric barriers G~V2 3) For asymmetric barrier only G~V+const*V2

Voltage dependence of TMR and tunnel current

SLIDE 18

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Exemple of experimental I(V) characteristics in Co|AlOx|Co tunnel junction

T. Dimopoulos et al

Dynamic conductance=dI/dV See lectures of C. Tiusan and S. Valenzuela for epitaxial Fe|MgO MTJs

Voltage dependence of TMR and tunnel current

SLIDE 19

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Pros/Cons of Julliere/Slonczewski Models

AlOx tunnel barriers are amorphous.
In amorphous materials, all electronic effects related to crystal symmetry

are smeared out.

Evanescent waves in alumina have “free like” character.
Free electron models work OK in this case.
However, they fail with crystalline barriers. Additional band structures effect

in the electrodes and barrier must be taken into account (Bloch state symmetry based spin filtering). 1995-2005 AlOx barriers >2005 MgO barriers Best MR~80% Best MR~600% See lectures of C. Tiusan, S. Valenzuela for cristalline Fe|MgO MTJs

SLIDE 20

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

This lecture: Tunnel magnetoresistance (TMR) Spin transfer torques (STT)

Landau Lifshitz equation (LLG)
Quantum origin of spin transfer torque
Description of spin currents and spin transfer torques
Free electron model
Tight-binding model
Voltage dependence of STT
symmetric MTJs
asymmetric MTJs

Interlayer exchange coupling …

SLIDE 21

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Transfer Torque (STT): current acts on magnetization

Prediction:

J. Slonczewski (1996)
L. Berger (1996)

First observations:

M. Tsoi et al, PRL 80, 4281 (1998)
J. Katine et al, PRL 84, 3149 (2000)
Y. Huai et al, APL 84, 3118 (2004)
G. Fuchs, et al., APL 85, 1205 (2004)

j 



T

||

T

free ref

M ' M



M ' M

AP P 

P AP 

 

M M M M M M M H M M          



' '

||

T T g dt d M dt d

B e s

   

precession damping

parallel field-like

exchange of angular momentum between conduction and localized electrons
conservation of total angular momentum

Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation: Quantum

rigin?

) V (

1   Τ

Τ

Interlayer Exchange Coupling (IEC)

J. Slonczewski (1989), R.P.

Erickson (1993)

S. Zhang, P. M. Levy and A. Fert (2002)
M. D. Stiles and A. Zangwill (2002)

s spin valve tallic m for ~

e

 T

A. Kalitsov et al, JAP 99, 08G501 (2006)

MTJs for ) V (   T

SLIDE 22

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Unpolarized Electrons q Polarizer P Free Layer M Polarized Electrons Transmitted Electrons

t Electron Flow

Transfer of spin angular momentum m = Spin Torque

incoming transmitted

m

Conduction Electrons M

m

Mo Local Magnetization

Spin Momentum Transfer - Concept

Flow of angular momentum has a source or sink

Local exchange interaction between conduction electron spins and local magnetization M

SLIDE 23

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Transfer Torque

particle density

Particle transport

current density

Spin transport Continuity equation

conserved spin density spin current density

not conserved

Torque

M.D.Stiles and A.Zangwill, PRB 66 (2002) 014407

SLIDE 24

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Particle density:

Particle transport

Current density: Continuity equation: where Spin density:

Spin transport

Spin current density: where

Vector of Pauli matrices

Continuity equation:

      t s Q

) (r s

SLIDE 25

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin density:

 



   

 

i i i i i

   

* * x

2 s 

 



   

 

i i i i i

i i    

* * y

2 s 

 



   

 

i i i i i

   

* * z

2 s 

Spin current density:

 



   

 

i i i i i

    v v Q ˆ ˆ Re

* * x

 



   

 

i i i i i

    v v Q ˆ ˆ Re

* * z

 



   

 

i i i i i

i i     v v Q ˆ ˆ Re

* * y

Tensor quantity with elements with i=x,y,z in spin space and j=x,y,z in real space

ij

Q

xy 

Q

yy 

Q

zy 

Q

Current flows in y direction

) (r s

SLIDE 26

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin current tensor:

zy 

Q

xy 

Q

yy 

Q

Current flows in y direction

ik kQ

     Q T

i=x, y, z in spin space k=x, y, z in real space

ik

Q

Spin current and spin torque in non-collinear case Spin torque:

not conserved conserved

       

   

J J J J

Current matrix:

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

parallel (Slonczewski)

,

) ( (||)

 

 y x

T T

perpendicular (field-like)

)) ( ) ( ( 2 ) ( )) ( ) ( ( 2 ) ( q q q q q q

   

    J J e J J J e Qzy  

) ( ) ( ) ( TMR   J J J  

T T||

q

M. D. Stiles and A.Zangwill, PRB 66 (2002) 014407
A. Manchon et al, JPCM 20 (2008) 145208

SLIDE 27

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Physical origin of Spin transfer torque (sd model) Consider two populations of electrons:

1) s conduction electrons (spin-polarized)
2) d more localized electrons responsible for magnetization

The spin-polarized conduction electrons and localized d electrons interact by exchange interactions

) ( ) ( 2

2 d

.S σ 

sd

J r U m p H   

Hamiltonian of propagating s electrons:

In non-colinear geometry, exchange of angular momentum takes place between the two populations of electrons but total angular moment is conserved.

Kinetic Potential Exchange sd Pauli matrices vector

Unit vector//M

) , ( electrons s to due

n

Torque t r Jsd

d

s S S

d 

 

s=local spin-density of s electrons

A. Manchon et al, JPCM 20 (2008) 145208

SLIDE 28

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Physical origin of Spin transfer (sd model) (cont’d)

Local spin density at r and t : Electron wave-function

) , ( t r  ) , ( 2 ) , ( ) , (

*

t r t r t r   σ s   

Temporal variation of local spin density:

 

          σ σ s

* *

2 ) , (   t r

Schrödinger equation :

) , ( ) , ( t r H i t r      

(1) (2)

Substitution (2) in (1) :

 

 

    σ σ s   

* *

2 1 ) , ( H H i t r  

 

) , ( , ) , ( t r J t r t r

sd

s S Q s

d 

     

…

Q is the spin density current

3x3 tensor Spin space x real space

   

 

t r t r m , , Im 2

* 2

 

r

σ Q           

 

) , ( ) , ( t r t r  

A. Manchon et al, JPCM 20 (2008) 145208

SLIDE 29

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Physical origin of Spin transfer (sd model) (cont’d)

 

) , ( , t r J t r

sd

s S Q T

d 

    

In ballistic systems:

The exchange interaction between spin-polarized s electrons and more localized d electrons is responsible for spin-transfer torque. This interaction yields a precessional motion of spin-density of s electrons around the local

magnetization. In ballistic regime, the spin-transfer torque is also equal to the

divergence of spin-current.

In diffusive systems:

 

) , ( , t r J t r

sd SF

s S s Q T

d 

      

Takes into account the spin-memory loss by scattering with spin lifetime

SF



can be fully calculated by solving Schrodinger equation in non-colinear geometry

T

See lectures of G. Bauer, T. Jungwirth, S. Valenzuela for metallic spin valves

SLIDE 30

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Let’s derive STT expressions

1 1

, k k

 

2 2

, k k

 

k

z y  x (||)

Barrier FM’ M’ FM M f 1 2

1 1 1

1

W.F. in layer 1 W.F. in layer 2: W.F. in layer 3: (quant. axis || M): (quant. axis || M') (quant. axis || M')

ik y ik y ik y

e r e r e

  

   

     Y     

2 2

2 ik y k y k y k y k y ik y

t e A e B e A e B e t e

 

       

       Y  Y          

1 1 2

component of majority spin ˆ momentum with M as quantization axis component of minority spin ˆ momentum with M as quantization axis component of majority spin k z k z k z

  

     

2

ˆ momentum with M as quantization axis component of minority spin ˆ momentum with M as quantization axis k z



   

SLIDE 31

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Rotate Y1 in respect to direction of M’

         



   



 

1 1 1 1 1 1 1 1 1

1

cos / 2 sin / 2 sin / 2 cos / 2 cos / 2 sin / 2 sin / 2 cos / 2

ik y ik y ik y ik y ik y ik y ik y ik y ik y

e r e r e e r e r e e r e r e        

        

           

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

Rotate Y1 about y axis through angle f. See G. Bauer’s lecture

1 1

, k k

 

2 2

, k k

 

k

z y  x (||)

Barrier FM’ M’ FM M f 1 2

SLIDE 32

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Wave functions for non-collinear MTJ

z y  x (||)

Barrier FM’ M’ FM M  1 3 2 4 systems of

8Eqs. and

8Uknowns

SLIDE 33

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

         

 

where ), ( ) ( ) ( ) V ( ) ( ' ) ( sin ) ( ' ) ( cos ) )( ( e sin ) ( ) )( )( ( ) ( ) (

1 2 ) ( 2 2 2 2 2 ||

E T E T E T e E f E f y k k k k a q y k k k k a q Den k k q k k k k a q q E T

R L R R R R R R R R dy y q L L R R L L

a

                 

              

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

 

               

' ) ( sin ) ( ) )( ( ) ( ) )( ( ' ) ( cos ) ( ) ( ) )( )( ( ) ( ) V ( 2 e sin ) )( )( ( ) ( ) (

2 2 2 2 ) ( 2 2 2 2

y k k k k q k k a q k k a q k k q y k k k k a q k k q k k k k a q q e E f Den k k k k a q q E T

R R L L R R R R L L R R R R L L R R L L R dy y q R R L L

a

                         

                    

         

 

) V ( ) ( ' ) ( cos ) ( ' ) ( sin ) )( ( e sin ) ( ) )( )( ( ) ( ) (

2 ) ( 2 2 2 2 2 1

e E f E f y k k k k a q y k k k k a q Den k k q k k k k a q q E T

R L R R R R R R R R dy y q L L R R L L

a

           

               



a Free electron model

Wave vectors depends on V and band positions
Boundary conditions for Green functions and derivatives

Explicit analytical expressions for STT

In the right FM layer (as an example):

M. Chshiev, A. Manchon, A. Kalitsov et al, Phys. Rev. B (2015)

SLIDE 34

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

  a Free electron model

   

  

i i i i i

k k k k P

   

  

i i i i i i i

k k q k k q

2 2



   

  

i i i i i i i

k k q k k q

2

) ( 

Local torques (derivatives of Q):  Oscillations of different periods  Shorter period for RKKY coupling  Longer period for voltage induced

SLIDE 35

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

  a Free electron model

   

  

i i i i i

k k k k P

   

  

i i i i i i i

k k q k k q

2 2



   

  

i i i i i i i

k k q k k q

2

) ( 

Local torques (T = ∇Q):  Oscillations of different periods  Shorter period for RKKY coupling  Longer period for voltage induced Transverse characteristic length scales:

Larmor spin precession length, 𝑀
Transverse spin decay length, 𝑒
Applied voltage dependent
M. Chshiev, A. Manchon, A. Kalitsov et al, Phys. Rev. B (2015)

SLIDE 36

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

  a Free electron model

   

  

i i i i i

k k k k P

   

  

i i i i i i i

k k q k k q

2 2



   

  

i i i i i i i

k k q k k q

2

) ( 

Total torques:  Deviations from sine dependence in case of low/thin barrier  Eventually for metallic spin valves

SLIDE 37

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

  a Free electron model

   

  

i i i i i

k k k k P

   

  

i i i i i i i

k k q k k q

2 2



   

  

i i i i i i i

k k q k k q

2

) ( 

Total torques:  Case of thick barrier  Parallel torque related to longitudinal spin current

i i i i i S i

P P P P  

 



Slonczweski polarization
out-of-plane polarization

2 2 i i i i

T     

Spin averaged interfacial

transmission probability

M. Chshiev, A. Manchon, A. Kalitsov et al, Phys. Rev. B (2015)

SLIDE 38

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

 L

k

 L

k

 R

k

 R

k

) (y q

V e

U

EF



E



E 2 2

  a Free electron model

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

V e

B



  2 2





















Tight-binding model

Model parameters:

B

  ,

) ( 

on-site energies

t, tB – hopping

ta, t’b – couplings

SLIDE 39

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

V e

B



  2 2





















Tight-binding model

Model parameters:

B

  ,

) ( 

on-site energies

t, tB – hopping

ta, t’b – couplings

V , 1 1 ) ( . . 1 1 . . 1 1 ) V ( cos sin sin cos 2 1 1 2

B B B ' ' ' ' ' ' ' ) (

) ( ) ( ) ( ) (

e N i c c t c c H c h c c t H c h c c t H c c t c c e H H H H H H c c t c c H H H H H H H

B i i NN j i i i i B b b RB a a LB NN R R L NN L RB LB B R L

R L R L R L R L

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

     

           

        

                 

Hamiltonian

I. Theodonis et al, PRL 97, 237205 (2006)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)
A. Kalitsov et al, PRB 79, 174416 (2009)

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

SLIDE 40

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ M’ FM M

zy

Q

yy

Q

xy

Q

T T||

q

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

V e

B



  2 2





















Tight-binding model

Model parameters:

B

  ,

) ( 

on-site energies

t, tB – hopping

ta, t’b – couplings Charge current: Keldysh formalism with non-equilibrium Green functions Total torque:

1 ' , ' ' , 1 ' '  

 

    

Q Q Τ

Torque:

2 x 2 matrices

   

y J ˆ ' ' 8

1 ' , ' ' , 1 ' || 3       

 

 

T G T G r T dk dE e

   

 h

   

σ Q

       

 

 

' ' 16 1

1 ' , ' ' , 1 ' || 3 ' , 1 '

T G T G r T dk dE

     



Spin current:

) ( ) ' ( ) ' , (

' † ' ' '

t c t c i t t G

   

 

 

Non-collinear M and M’

        

   

G G G G G

 

 

         

    

' , 1 , 1 1 ' , ' ' , 1 ' ' '       

Q Q Q Q Τ Τ

  

D. M. Edwards et al, PRB 71, 054407 (2005)
I. Theodonis et al, PRL 97, 237205 (2006)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)



 

 

' ' '

ˆ

    G

O i O 

SLIDE 41

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

1. Using divergence of spin current Q: 2. Using magnetic moment and exchange splitting:

Two ways to find spin torque in ballistic regime

xy 

Q

yy 

Q

zy 

Q

Current flows in y direction

ik kQ

     Q T

i=x, y, z in spin space and k=x, y, z in real space

Δ μ T  

B

 1

z Δ ˆ 2

  

  

In ballistic regime:

 

) , ( , t r J t r

sd

s S Q T

d 

    

SLIDE 42

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

a μ T  

B

1 

Let’s check relation between T and  using its’ angular dependence. Suppose they are related via unknown vector a. Then: ) , , (

z

a a

|| ||

   

  z z z

T a T a T  

|| ||

 

 

   T T az

Δ a 

The two methods give quantitative agreement and are connected directly via exchange splitting

z Δ ˆ 2

  

  

Q Δ μ T     

B

1 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1.0
0.8
0.6
0.4
0.2

0.0 0.2 0.4

1.0
0.8
0.6
0.4
0.2

0.0 0.2 0.4

Torque (eV)

 rad

T|| T || 

 

V=0.1 V, N=5, i=1 (at FM/I interface)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 2.0x10

1

4.0x10

1

Tx/y= -Ty/x



(

 )/2=-0.1

(

 )/2=-0.2

(

 )/2=-0.3

A. Kalitsov et al, JAP 99, 08G501 (2006)

Two ways to find spin torque in ballistic regime

SLIDE 43

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

 

) , ( , t r J t r

sd

s S Q T

d 

    

In ballistic systems:

The exchange interaction between spin-polarized s electrons and more localized d electrons is responsible for spin-transfer torque. This interaction yields a precessional motion of spin-density of s electrons around the local

magnetization. In ballistic regime, the spin-transfer torque is also equal to the

divergence of spin-current.

In diffusive systems:

 

) , ( , t r J t r

sd SF

s S s Q T

d 

      

Takes into account the spin-memory loss by scattering with spin lifetime

SF



A. Manchon et al, JPCM 20 (2008) 145208

Two ways to find spin torque in ballistic regime

SLIDE 44

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

In the right FM layer site ’

Coupling amplitude decreases with exchange splitting

6 12 18 24 30

4.0x10
11
2.0x10
11

0.0 2.0x10

11

4.0x10

11

6.0x10

11

8.0x10

11

1.0x10

10

V=0, 

Torque (eV/a.u.)

'

T,  T, 

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

Period of oscillations is 

) /( 1

   k

k

Perpendicular torque component T is not zero @ zero bias describing exchange coupling between FM layers

J. C. Slonczewski, Phys. Rev. B 39, 6995 (1989);

ibid.71, 6995 (2005);

D. M. Edwards et al, Phys. Rev. B 71, 024405 (2005)
A. Manchon et al, JPCM 20, 145208 (2008)

e- Local torques in the right FM at zero voltage

Note RKKY period (summation of k)

SLIDE 45

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions» 5 10 15 20 25 30

1.0x10
10

0.0



  , V=0.5V, 

Torque (eV)

'

T|| T

5 10 15 20 25 30

1.0x10
10

0.0 1.0x10

10



  , V=0.5V, 

Torque (eV)

'

T|| T

Local torques in the right FM at positive/negative bias Period of oscillations is 

) /( 1

  k

k

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

A. Kalitsov et al., JAP 99, 08G501
A. Manchon et al, JPCM 20, 145208
M. Wilczyński et al., PRB 77, 054434
D. Ralph and M.Stiles, JMMM 320, 1190

e-

Note voltage (current) induced STT period (difference of k)

SLIDE 46

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Precession of spin state in exchange field of the magnet Case 1: insulating barrier (tunnel junctions)  precession period 2/(k↑ + k↓) for RKKY IEC  precession period 2/(k↑ - k↓) for STT voltage induced only electrons with k interface tunnel  selection of k-vectors integration over k-vectors does not average to zero

NM M2

Qtrans

M1

q

M2

x y z T

T||

Non-zero X and Y – component of torque!!!

SLIDE 47

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Precession of spin state in exchange field of the magnet Case 2: metallic structures Consequence of dephasing  away from the interface, reflected and transmitted spin currents are collinear to M2  The entire transverse spin current is absorbed by M2 at interface

Difference with metallic structures for STT

Only torque in x-direction M1

q

M2

x y z

SMT

NM In phase Dephased M2 M2 Qtrans Qrefl Qin

T

T||

X

SLIDE 48

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

3
2
1

1

1.0x10
4

0.0



t

Q(a.u.)

Energy (eV) Q

L , 0V

Q

R , 0V

Q

L , +0.1V

Q

R , +0.1V

Q

L , -0.1V

Q

R , -0.1V



t

EF

2.0x10
4

0.0 2.0x10

4

Energy (eV)

Q(a.u.)

Q

L ||, 0V

Q

L ||, +0.1V

Q

L ||, -0.1V

Q

R || , 0V

Q

R || , +0.1V

Q

R || , -0.1V

EF

1 ' 1 ' 1 ' ' '        

 

      Q Q Q Q Q Τ Τ

    

Spin current (total torque) on energy

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

Q|| Q

V e

B



  2









 



F



z y x (||)

) ( ) (

|| ||

E Q E Q

R L

 

} , min{

R L f

f E 

V ) ( V ) (

) V ( ) (

  > 

  e E Q E Q

L R R L

V V

) V ( ) (

  > 

  e E Q E Q

e-

R L

Q Q Q  

M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)

Back to tunnel junctions

SLIDE 49

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

1 ' 1 ' 1 ' ' '        

 

      Q Q Q Q Q Τ Τ

    

2.0x10
4

0.0 2.0x10

4

Energy (eV)

Q(a.u.)

Q

L ||, 0V

Q

L ||, +0.1V

Q

L ||, -0.1V

Q

R || , 0V

Q

R || , +0.1V

Q

R || , -0.1V

EF

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

R L

Q Q Q  

V e

B



  2









 



F



z y x (||)

3
2
1

1

1.0x10
4

0.0



t

Q(a.u.)

Energy (eV) Q

L , 0V

Q

R , 0V

Q

L , +0.1V

Q

R , +0.1V

Q

L , -0.1V

Q

R , -0.1V



t

EF

Q|| Q

) ( ) (

|| ||

E Q E Q

R L

 

} , min{

R L f

f E 

V ) ( V ) (

) V ( ) (

  > 

  e E Q E Q

L R R L

V V

) V ( ) (

  > 

  e E Q E Q

e-

M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)

Spin current (total torque) on energy

Back to tunnel junctions

SLIDE 50

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

1 ' 1 ' 1 ' ' '        

 

      Q Q Q Q Q Τ Τ

    

x x x x x x x x x x x x x x x x x

a   ’ ’ ’ i j b

V e

B



  2









 



F



z y x (||)



T

is an even parity function

f applied voltage!

||

T

is zero at zero voltage and is non monotonic function of applied voltage

R L

Q Q Q  

2.0x10
4

0.0 2.0x10

4

Energy (eV)

Q(a.u.)

Q

L ||, 0V

Q

L ||, +0.1V

Q

L ||, -0.1V

Q

R || , 0V

Q

R || , +0.1V

Q

R || , -0.1V

EF

3
2
1

1

1.0x10
4

0.0



t

Q(a.u.)

Energy (eV) Q

L , 0V

Q

R , 0V

Q

L , +0.1V

Q

R , +0.1V

Q

L , -0.1V

Q

R , -0.1V



t

EF

Q|| Q

e-

D. Ralph and M.Stiles, JMMM 320, 1190 (2008)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)

Spin current (total torque) on energy

Back to tunnel junctions

SLIDE 51

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

theory PRL 97, 237205 (2006) IEEE Trans. Mag. 44, 2543 (2008)

Total torques: Comparison of theory and experiment

H. Kubota et al,

Nature Physics 4, 37 (2008)

||

T



T

(field-like)

i i

C

2 2

V Τ Τ



 

 

SLIDE 52

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

||

T

~V

H. Kubota et al,

Nature Physics 4, 37 (2008)

J. C. Sankey et al, ibid. 4, 67 (2008)

~V2

Total torques: Comparison of theory and experiment



T

(field-like)

i i

C

2 2

V Τ Τ



 

 

theory PRL 97, 237205 (2006) IEEE Trans. Mag. 44, 2543 (2008)

SLIDE 53

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

||

T

~V

C. Heiliger et al, PRL 100, 186805 (2008)
A. Manchon et al, JPCM 20, 145208 (2008)
M. Wilczyński et al., PRB 77, 054434 (2008)
J. Xiao et al., PRB 77, 224419 (2008)
H. Kubota et al,

Nature Physics 4, 37 (2008)

A. Deac, ibid. 4, 803 (2008)
J. C. Sankey et al, ibid. 4, 67 (2008)

Total torques: Comparison of theory and experiment

theory

I. Theodonis et al,

PRL 97, 237205 (2006) IEEE Trans. Mag. 44, 2543 (2008)

~V2



T

(field-like)

i i

C

2 2

V Τ Τ



 

 

SLIDE 54

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

||

T

C. Heiliger et al, PRL 100, 186805 (2008)
A. Manchon et al, JPCM 20, 145208 (2008)
M. Wilczyński et al., PRB 77, 054434 (2008)
J. Xiao et al., PRB 77, 224419 (2008)
H. Kubota et al,

Nature Physics 4, 37 (2008)

A. Deac, ibid. 4, 803 (2008)
J. C. Sankey et al, ibid. 4, 67 (2008)

Total torques: Comparison of theory and experiment

theory

I. Theodonis et al,

PRL 97, 237205 (2006) IEEE Trans. Mag. 44, 2543 (2008)

~V2



T

(field-like)

i i

C

2 2

V Τ Τ



 

 

C. Wang et al., Nature Phys. (2011)

SLIDE 55

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

(fA) ) (

) (



s z

I

(AP) (P)     

(fA) ) (

) (



s z

I

(AP) (P)     

) (

z

Q ) (

z

Q The parallel (Slonczewski) torque T|| may be found from collinear currents

   

) ( ) ( ) ( ; ' ' ) ( ) ( 4 ) (

||

    

 

      J J Q Q Q e T

z z z

M M M 

         

 

2 1 2 1 3 2 2 1

, 2 / ) ( ), ( ) ( ) ( ) (                 where V O V V V J

,       

   

V Qz  ) (

Parallel magnetizations:

Brinkman model:

,

   

      

2

) ( V Qz  

Antiparallel magnetizations:

I. Theodonis et al, PRL 97, 237205, 2006

2 ||

V Τ 

) (

z

Q

may vanish

In-plane torque (T||) for symmetric MTJ

SLIDE 56

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Field-like torque (T) for (a)symmetric MTJ

V e

B



  2L

 L



 L



 



F



2 , 2

) ( ) ( ) ( ) ( ) ( ) (    

    

R L R L R L R L R L R L

    

) ( ) ( ) ( ) ( ) ( ) ( R L R L R L R L R L R L

     

 

   

i i i 2 2 V

C Τ







Symmetric MTJ: T is an even parity function of applied voltage:

(I. Theodonis et al, PRL 97, 237205 (2006); M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008))

Asymmetric MTJ (deviations from V2): T with odd parity terms appeared :

(C1 in A. Manchon et al, JPCM 20, 145208 (2008); M. Wilczyński et al., PRB 77, 054434) ; Xiao et al., PRB 77, 224419 (2008); S.-C. Oh et al, Nature Physics 5, 898 (2009) i i iV

C Τ







1

1

2.0x10
6

0.0





R eV





L



R eV

T (eV/)





L eV





L eV





L eV

Voltage

SLIDE 57

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

P->AP (AP->P)

Spin transfer MRAM: (STT-MRAM) Uncontroled phenomenon during «bit» writing in STT-MRAMs: “back-switching” ON

jSTT Vdd écriture “1”

ON

jSTT

free pinned

Vdd écriture “0”

Spin Transfer Torques in Magnetic Tunnel Junctions

back switching is a problem for MRAM

experiment

Could theory help understanding a problem?

Yes!

SLIDE 58

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

 

M M M M M M M H M M          



' '

||

T T g dt d M dt d

B e s

   

precession damping

Slonczewski

Landau-Lifshitz-Gilbert (LLG) equation:

field-like STT: Current acts on Magnetization

M’ M

j 



T

||

T

ref free

P->AP (AP->P)

T>0 T||>0 T>0 T||<0 back switching is a problem for MRAM

I. Theodonis et al, PRL 97, 237205 (2006)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)
A. Manchon et al, JPCM 20, 145208 (2008)
A. Kalitsov et al, PRB 79, 174416 (2009)

For symmetric MTJ theory predicted:

For V>0: T(V) =- T||(V)

Could theory provide a solution for backswitching?

Yes!

experiment

V

Τ

; V Τ

// 2

 



Spin Transfer Torques in Magnetic Tunnel Junctions

SLIDE 59

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

STT: Current acts on Magnetization

M’ M

j 



T

||

T

ref free

P->AP (AP->P)

T>0 T||>0 T>0 T||<0 back switching is a problem for MRAM

i i iV

C Τ







For asymmetric MTJ theory predicts linear term experiment

V e

B



 

ref

 

F



free

ref ≠ free

S.-C. Oh, S.-Y. Park, A. Manchon, M. Chshiev et al, Nature Physics 5, 898 (2009)

Theory Exp.

For asymmetric MTJs (ref < free) backswitching voltage can be shifted up (blue curves) away from writing voltage

(which is also observed in experiment)

Spin Transfer Torques in Magnetic Tunnel Junctions

SLIDE 60

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Transfer Torques and TMR in Magnetic Tunnel Junctions

STT: MTJ with asymmetric barrier

V e

B



  2 2



















 ' 

M’ M

j 



T

||

T

ref free

A. Kalitsov et al, PRB 88, 104430 (2013)
1.0
0.5

0.0 0.5 1.0 10 20 30

1.0
0.5

0.0 0.5 1.0

16
12
8
4

T|| (peV/ ฀) Voltage (V)

clean left center right

(a) (b) T (peV / ฀) Voltage (V)

฀

1.0
0.5

0.0 0.5 1.0

0.3
0.2
0.1

0.0 0.1 0.2 0.3

1.0
0.5

0.0 0.5 1.0

0.2
0.1

0.0 0.1 0.2

1.0
0.5

0.0 0.5 1.0

60
40
20

20 40 60

T|| / I (h / 2e) Voltage (V)

clean left center right

(a) (b)

(T - T

) / I (h / 2e)

Voltage (V)

(c)

TMR (%) Voltage (V)

STT and TMR voltage dependence tuning by Interface engineering

T||(V) and T(V) vs additional layer position in the barrier STT efficiency and TMR vs additional layer position in the barrier

t 6 '

B 

  

(resonant regime)

t 6 '

B 

>  

(tunneling regime)

SLIDE 61

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Transfer Torques and TMR in Multiferroic Magnetic Tunnel Junctions

A. Useinov, M. Chshiev and A. Manchon, Phys. Rev. B 91, 064412 (2015)

See lecture of A. Barthelemy

SLIDE 62

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

A. Useinov, M. Chshiev and A. Manchon, Phys. Rev. B 91, 064412 (2015)

Spin Transfer Torques and TMR in Multiferroic Magnetic Tunnel Junctions

SLIDE 63

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Filtering (SF) based on magnetic insulators (EuO, EuS, ferrites, etc.)

A. V. Ramos1, M.-J. Guittet1, J.-B. Moussy1, R. Mattana2, C. Deranlot2, F. Petroff2, and C. Gatel3

See lecture of S. Valenzuela

SLIDE 64

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

C. Ortiz Pauyac et al, Phys. Rev. B 90, 235417 (2014)

SLIDE 65

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

C. Ortiz Pauyac et al, Phys. Rev. B 90, 235417 (2014)

SLIDE 66

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin filtering in crystalline MTJs (Fe|MgO|Fe)

Huge TMR in crystalline MTJ if:

Good epitaxial fit between FM and I(SC)
Evanescent states in I(SC) with the same

Bloch state symmetry

High symmetry Bloch state (1) for one of two e-

spin states in FM electrodes (“half-metallic”-like)

Spin Transfer Torque (STT)

I. Theodonis et al, PRL 97, 237205 (2006)
A. Manchon et al, JPCM 20, 145208 (2008)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)
A. Kalitsov et al, PRB 79, 174416 (2009)
A. Khalil et al, IEEE Trans. Mag. 46, 1745 (2010)?

Models seems to be ok

M’ M

j 



T

||

T

ref free

W. H. Butler et al, PRB 63, 054416 (2001); IEEE Trans. Mag. 41 (2005) 2645

MgO

3 bcc Fe ↑

s-like
low filled

Spin Transfer Torques and TMR in Magnetic Tunnel Junctions

SLIDE 67

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

FM

MgO FM

Cr

 F

E

 F

E

F. Greullet et al, PRL 99, 187202 (2007)

What about effect of Cr on STT?

TMR in Fe|Cr|MgO|Fe Magnetic Tunnel Junctions

SLIDE 68

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Model (NEGF):

       

    ) ( ) ( ) ( ) ( d s d s d s d s

J J J J

Current matrix:

x z y

Barrier FM’ FM M

)) ( ) ( ( 2 ) (

) ( ) ( ) (

q q q

 

 

d s d s d s

J J e J 

) ( ) ( ) ( TMR   J J J  

q

V e

B

d s

U

) (

) ( ) (   d s

U

NM

NM d s

U

) ( ) ( ) (   d s

U

M’

 

  

           

 

 

'

) ' , ( '

z z

z z G z z dE d J

 

  

            

' ' ' '

) ' , ( '

   

 

z z spin

z z G z z dE d s J

Charge current: Spin current: Spin torque:

spin

J T   

b d s NM d s d s

m m m

) ( ) ( ) ( ) (

, ,

 

Effective mass:

M. E. Eames et al, APL, 88, 252511 (2006)
J. Callaway et al, PRB 16, 2095 (1977)
J. Schäfer et al, ibid. 72, 155115 (2005)
A. H. Davis et al, JAP 87, 5224 (2000)
W. H. Butler, et al. PRB 63, 054416 (2001)

Refs for parameters

a

5 1

' ' ' '     d s

A. Manchon et al, JPCM, 20, 145208 (2008)
A. Vedyaev et al, J. Appl. Phys. 107, 09C720 (2010)

SLIDE 69

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Results for Fe|Cr(a)|MgO|Fe

40
30
20
10
20

20 40 60 Torque, oE Z, nm a=0 a=4

20
10

0.0 5.0x10

4

1.0x10

5

Torque, oE Z, nm a=0 a=4

Torque is mainly due to s-electrons
It almost vanishes when Cr is inserted

(Cr acts as barrier for s-electrons, i.e. 1)

Torque due to d-electrons is weak and

almost insensitive in value to Cr insertion

Phase of oscillations is affected

s-electrons d-electrons Torque distribution in the left Fe layer

SLIDE 70

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin filtering in crystalline MTJs (Fe|MgO|Fe)

Huge TMR in crystalline MTJ if:

Good epitaxial fit between FM and I(SC)
Evanescent states in I(SC) with the same

Bloch state symmetry

High symmetry Bloch state (1) for one of two e-

spin states in FM electrodes (“half-metallic”-like)

Spin Transfer Torque (STT)

I. Theodonis et al, PRL 97, 237205 (2006)
A. Manchon et al, JPCM 20, 145208 (2008)
M. Chshiev et al, IEEE Trans. Mag. 44, 2543 (2008)
A. Kalitsov et al, PRB 79, 174416 (2009)
A. Khalil et al, IEEE Trans. Mag. 46, 1745 (2010)?

Models seems to be ok Interlayer Exchange Coupling (IEC)

M’ M

j 



T

||

T

ref free

W. H. Butler et al, PRB 63, 054416 (2001); IEEE Trans. Mag. 41 (2005) 2645
H. X. Yang et al, APL 96, 262509 (2010)
J. Faure-Vincent et al,

PRL 89, 107206 (2002)

Tight-binding results with a choice of parameters used successfully for STT behaviour

DFT with GGA for Vxc
PAW pseudopotentials
VASP

MgO

Interlayer Exchange Coupling in Magnetic Tunnel Junctions 3

bcc Fe ↑

s-like
low filled

SLIDE 71

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

z y  x (||)

Barrier FM’ FM

x x x x x x x x x x x x x x x x x

Total energy differences for P and AP

IEC period and amplitude are nonmonotonic functions of the Fermi level

5 10 15 20 25 30

8,0x10
6
4,0x10
6

0,0 4,0x10

6

8,0x10

6



0=+3.4



0=+3.6

Left layer thickness (ML) IEC (a.u.)



dR=5

5 10 15 20 25 30

1,2x10
5
1,2x10
5
1,1x10
5



dR=5 Left layer thickness (ML) IEC (a.u.) 

0=+3.8

5 10 15 20 25 30

1,4x10
5
1,4x10
5



dR=5 IEC (a.u.) Left layer thickness (ML) 

0=+4

dL dR q

Equilibrium IEC on FM layers thickness

1

S 

2

S 

B



  2 2





















Period of oscillations T

T~5 ML T~7 ML T~5 ML T~7 ML

P.Bruno, PRB 52, 411 (1995) L.E.Nistor et al, PRB 81, 220407 (2010)

SLIDE 72

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

5 10 15 20 25 30

1.2x10
5
1.2x10
5
1.1x10
5



dR=5 FM layer thickness (ML) IEC (a.u.) 

0=+3.8

theory

MTJ with perpendicular magnetic anisotropy (pMTJ) First observation of oscillatory AF IEC in perpendicular MTJs (pMTJ) FM layers thickness dependence in MTJ with PMA (pMTJ)

L.E.Nistor et al,

Phys. Rev. B 81, 220407 (2010)

Λ~5 ML

en accord avec P.Bruno, PRB 52, 411 (1995)

exp

Interlayer Exchange Coupling in Magnetic Tunnel Junctions

SLIDE 73

M. Chshiev

«Theory of spintronic phenomena in magnetic tunnel junctions»

Spin Transfer Torques and TMR:
Free electron and a tight-binding descriptions
Theory predicted STT voltage dependences in MTJs
Field-like torque is an even-parity function of applied voltage

for symmetric MTJs

Linear term appears in case of asymmetric MTJs
provides with a solution for “back-switching” problem
Models are satisfactory for TMR, STT and IEC

Summary

ON

jSTT Vdd écriture “1”

M’ M

j 



T

||

T

ref free

Thank you!

Acknowledgments:

A. Manchon, A. Kalitsov, H.-X. Yang, A. Schuhl, B. Dieny, W. H. Butler, K.-J. Lee, C. Ortiz Pauyac,
I. Theodonis, J. Velev, L. Nistor, N. Kioussis, A. Vedyayev, N. Strelkov, N. Ryzhanova and all colleagues