Spin transfer torque and magnetization dynamics in in...

Spin transfer torque and magnetization dynamics inin-plane and out-of-plane magnetized spin valves

Pavel Baláž

Institute of Molecular Physics in PoznanPolish Academy of Sciences

andFaculty of Physics

A. Mickiewicz University in Poznan

Univerzita Karlova, 5 December 2013

P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 1 / 35

Nanoscale spin torque devices for spin electronicsJoint research project under the framework of Polish-Swiss research programme

nanospin.agh.edu.pl

Partners

• AGH University of Science and Technology in KrakówT. Stobiecki – coordinator

• Institute of Molecular Physics in Poznan, Polish Academy of SciencesJ. Dubowik – experiment, J. Barnas – theory

• Ecolé Polytechnique Fédérale in LausanneJ.-Ph. Ansermet

Objectives

jointly developing novel nanoscale spintronic devices based on the spin transfer torqueeffect, which promises unrivaled future scaling, flexibility and low power consumption


1 Introduction

2 Spin-torque in metallic spin valves

3 Dual spin valve

4 Nonlinear magnetoresistance in dual spin vales

5 Current-induced switching in metallic spin valves with perpendicular polarizers


Introduction

Outline

1 Introduction


3 Dual spin valve




Introduction

Spin valves and Giant magnetoresistance

spin

spin

M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas

Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices

Phys. Rev. Lett. 61, 2472–2475 (1988)

G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn

Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange

Phys. Rev. B 39, 4828–4830 (1989)

R. E. Camley and J. Barnas

Theory of giant magnetoresistance effects in magnetic layered structures with antiferromagnetic couplingPhys. Rev. Lett. 63, 664–667 (1989)

T. Valet and A. Fert

Theory of the perpendicular magnetoresistance in magnetic multilayersPhys. Rev. B 48, 7099–7113 (1993)


Introduction

Current-induced dynamics and magnetization switching

Magnetization can be switched by electric current without need of magnetic field

Slonczewski’s model (ballistic)

J. Magn. Magn. Mater. 159, L1-L7 (1996)

0.0

0.1

0.2

0.3

0 0.25 0.5 0.75 1

g(θ)

si

n(θ)

θ/p

0.2

0.3 (Py)

0.35 (Co)

0.4

τSloncz =Ig(θ )

es×

(

s× S)

where

g(θ ) =

[

−4+(1+P)3 3+cos θ

4P3/2

]−1


Introduction

Current-induced dynamics and magnetization switching

Magnetization can be switched by electric current without need of magnetic field

Slonczewski’s model (ballistic)

J. Magn. Magn. Mater. 159, L1-L7 (1996)

0.0

0.1

0.2

0.3

0 0.25 0.5 0.75 1

g(θ)

si

n(θ)

θ/p

0.2

0.3 (Py)

0.35 (Co)

0.4

τSloncz =Ig(θ )

es×

(

s× S)

where

g(θ ) =

[

−4+(1+P)3 3+cos θ

4P3/2

]−1

Unified description (diffusive)

Description of spin-transfer torque

should be consistent with description

of giant magnetoresistance (Valet-Fert

model)

J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev

From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)

Spin-transfer torque

τθ = a(θ ) I s×(

s× S)

τφ = b(θ ) I s× S


Introduction

Equation of motion

Landau-Lifshitz-Gilbert equation

ds

dt=−|γg|µ0 s×Heff −α s×

ds

dt+

|γg|

Msd

(

τθ + τφ

)

Effective magnetic field

Heff =−Hextez −Hani (s · ez) ez +Hdemag


τθ = a(θ ) I s×(

s× S)

τφ = b(θ ) I s× S


Spin-torque in metallic spin valves

Outline

1 Introduction


3 Dual spin valve





Mathematical description

Two channels model

bulk resistivities

ρ↑(↓) = 2ρ∗ (1∓β )

interface resistances

R↑(↓) = 2R∗ (1∓ γ)

β bulk asymmetry paramters

γ interfacial asymmetry parameter

Diffusive transport

∂ 2(µ↑− µ↓)

∂x2=

1

l2sf

(µ↑− µ↓)

∂ 2(µ↑+ µ↓)

∂x2= η

∂ 2(µ↑− µ↓)

∂x2






Two channels model

bulk resistivities

ρ↑(↓) = 2ρ∗ (1∓β )

interface resistances

R↑(↓) = 2R∗ (1∓ γ)

β bulk asymmetry paramters

γ interfacial asymmetry parameter

Diffusive transport

∂ 2(µ↑− µ↓)

∂x2=

1

l2sf

(µ↑− µ↓)

∂ 2(µ↑+ µ↓)

∂x2= η

∂ 2(µ↑− µ↓)

∂x2

for electrochemical potentials we get

µ↑ = (1+η)[

Aex/lsf +Be−x/lsf

]

+Cx+G

µ↓ = (η −1)[

Aex/lsf +Be−x/lsf

]

+Cx+G






Magnetic layer

ˇµ = µ01+gσz

µ0 =µ↑+ µ↓

2, g =

µ↑− µ↓

2

with g being spin accumulation

j =−ρ(EF)D∂ ˇµ

∂x

j =1

2

(

j01+ jzσz

)

with jz being spin current

Diffusive transport

∂ 2(µ↑− µ↓)

∂x2=

1

l2sf

(µ↑− µ↓)

∂ 2(µ↑+ µ↓)

∂x2= η

∂ 2(µ↑− µ↓)

∂x2


µ↑ = (1+η)[

Aex/lsf +Be−x/lsf

]

+Cx+G

µ↓ = (η −1)[

Aex/lsf +Be−x/lsf

]

+Cx+G






Nonmagnetic layer

has no natural quantization axis

ˇµ = µ01+g.σ

j =1

2

(

j01+ j.σ)

where

g = (gx,gy,gz) , j = (jx, jy, jz)

are 3D vectors written in the

coordinate system of one of the

adjacent magnetic layers

Diffusive transport

∂ 2(µ↑− µ↓)

∂x2=

1

l2sf

(µ↑− µ↓)

∂ 2(µ↑+ µ↓)

∂x2= η

∂ 2(µ↑− µ↓)

∂x2


µ↑ = (1+η)[

Aex/lsf +Be−x/lsf

]

+Cx+G

µ↓ = (η −1)[

Aex/lsf +Be−x/lsf

]

+Cx+G





Boundary conditions at N/F interface

• particle current is continuous across all interfaces

e2j0 = (G↑+G↓)(µF0 − µN

0 )+(G↑−G↓)(gFz −gN

z )

• spin current component parallel to the magnetization is continuous across the

interface

e2jz = (G↑−G↓)(µF0 − µN

0 )+(G↑+G↓)(gFz −gN

z )

• transversal component of the spin current vanishes in the magnetic layer – jump at

the interface

e2jx =−2ReG↑↓gNx +2ImG↑↓gN

y

e2jy =−2ReG↑↓gNy −2ImG↑↓gN

x

A. Brataas, Yu.V. Nazarov, G.E.W. Bauer

Spin-transport in multi-terminal normal metal-ferromagnet systems with non-collinear magnetizationsEur. Phys. J. B 22, 99 (2001)





e2j0 = (G↑+G↓)(µF0 − µN

0 )+(G↑−G↓)(gFz −gN

z )


interface

e2jz = (G↑−G↓)(µF0 − µN

0 )+(G↑+G↓)(gFz −gN

z )


the interface


y


x


τ =h

2(j⊥L − j⊥R)





e2j0 = (G↑+G↓)(µF0 − µN

0 )+(G↑−G↓)(gFz −gN

z )


interface

e2jz = (G↑−G↓)(µF0 − µN

0 )+(G↑+G↓)(gFz −gN

z )


the interface


y


x

Components

in-plane τθ =−h

2j′y|N/F

out-of-plane τφ =h

2j′x|N/F



ResultsCalculations for real structures

Standard spin valve

Py(20)/Cu(10)/Py(8)

-0.04

0

0.04

0.08

0.12

0.16

0 p/4 p/2 3p/4 p

ST

T /

(h I

/ |e

|)

θ

τθ

102 τφ

Nonstandard spin valve

Co(8)/Cu(10)/Py(8)

-0.16

-0.12

-0.08

-0.04

0

0.04

0.08

0.12

0 p/4 p/2 3p/4 pS

TT

/ (

h I

/ |e

|)

θ

τθ

-102 τφ


Dual spin valve

Outline

1 Introduction


3 Dual spin valve




What is a dual spin valve?

Dual spin valve

Spin accumulation in dual spin valve

spin accumulation in single spin valve

10 20 30 40x

-0.2

-0.1

0.1

0.2spin accumulation


Dual spin valve

Spin accumulation in dual spin valve

spin accumulation in single spin valve

10 20 30 40x

-0.2

-0.1

0.1

0.2spin accumulation

spin accumulation in dual spin valve

20 40 60 80x

-0.2

-0.1

0.1

0.2

0.3

spin accumulation

L. Berger

Multilayer Configuration for Experiments of Spin Precession Induced by a DC CurrentJ. Appl. Phys. 93, 7683 (2003)


Dual spin valve

Enhancement of switchingsingle vs. dual spin valve

Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20)


0

0.04

0.08

0.12

0.16

0.2

0 0.25 0.5 0.75 1

ST

T /

(h

I /

|e|)

θ / p

Dual SV

Single SV


Dual spin valve




0

0.04

0.08

0.12

0.16

0.2

0 0.25 0.5 0.75 1

ST

T /

(h

I /

|e|)

θ / p

Dual SV

Single SV

Switching time

0 1 2 3 4 5 6 7

8 9

0.5 1 1.5 2 2.5 3 3.5 4sw

itch

ing

tim

e [n

s]I / (108 A cm-2)

Dual SV

Single SV


Dual spin valve




0

0.04

0.08

0.12

0.16

0.2

0 0.25 0.5 0.75 1

ST

T /

(h

I /

|e|)

θ / p

Dual SV

Single SV

Switching time

0 1 2 3 4 5 6 7

8 9

0.5 1 1.5 2 2.5 3 3.5 4sw

itch

ing

tim

e [n

s]I / (108 A cm-2)

Dual SV

Single SV

Is this all?


Question: How torque changes in non-collinear configurations?

I>0

Dual spin valve

Noncollinear configurations in dual spin valvesCo(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8)

I>0

P.B., M. Gmitra, J. Barnas

Current-induced dynamics in non-collinear dualspin-valvesPhys. Rev. B 80, 174404 (2009)


Dual spin valve


I>0




Dual spin valve


I>0



Current-induced dynamics

We calculated average

〈sz〉=1

tend − teq

∫ tend

teqsz dt

and dispersion

D(sz) =

√

⟨

s2z

⟩

−〈sz〉2

for each couple of I and Ω to map the dynamicbehaviour.


Dual spin valve


I>0


Nonlinear magnetoresistance in dual spin vales

Outline

1 Introduction


3 Dual spin valve






Experimental works

A. Aziz, O. P. Wessely, M. Ali, D. M. Edwards, C. H. Marrows,

B. J. Hickey, and M. G. BlamireNonlinear giant magnetoresistance in dual spin valves

Phys. Rev. Lett. 103, 237203 (2009)

N. Banerjee, A. Aziz, M. Ali, J. W. A. Robinson, B. J. Hickey,

and M. G. Blamire

Thickness dependence and the role of spin transfer torque in

nonlinear giant magnetoresistance of permalloy dual spin

valves

Phys. Rev. B 82, 224402 (2010)

N. Banerjee, J. W. A. Robinson, A. Aziz, M. Ali, B. J. Hickey,

and M. G. BlamireNonlocal Magnetization Dynamics in Ferromagnetic Hybrid

Nanostructure

Phys. Rev. B 86, 134423 (2012)

Experimental results [Aziz et al, PRL (2009)]: (b) minor loops for

Co90Fe10 (6)/Cu(4)/Py(1)/Cu(2)/Co90Fe10 (6)/IrMn(10) (c) Py thickness: 1 nm

(blue), 2 nm (red), and 8 nm (magenta)



Nonlinear magnetoresistance in dual spin valesModel’s assumptions

• Spin accumulation in the central layer changes density of states on Fermi level

• This may change bulk/interfacial material parameters in the central layer

We extended the diffusion transport model


From giant magnetoresistance to current-induced switching by spin transferPhys. Rev. B 72, 024426 (2005)

Bulk contribution

ρ∗ = ρ∗0 +q〈g〉

β = β0 +ξ 〈g〉

Interfacial contribution

R∗ = R∗0 +q′ g(xi)

γ = γ0 +ξ ′g(xi)

where

• g(x) is spin accumulation

• ρ∗0 and R∗

0 are zero-current bulk resistivity and interfacial resistance

• β0 and γ0 are zero-current bulk/interfacial asymmetry parameters

• q, ξ , q′, ξ ′ are phenomenological parameters

P. Baláž, and J. Barnas

Nonlinear magnetotransport in dual spin valvesPhys. Rev. B 82, 104430 (2010)



Nonlinear magnetoresistance in dual spin valesCalculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu

Bulk parameters

22.76

22.78

22.8

22.82

22.84

0 0.25 0.5 0.75 1

R [

fΩ m

2 ]

θ / p

i = 3i = -3

-0.06

-0.04

-0.02

0

0.02

0.04

-5 -4 -3 -2 -1 0 1 2 3 4 5

∆R [

fΩ m

2 ]

Reduced current density

(1)only ρ*

only β



Interfacial parameters

23.04

23.08

23.12

23.16

23.2

23.24

0 0.25 0.5 0.75 1

R [

fΩ m

2 ]

θ/p

i = 3i = -3

-0.15

-0.1

-0.05

0

0.05

0.1

-5 -4 -3 -2 -1 0 1 2 3 4 5∆R

[fΩ

m2 ]

Reduced current density

d = 2 nmd = 8 nmd = 16 nm

for q = 0.1, ξ = 0.1, I0 = 108Acm−2



Nonlinear magnetoresistance in dual spin valesCalculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu

Bulk parameters

-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~

-0.45

-0.3

-0.15

0

0.15

0.3

0.45

iξ~

-0.06-0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04

∆R

[f

Ω m

2]

∆R > 0 ∆R < 0

-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~

-0.45

-0.3

-0.15

0

0.15

0.3

0.45

iξ~

∆R > 0 ∆R < 0

Interfacial parameters

-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~¢

-0.45

-0.3

-0.15

0

0.15

0.3

0.45

iξ~ ¢

-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5

∆R

[f

Ω m

2]

∆R > 0

∆R < 0

-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~¢

-0.45

-0.3

-0.15

0

0.15

0.3

0.45

iξ~ ¢

∆R > 0

∆R < 0

for interfaces ∆R is symmetric with current density




Perpendicular polarizer

Outline

1 Introduction


3 Dual spin valve





Model of the polarizer

I>0

PP FL IPNL NR

(a)

P. Baláž, M. Zwierzycki, J. Barnas

Spin-transfer torque and current-induced switching in metallic spin valves with perpendicular polarizersPhys. Rev. B 88, 094422 (2013)



Transport through the polarizer

• We considered the perpendicular polarizer as amagnetized ballistic scaterrer in frame ofcoherent transport regime

• To calculate the transport properties of thepolarizer we used Ab initio wave functionmatching method

M. Zwierzycki et al

Calculating scattering matrices by wave functionmatchingPhys. Stat. Sol. (b) 245, 623 – 640 (2008)

• In our formalism the scaterrer coresponds to asingle interface.






M. Zwierzycki et al








M. Zwierzycki et al



Outputs of the calculation:

• channel conductances G↑, G↓

• mixing conductance

G↑↓ = g↑↓r + ig

↑↓i

• mixing transmission conductance

T↑↓ = t↑↓r + i t

↑↓i

Differences in definitions

Gσσ ′ = ∑nn′

[

δnn′ − rσnn′

(

rσ ′

nn′

)∗]

Tσσ ′ = ∑nn′

tσnn′

(

tσ′

nn′

)∗



Boundary conditions

Longitudinal components

e2

j0

jz

=

G↑+ G↓ G↑− G↓

G↑− G↓ G↑+ G↓

µR0 −µL

0

µRz −µL

z

Transverse components

e2

jR⊥

jL⊥

=

G T′

T G′

µµµR⊥

µµµL⊥

where

jR/L⊥ =

jR/Lx

jR/Ly

µµµR/L⊥ =

µR/Lx

µR/Ly

and

G = 2

−g↑↓r g

↑↓i

−g↑↓i −g

↑↓i

T = 2

t↑↓r −t

↑↓i

t↑↓i t

↑↓r

Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin

Nonlocal Magnetization Dynamics in Ferromagnetic Hybrid NanostructureRev. Mod. Phys 77, 1375 (2005)



Spin transfer torque

Spin torque acting on the free layer

τ⊥ = Is×[

SOP ×(

aOPSOP +aIPSIP

)]

τ‖ = Is×(

bOPSOP +bIPSIP

)

aOP =−h

2

j′1y |N1/F1

I sinθOPbOP =

h

2

j′1x |N1/F1

I sinθOP

aIP =−h

2

j′′2y |F1/N2

I sinθIPbIP =

h

2

j′′2x |F1/N2

I sinθIP

where cosθOP = s · SOP and cosθIP = s · SIP



Studied structures

Cu - PP / Cu(6) / Py(5) / Cu(12) / Py(20) - Cu


PP1 = Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1

PP2 = Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)



Results for PP1Spin transfer torque

Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1

-0.10

-0.05

0.00

0.05

0.10

0 0.5 1 1.5 2

Spin

torq

ue τ ||

PP polarizer

(a)

L=1L=3L=5

-0.15-0.10-0.050.000.05

0.100.15

0 0.5 1 1.5 2

IP polarizer

(b)

-0.25

-0.15

-0.05

0.05

0.15

0.25

0 0.5 1 1.5 2

Spin

torq

ue 1

0 ´ τ ^

angle θP / p

(c)

-0.01

0.00

0.01

0 0.5 1 1.5 2

angle θI / p

(d)

wavelike angular dependence for the perpendicular polarizer



Results for PP1Current-induced switching from ⇑ to ⇓ at T = 300K

Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1

0.0

0.2

0.4

0.6

0.8

1.0

-4 -2 0 2 4

P sw

tp = 50 ps

L=1L=3L=5

0.0

0.2

0.4

0.6

0.8

1.0

-4 -2 0 2 4

P sw

Im / 1012 [Am-2]

tp = 1 ns

0.0

0.2

0.4

0.6

0.8

1.0

-4 -2 0 2 4

tp = 100 ps

0.0

0.2

0.4

0.6

0.8

1.0

-4 -2 0 2 4

Im / 1012 [Am-2]

tp = 10 ns



Switching mechanism

For I < 0 For I > 0



Results for PP2Spin transfer torque

Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)

-0.20-0.15-0.10-0.050.000.050.100.150.20

0 0.5 1 1.5 2

Spin

torq

ue τ ||

Clean PP

(a)

L=1L=3L=5

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 0.5 1 1.5 2

Disordered PP

(b)

L=3L=4L=6

-0.06-0.04-0.020.000.020.040.06

0 0.5 1 1.5 2

Spin

torq

ue 1

0 ´ τ ^

angle θP / p

(c) -0.08

-0.04

0.00

0.04

0.08

0 0.5 1 1.5 2

angle θP / p

(d)



Results for PP2Current-induced switching from ⇑ to ⇓

Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)

0.0

0.2

0.4

0.6

0.8

1.0

-4 -3 -2 -1 0 1 2 3 4

P sw

tp = 50 ps

L=1L=3L=5

0.0

0.2

0.4

0.6

0.8

1.0

-4 -3 -2 -1 0 1 2 3 4

P sw

Im / 1012 [Am-2]

tp = 1 ns

0.0

0.2

0.4

0.6

0.8

1.0

-4 -3 -2 -1 0 1 2 3 4

tp = 100 ps

0.0

0.2

0.4

0.6

0.8

1.0

-4 -3 -2 -1 0 1 2 3 4

Im / 1012 [Am-2]

tp = 10 ns



Summary

Noncollinear diffusive model is an useful and flexible framework for dealing

with spin dependent electronic transport in metalic multilayers

• spin tranfer torque and magnetoresistance in single and dual spin

valves

• nonlinear effects in magnetoresistance

• spin transfer torque due to a perpendicular polarizer

• also spin torque and dynamics in composite free layers (synthetic

ferro- or antiferromagnets)



Thank you for your attention


Date post:	30-Apr-2018
Category:	Documents
Upload:	trannhan
View:	224 times
Download:	2 times

Spin transfer torque and magnetization dynamics in in...

Documents