Spin transfer & Current-induced magnetization reversal Andr - - PowerPoint PPT Presentation

European School of Magnetism, Constanta, 2005: André THIAVILLE 1

Spin transfer & Current-induced magnetization reversal

André Thiaville Laboratoire de physique des solides Université Paris-sud, Orsay France

European School of Magnetism, Constanta, 2005: André THIAVILLE 2

Electronic structure of magnetic 3d metals

s EF The simple s-d model d electrons : localized, carry magnetism s electrons : delocalized, carry current d

m ne τ σ

2

= ) ( 2 1

2 F B diff

E N T k V h π τ =

Minority electrons Majority electrons

↓ ↑ > σ

σ

usually

European School of Magnetism, Constanta, 2005: André THIAVILLE 3

Spin transfer : principle

I (large) F2 F1 electrons After reorientation of their spin to m, an angular momentum has been given m p F1 F2

European School of Magnetism, Constanta, 2005: André THIAVILLE 4

Magnitude of the spin transfer effect

m J : current density [C/(m2 s)] m1

( )

L d P s s dt e J r r r h = −

2 1

2

per unit surface s s1

m D M L

s

r r γ − =

Ultrathin layer of thickness D

( ) ( )

m m m m m D eM P Jg dt m d

s B transfer spin

r r r r r r × × = − =   

⊥ − 1 1

1 2 τ µ

European School of Magnetism, Constanta, 2005: André THIAVILLE 5

LLG + spin transfer term

( )

m m m dt m d m m H dt m d

eff

r r r r r r r r × × + × + × =

1

1 τ α γ

transfer spin

dt m d    r

m1 m destabilizing stabilizing

European School of Magnetism, Constanta, 2005: André THIAVILLE 6

Sign of the spin transfer effect (mnemonics)

m m1 electrons in

• ut

given Favors a parallel alignment

• f F to F1

in

• ut

m m1 in

• ut

electrons given Favors an anti-parallel alignment

• f F to F1
• ut

in

European School of Magnetism, Constanta, 2005: André THIAVILLE 7

Electron motion through a multilayer

m m1 in

• ut

electrons

↓> + ↑> = > ) 2 / sin( ) 2 / cos( θ θ θ

Spin-dependent transmission and reflection

European School of Magnetism, Constanta, 2005: André THIAVILLE 8

Order of magnitude of the current needed

( )

m m m dt m d m m H dt m d

eff

r r r r r r r r × × + × + × =

1

1 τ α γ

s critical

M 1 γ α τ =

Stability calculation

P D e M J

s critical

h

2

αµ =

2 11

/ 10 3 . 1 % 30 , 3 , / 8 . , 01 . m A J P nm D m MA M

c s

= ⇒ = = = = α

European School of Magnetism, Constanta, 2005: André THIAVILLE 9

Samples have to be small

Oersted field associated with the current

R 2 2 2 R J R I HOersted = = π τ γ 1 =

−transfer spin

H

2

R J I π = D M e P R H H

s Oersted transfer spin

µ h < ⇔ >

−

nm R nm D T M P

s

200 3 , 1 , 1 < → = = = µ

First demonstration

• f current-induced magnetization reversal

J.A. Katine et al.

• Phys. Rev. Lett. 84, 3149 (2000)

diameter ≈ 150 nm 5 1011 A/m2

size ≈ 60x100 nm2 5 1011 A/m2 F.J. Albert et al.

• Appl. Phys. Lett. 77 (2000)

European School of Magnetism, Constanta, 2005: André THIAVILLE 12

The second experimental demonstration

• f current-induced magnetization reversal

Pillar cross-section : 200 x 600 nm2

• J. Grollier et al.,
• Appl. Phys. Lett. 78, 3663 (2001)

European School of Magnetism, Constanta, 2005: André THIAVILLE 13

Main sample architectures e-

Pillars Point Contacts

e-

H

z

• J. Miltat, Nano Spin School, Cargese 05-2005

Experimental results : point contact geometry

• W. H. Rippard et al., PRL'2004

Point Contact Geometry : ≈ 40 nm diameter

∆R ≈ ∆RMax 1− m1 ⋅m2

( )

Experimental Results : Pillar Geometry A Rather Complex Set of Experimental Results

• S. I. Kiselev et al., NATURE'2003

European School of Magnetism, Constanta, 2005: André THIAVILLE 16

Experimental Results : Pillar Geometry with Exchange Biasing at a Skewed Angle

• I. Krivorotov et al., Science'2005

European School of Magnetism, Constanta, 2005: André THIAVILLE 17

Energy and spin transfer effect

( ) ( )

m m m m m D eM P Jg dt m d

s B transfer spin

r r r r r r × × = − =   

⊥ − 1 1

1 2 τ µ

Effective field for the spin transfer term

1 er spintransf eff,

1 m m H r r × = τ γ γτ θ τ γ µ d m d m m m d H M dE

eff s

= × = − = r r r r r ). ( 1 .

1

θ

No energy term to be associated with the spin transfer torque term ! m1 m

European School of Magnetism, Constanta, 2005: André THIAVILLE 18

Elliptical Elements

x

M HEff

European School of Magnetism, Constanta, 2005: André THIAVILLE 19

Micromagnetic Regime: Precessional States (T=300 °K)

Eigenmode Driven Mode

• B. Montigny & J. Miltat, J. Appl. Phys. 97 10C708 (2005)

European School of Magnetism, Constanta, 2005: André THIAVILLE 20

Micromagnetics vs experiments

Switching, generation of microwaves, are qualitatively reproduced perfectly, but Computed Power Spectral Density line widths too large when compared to experimental data even in the MS approximation Comparison between experiments and micromagnetic simulations strongly suggest that micromagnetics leads to excessive spatial incoherence At the same time, extremely narrow line widths, even in the pillar geometry, call for markedly weakly damped systems Such features seem hardly compatible within the framework

• f existing theories
• J. Miltat, Nano Spin School, Cargese 05-2005

European School of Magnetism, Constanta, 2005: André THIAVILLE 21

Giant magnetoresistance (GMR)

I (CIP) I (CPP) RAP = 2RP RP CIP : needs layers thinner than the mean free path CPP : needs layers only thinner than the spin diffusion length

European School of Magnetism, Constanta, 2005: André THIAVILLE 22

Current polarization variation

sf

l

Co

↓ ↓ ↑ ↑

= σ σ / / j j α σ σ = =

↓ ↑ ↓ ↑

/ / j j 2 / j j j = =

↓ ↑

= P

↓

j

↑

j m δ

Spin accumulation Cu Majority spins

β α α = + − = + − =

↓ ↑ ↓ ↑

1 1 j j j j P

M.D. Stiles, A. Zangwill,

• J. Appl. Phys. 91, 6812 (2002)

European School of Magnetism, Constanta, 2005: André THIAVILLE 23

A non-collinear spin enters

Ferromagnetic metal E EF

↓> + ↑> = > ) 2 / sin( ) 2 / cos( ) ( θ θ θ ∆ ↓> + ↑> = >

↓ ↑

) 2 / sin( ) exp( ) 2 / cos( ) exp( ) ( θ θ θ x ik x ik x ) (E n↑ ) (E n↓ ) ( ) ( E k E k

↓ ↑

> nm E k k k

F F

1 4 2 ≈ ∆ = −

↓ ↑

π π

Disparition of the transverse component

European School of Magnetism, Constanta, 2005: André THIAVILLE 24

Wall displacement by current

Pulses : 0.5 µs 1.2 1012 A/m2

• A. Yamaguchi et al.
• Phys. Rev. Lett. 92 077205 (2004)

European School of Magnetism, Constanta, 2005: André THIAVILLE 25

Conclusions

A fascinating field Experiments are far away before theory Just putting the simple Slonczewski term into LLG does not suffice to explain quantitatively everything