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Spin-dependent transport inlayered magnetic metals

Patrick BrunoMax-Planck-Institut für Mikrostrukturphysik, Halle, Germany

Summary:

introduction: what is spin-electronics

giant magnetoresistance (GMR)

tunneling magnetoresistance (TMR)

hot-electron spin-transistor

magnetization switching due to spin-injection

ab initio calculations of perpendicular current GMR

domain wall magnetoresistance

theory of TMR

introduction: what is spin-electronics ?

what is an electron ?

particle with negative electric charge q = - e

and spin 1/2 (magnetic moment m = µ B )

-----

- ------

- - + =

-----

- -electron as seen by an electronician:

electronics = manipulation of electronsby using their charge for storage andprocessing of information

the spin is (almost) completely neglected

principal electronic device: MOSFET

inconvenients: volatility of the information

energy consumption

limited density of information

application:logic gates

random access memory

semi-conductor (Si)

oxide(SiO2)metallic gate

conducting channel(2D electron gas)

source drain

transistor blocked

+- metallic gate

-----

- -electron as seen by a magnetician:

purpose of magnetism: develop materials in which the electron spinstend to align parallel to each (magnets)

the charge of the electrons plays a secondary role

application: mass storage of information

(magnetic disks and tapes)

advantages:non-volatility

high storage density

no energy consumption

inconvenients:mechanical access to information

Purpose of spin-electronics: ``Teaching electrons new tricks´´

combine electronics and magnetism in order to make new devicesin which both the charge and the spin of the electron play an active role

new fundamental physical questions

new phenomena

new devices and applications

giant-magnetoresistance

Giant magneto-resistance (GMR)

current perpendicularto the plane (CPP)

current in-plane(CIP)

ferromagnetic metal (Fe, Co, ...)

non-magnetic metal (Cu, Ru, ...)

Baibich et al., PRL 61, 2472 (1988)

Binasch et al., PRB 39, 4828 (1989)

definition conventions for the magnetoresistance ratio

P

PAPR

RRA

−=

AP

PAPR

RRA

−=

PAP

PAPRRRR

A+−=

H

R

``optimistic´´ definition

``pessimistic´´ definition

reasonable definition

Ni80Co20 / Ru / Ni80Co20

Parkin and Mauri, PRB 44, 7131 (1991)

interlayer exchange coupling

Parkin et al., PRL 64, 2304 (1990)

Co / Ru / Co

Barnas et al., Vacuum 41, 1241 (1990)

Co / Au / Co / Au(111)

GMR without interlayer exchange coupling

T = 130 K

T = 80 K

FM

FM

NM

AF

interfacial exchangeinteraction

Exchange biasing to an antiferromagnet

Diény et al., PRB 43, 1297 (1991)

FeNi

FeNi

Cu

FeMn

artificial AFstrong AFcoupling

weakcoupling

pinned FM layer

free FM layer

Biasing by artificial antiferromagnet

Applications of GMR: reading head for magnetic disks

1 GByte drive

Evolution of magnetic storage density

ferromagnetic (F) configuration

RF < RAF

antiferromagnetic (AF) configuration

mechanism of GMR: spin-dependent scatteringtwo-current model

FAF

FAFRRRR

A+−≡ can be larger than 50%

spin-dependent scattering probability

DOS

E

P↓ > P↑

DOS

E

P↑ > P↓

Fe1-xVx / Au / Co

x = 0

x = 0.18

x = 0.3

x = 0.3

Renard et al., PRB 51, 12821 (1995)

tunneling-magnetoresistance

θ

insulating barrier

ferromagnetic electrodes

Jullière, Phys. Lett. 54A, 225 (1975)Moodera et al., PRL 74, 3273 (1995)

Tunneling magneto-resistance (TMR)

Mechanism of tunneling magneto-resistance

parallel (P)configuration

antiparallel (AP)configuration

GP > GAP

"word" lines

"bit" lines

FM electrodes

tunnel barrier

Applications of TMR: magnetic random access memories (M-RAM)



Monsma et al. PRL 74, 5260 (1995)Science 281, 407 (1998)

magnetization switchingdue to spin-injection

Magnetization switching due to spin-injection

current density

differentialresistance

AF

F

Myers et al., Science 285, 867 (1999)Katine et al., PRL 84, 3149 (2000)

ab initio calculations of perpendicular current GMR

model considered:

L

M

M

ideal lead ideal leadcentral region (disorder, ...)

xy

z

periodic repetition of the supercell in x and y directions

current

↓↑ += CCC

),(1

////

2

//FT

Nhe

C εσσ kk∑=

( ) 1,0)0(0,0

)0(0,00,11 HGGHi −+ −=Γ

[ ]−+ ΓΓ= 1,11// Tr),( NNNF GGT εσ k

(spin-colinear case)

Conductances within the Landauer-Büttiker formalism

transmittance for spin σ, wavevector k// and energy εF :

0 1 N N+1

1,0H 1, +NNH+NG ,1

+++

)0(1,1NNG

+)0(0,0G

recursive calculation ofthe Green’s function

calculation of the surface Green’s function:layer addition (or removal) invariance→→→→ self-consistent (Dyson-like) equation

+

Computational details:

• density functional theory (local density approximation)

• TB-LMTO method (Green’s function)well adapted to surface problems

• imaginary energy for GF calculations: 10-7 Ry

• disordered systems:

- 5 x 5 supercell averaged over 5 configurations, or7 x 7 supercell averaged over 3 configurations

- on-site potential parameters obtained from (layer dependent) CPA method

• k// -integration: 10 000 points in the full fcc(001) SBZ

• definition of GMR ratio:AF

AFFCCC

GMR−≡

0

25

50

75

100

125

0 10 20 30 40 50

GM

R (

%)

Magnetic layer thickness (MLs)

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2

Magnetic layer thickness (MLs)

AFF↓↓↓↓

F↑↑↑↑

Cu∞ / Co / Cu / Co / Cu∞

variablethickness

5 ML

Cu Co ↑ Co ↓

110

115

120

0 10 20 30 40 50 60 70 80 90 100

GM

R (

%)

Spacer layer thickness (MLs)

0.22

0.23

0.24

0.25

0 10 20 30 40 50 60 70 80 90 100Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2


AF

F↓↓↓↓


5 ML variablethickness

100

125

15.0

175

200

0 2 4 6 8 10 12 14 16 18 20

GM

R (

%)

Number of repetitions

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2

Number of repetitions

AF

F↓↓↓↓

F↑↑↑↑

Cu∞ / (Co / Cu / Co / Cu) / Cu∞

5 ML

repeated N+1 times

30

60

90

120

0 2 4 6 8 10

GM

R (

%)


0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2


AF (ideal)

AF (interdiffused)

F↑↑↑↑ (ideal)

F↑↑↑↑ (interdiffused)

F↓↓↓↓ (ideal)

F↓↓↓↓ (interdiffused)

interdiffused

ideal



interfaces with15% interdiffusion

30

60

90

120

0 2 4 6 8 10

GM

R (

%)


0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2


x= 0 (ideal)

x= 15%

x= 50%

AF (ideal)

F↓↓↓↓ (ideal)

F↑↑↑↑ (ideal)

AF (x=15%)

F↓↓↓↓ (x=15%)

F↑↑↑↑ (x=15%)

Cu∞ / Co / Cu(1-x)Pdx / Co / Cu∞


30

60

90

120

0 2 4 6 8 10

GM

R (

%)


0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2


Co

Co85Ni15

AF (Co85Ni15)

AF (Co)F↓↓↓↓ (Co)

F↓↓↓↓ (Co85Ni15)

F↑↑↑↑ (Co)

F↑↑↑↑ (Co85Ni15)

Cu∞ / Co(1-x)Nix / Cu / Co (1-x)Nix / Cu∞


30

60

90

120

0 2 4 6 8 10

GM

R (

%)


0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2


Co

Co85Cr15

F↑↑↑↑ (Co85Cr15)

F↑↑↑↑ (Co)

AF (Co)

AF (Co85Cr15)F↓↓↓↓ (Co85Cr15)

F↓↓↓↓ (Co)

Cu∞ / Co(1-x)Crx / Cu / Co (1-x)Crx / Cu∞


domain wall magnetoresistance

easy axis

Bloch wall

Néel wall

w

KA

w ∝

22 M

Aw

π∝

0

50

100

150

200

250

0 10 20

GM

R (

%)

Domain-wall thickness (MLs)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20Con

duct

ance

s / a

tom

(in

uni

ts e

/h)

2

Domain-wall thickness (MLs)

AF (wall)

F (no wall)

Co∞ / Co / Co∞

magnetic wall of variable thickness(linear rotation of magnetization)

electric current

atomic point contact

FM configuration

AF configuration

ferromagnetic wire

Giant magnetoresistance of ferromagnetic atomic point contacts

explaination requires:

• narrow magnetic wall in an atomic point contact

• large resistance due to a narrow wall

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

Mz

/ Ms

x / w0

unconstrained wall

constrained wall

geometrical constriction →→→→ new kind of magnetic wall:

structure (almost) entirely determined by the constriction geometry

energy = (almost) pure exchange energy

width determined by the characteristic size of the constriction

→→→→ wall can be extremely narrow in an atomic point contact

P. Bruno, PRL 83, 2425 (1999)

20 nm X 20 nm

theory of tunnelingmagnetoresistance

simple approach: Jullière modelθ

assumptions: ↓↑ += GGG

)()( 21 FFG ερερσ σσ∝

21 PPGGGG

APAP

PAP =+−≡

)()(

)()(

FF

FFPερερ

ερερ↓+↑

↓−↑≡

DOS

E

with

measurement of the spin-polarization byspin-injection into a superconductor

Soulen et al., Science 282, 85 (1998)

ab initio calculation of tunnel conductance

J. Henk (MPI Halle)

Ni / vacuum / Ni(001)

J. Henk (MPI Halle)

MgO

Fe

Fe / MgO / Fe(001)

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