• Funded by Hewlett-Packard Laboratories, Palo Alto, CA

Giant magnetoresistancein magnetic metallic multilayers

E.Y.Tsymbal and D.G.Pettifor

Department of Materials, University of Oxford, UK

Synopsis

• Introduction

• Physical origin

• The theoretical model

• Co/Cu and Fe/Cr multilayers

• Application to experiments:

Thermoelectric powerThickness-dependent conductanceInterface resistance

• Conclusions

Giant magnetoresistance (GMR)

Antiparallelmagnetizations

Parallelmagnetizations

Ferromagnet (Co)

Ferromagnet (Co)Nonmagnetic metal (Cu)

R↑↑

R↑↓

Resistance

Magnetic field

↑↑

↑↑↑↓ −R

RRGMR=

Magnetic multilayer

FMNM

FM (ferromagnetic layer)NM (nonmagnetic metallic layer)FMNMFMNM

NMFM

FM

GMR structures

♦ antiferromagnetic exchange coupling

♦ highest values of GMR, in Co/Cu and Fe/Cr multilayers ~ 100%

Granular material

FM - hardNMFM - soft

Pseudo spin valve

AF (antiferromagnet)FM - pinnedNMFM - free

Spin valve

♦ different coercivities ♦ exchange biasing

Spin valve

-400 -200 0 200

0

4

8

12

GM

R

Magnetic field (G)

Magnetic field sensor

recorded bits

sensingcurrent

spin valve

FeMnNiFe/Co

CuCo/NiFe

Pinning layerPinned layerSpacer layerFree layer

Simple model for GMR

Two-current model: =

- up spins

ρ↑ ≠ ρ↓In ferromagnets

ρ↑

ρ↓

ρtot

- down spins

ρ↑

ρ↓

ρ↑

ρ↓

R↑↑=

ρ↑

ρ↓ ρ↑

ρ↓

R↑↓=

αα

ρρρρ

4

)1(

4

)( 22 −=−

↑↓

↑↓GMR=

up spin down spin up spin down spin

is spin asymmetry parameter↑

↓=ρρ

α

Electrical conduction in metals

Drude formulamfp

F l

ke

m

ne

3

222

πτσ ==

Mean free pathFscat

FFmfp NVl 2

12

vv== τ

Nonmagnetic metal (Cu)

d-band sp-bandE

N(E) EF

Magnetic metal (Co)

d-band sp-bandE

N(E) EF

up spins

down spins

majority spins

minority spins

σ↑ =σ↓

σ↑ >>σ↓

High resolution electron micrograph of Co/Cu spin valve

P.Baile-Guillemaud, A.K.Petford-Long

The theoretical model for GMRPhys.Rev.B 54, 15314 (1996)

Kubo-Greenwood formula:

)(v)(v2

HEHETre

FF −−Ω

= δδπσ

scatVHH += 0

scatV - scattering potential effecting on-site atomic energy levels randomly

Perfect lattice:

Ed Es Ed Es EE

Defective lattice:

γ γ

• γ is assumed to be spin-independent

♦ Realistic electronic band structure♦ Scattering is due to structural defects within a multilayer

0

2

4

-6 -4 -2 010-3

10-2

10-1

EF

total sp d

DO

S (e

V-1)

σ (µ

Ω-1cm

-1)

Energy(eV)

Conductivity of bulk Cu

0

2

4

4

2

minority

majority

DO

S (e

V-1)

σ (µ

Ω-1cm

-1)

-6 -3 0 3

10-2

10-1

majority minority

EF

Energy (eV)

Conductivity of bulk Co

10-2

10-1

σ (µ

Ω-1cm

-1) majority (P)

minority (P) AP

-6 -3 0 30

100

200

FE

MR

(%

)

Energy (eV)

0

1

2

Co/Cu multilayer

majority (P)D

OS

2

1

0

minority (P)

10-2

10-1

majority (P) minority (P) AP

σ (µ

Ω-1cm

-1)

-6 -4 -2 0 2 40

50

100

Fe/Cr multilayer

EF

MR

(%

)

Energy (eV)

0

1

2

majority

DO

S

2

1

minority

Thermoelectric power (TEP)

V

T1

T1

T0

♦ Experimentally TEP and magneto-TEP is negative for Co/Cu multilayers,

but positive for Fe/Cr multilayers

Mott formula:Ee

Tk

E

S

F∂

∂−= σπ ln

3

22

Co/Cu multilayer Fe/Cr multilayer

PRB 59, 8371 (1999)

Experiments:J.Shi, Motorola Research LabsM.Salamon, University of Illinois

-0.2 -0.1 0.0 0.1 0.2

0

2

4

0.00

0.02

0.04

0.06

0.08

0.01

0.02

0.03

0.04

-0.2 -0.1 0.0 0.1 0.2-2

-1

0

Experiment

Energy (eV)Energy (eV)

dlnσ

/dE

(eV

-1)

EF

P AP

σ (µ

Ω-1cm

-1)

EF

P AP

Experiment

0.00

0.04

0.08

0.12

ρsat

(µΩcm)

σ (µ

Ω-1cm

-1)

majority (P) minority (P) AP

0.4 0.8 1.20

50

100

∆R/R

(%

)

γ (eV)

0

50

100

20 40

Effect of disorder

Layer-dependent conductance

0.00

0.02

0.04

0.06

majority (P) minority (P) spin 1 (AP) spin 2 (AP)

σ (µ

Ω-1cm

-1)

0 10 20 30 400

10

20

30

40

bulk disorder bulk & outer-boundary disorder bulk & interface disorder

CoCuCo

Layer number

GM

R (

%)

Thickness-dependent conductance

PRB 61, 1330 (2000)

0 1 2 3 4 5 60.00

0.02

0.04

Co4Co(t)

Co4Co(t)Co

n

Shee

t con

duct

ance

(Ω

-1)

Total film thickness (nm)

Co

Theory:

Experiments:

W.Bailey and S.Wang, Stanford University

Conductance is measured in situ during ion-beam deposition

Conductance drop results from strong interface scattering, as a consequence of high density of empty Co d states at Cu boundaries

• Co4Cu(t) Co4Cu(t)Con

Experiments: D. Bozec at al, University of Leeds

Failure of resistor model for CPP GMR

0 2 4 6 8 10 120

2

4

6

8

10

Parallel magnetizations Interleaved configuration Separated configuration

CoCuCoCuCoCuCo

Thickness (nm)

Res

ista

nce

(fΩ

m2 )

Theory:

Separated configuration

Interleavedconfiguration

PRL 85,1314 (2000)

♦ single-band tight-binding model

♦ Kubo formula within Anderson model of disorder

♦ two different metals, characterized by different on-site atomic energies

Layer-thickness-dependent interface resistance

PRB 61, 506 (2000)

0

20

40

60

0 50 100 150 200

0

10

no interfaces one interface two interfaces

AR

(ha

2 /e2 )

interface resistance

d (a)

Conclusions

The model for giant magnetoresistance

predicts

•••• Decreasing GMR with disorder•••• Enhancement of GMR in Co/Cu multilayers for hot electrons;

no such enhancement for Fe/Cr multilayers•••• Sizeable contribution from the spacer layer in spin valves• Importance of layer-thickness-dependent interface resistance

for CPP GMR

and explains

• Thermoelectric power in Co/Cu and Fe/Cr multilayers •••• Conductance of in-situ grown Co/Cu spin valves •••• Failure of the resistor model for CPP GMR