• 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