Spin-dependent transport in

layered magnetic metals

Patrick Bruno
Max-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 electrons

by using their charge for storage and
processing of information

the spin is (almost) completely neglected

principal electronic device: MOSFET

oxide drain
source
metallic gate (SiO2)

application: semi-conductor (Si) conducting channel

logic gates (2D electron gas)
random access memory

+
- metallic gate
inconvenients:
volatility of the information
energy consumption
limited density of information transistor blocked

electron as seen by a magnetician: -- --

- - -

purpose of magnetism: develop materials in which the electron spins

tend 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 devices

in 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)

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

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

ferromagnetic metal (Fe, Co, ...)

current in-plane
(CIP)

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

current perpendicular
to the plane (CPP)
definition conventions for the magnetoresistance ratio

R AP − RP
A= ``optimistic´´ definition
RP

R AP − RP H
A= ``pessimistic´´ definition
R AP

R AP − RP
A= reasonable definition
R AP + RP

interlayer exchange coupling

Ni80Co20 / Ru / Ni80Co20

Parkin and Mauri, PRB 44, 7131 (1991)

 Co / Ru / Co

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

GMR without interlayer exchange coupling

Co / Au / Co / Au(111)

T = 80 K

T = 130 K

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

 Exchange biasing to an antiferromagnet

FM

NM

FM

AF

interfacial exchange
interaction

FeNi

Cu

FeNi

FeMn

Diény et al., PRB 43, 1297 (1991)

Biasing by artificial antiferromagnet

free FM layer

pinned FM layer
weak
coupling

strong AF
artificial AF coupling

Applications of GMR: reading head for magnetic disks

Evolution of magnetic storage density

1 GByte drive

mechanism of GMR: spin-dependent scattering

two-current model

ferromagnetic (F) configuration

RF < RAF

antiferromagnetic (AF) configuration

R AF − RF
A≡ can be larger than 50%
R AF + RF
spin-dependent scattering probability

E E

P↓ > P↑ P↑ > P↓

DOS DOS
 Fe1-xVx / Au / Co

x=0 x = 0.3

x = 0.3
x = 0.18

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

tunneling-magnetoresistance
 Tunneling magneto-resistance (TMR)

Jullière, Phys. Lett. 54A, 225 (1975)

Moodera et al., PRL 74, 3273 (1995) insulating barrier

ferromagnetic electrodes

Mechanism of tunneling magneto-resistance

parallel (P)
configuration

GP > GAP

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

"bit" lines

tunnel barrier

FM electrodes

"word" lines

hot-electron spin-transistor
hot-electron spin-transistor

Monsma et al. PRL 74, 5260 (1995)

Science 281, 407 (1998)
 magnetization switching
due to spin-injection

Magnetization switching due to spin-injection

 differential
resistance
AF
F

current density

Myers et al., Science 285, 867 (1999)

Katine et al., PRL 84, 3149 (2000)

ab initio calculations of
perpendicular current GMR
 model considered:

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

M

y
x
M current
L
z

periodic repetition of the supercell in x and y directions

Conductances within the Landauer-Büttiker formalism

0 1 N N+1
C = C↑ + C↓ (spin-colinear case)

e2 1
Cσ = σ
∑ T (k // , ε F )
h N // k
//

transmittance for spin σ, wavevector k// and energy εF : H0,1 G + HN,N +1

1,N

[
T σ (k // , ε F ) = Tr Γ1 G1+,N ΓN GN
−
1 ]
G0(0,0)+ ( 0 )+
GN +1,N +1

( )
Γ1 = i H1,0 G0(0,0)+ − G0(0,0)− H0,1
recursive calculation of
the 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, or
7 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

CF − C AF
• definition of GMR ratio: GMR ≡ C AF
 125
100

GMR (%)
Cu∞ / Co / Cu / Co / Cu∞ 75
50
25
0
variable 0 10 20 30 40 50
5 ML
thickness Magnetic layer thickness (MLs)

1.0

Conductances / atom (in units e 2/h)

Cu Co ↑ Co ↓
0.8

F↑
0.6

0.4

0.2
F↓ AF
0.0
0 10 20 30 40 50
Magnetic layer thickness (MLs)

120
GMR (%)

Cu∞ / Co / Cu / Co / Cu∞ 115

110

5 ML 0 10 20 30 40 50 60 70 80 90 100
variable
Spacer layer thickness (MLs)
thickness
0.25
Conductances / atom (in units e 2/h)

F↓
0.24

0.23

AF
0.22
0 10 20 30 40 50 60 70 80 90 100
Spacer layer thickness (MLs)
 repeated N+1 times
200

GMR (%)
175
Cu∞ / (Co / Cu / Co / Cu) / Cu∞
15.0

125

100
5 ML 0 2 4 6 8 10 12 14 16 18 20
Number of repetitions

1.0

Conductances / atom (in units e 2/h)

F↑
0.8

0.6

0.4
F↓
0.2

AF
0.0
0 2 4 6 8 10 12 14 16 18 20
Number of repetitions

120

interfaces with ideal

GMR (%)

90
15% interdiffusion
60
interdiffused

30
0 2 4 6 8 10
Cu∞ / Co / Cu / Co / Cu∞ Spacer layer thickness (MLs)

1.0
Conductances / atom (in units e 2/h)

0.8 F↑ (ideal)
5 ML variable
thickness
0.6 F↑ (interdiffused)
AF (interdiffused)
0.4 F↓ (interdiffused)

0.2
F↓ (ideal) AF (ideal)
0.0
0 2 4 6 8 10
Spacer layer thickness (MLs)
 120
x= 0 (ideal)

GMR (%)
90
x= 15%
60
x= 50%
30
0 2 4 6 8 10
Cu∞ / Co / Cu(1-x)Pdx / Co / Cu∞ Spacer layer thickness (MLs)

1.0

Conductances / atom (in units e 2/h)

0.8 F↑ (ideal)
5 ML variable
thickness
0.6 F↑ (x=15%)

0.4
AF (x=15%) F↓ (ideal)

0.2
F↓ (x=15%) AF (ideal)
0.0
0 2 4 6 8 10
Spacer layer thickness (MLs)

120

Co
GMR (%)

90

60 Co85Ni15

30
Cu∞ / Co(1-x)Nix / Cu / Co (1-x)Nix / Cu∞ 0 2 4 6 8 10
Spacer layer thickness (MLs)

1.0
Conductances / atom (in units e 2/h)

5 ML variable F↑ (Co85Ni15)
0.8
thickness
0.6 F↑ (Co)

0.4 F↓ (Co85Ni15) AF (Co85Ni15)

0.2
F↓ (Co) AF (Co)
0.0
0 2 4 6 8 10
Spacer layer thickness (MLs)
 120

90 Co

GMR (%)
60

30 Co85Cr15

Cu∞ / Co(1-x)Crx / Cu / Co (1-x)Crx / Cu∞ 0 2 4 6 8 10

Spacer layer thickness (MLs)

1.0

Conductances / atom (in units e 2/h)

5 ML variable F↑ (Co)
0.8
thickness
F↑ (Co85Cr15)
0.6
F↓ (Co85Cr15)
0.4 AF (Co85Cr15)

0.2
F↓ (Co) AF (Co)
0.0
0 2 4 6 8 10
Spacer layer thickness (MLs)

domain wall
magnetoresistance
 w

A
Bloch wall w∝
K

easy axis

A
Néel wall w∝
2π M 2

250
200
GMR (%)

Co∞ / Co / Co∞ 150

100
50
0
magnetic wall of variable thickness 0 10 20
(linear rotation of magnetization) Domain-wall thickness (MLs)
Conductances / atom (in units e 2/h)

3.0 F (no wall)

2.5

2.0 AF (wall)
1.5

1.0

0.5

0.0
0 10 20
Domain-wall thickness (MLs)
Giant magnetoresistance of ferromagnetic atomic point contacts

atomic point contact

FM configuration

ferromagnetic wire electric current

AF configuration

explaination requires:

• narrow magnetic wall in an atomic point contact

• large resistance due to a narrow 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

1.0

0.5
Mz / Ms

unconstrained wall
0.0

-0.5 constrained wall

-1.0

-1.0 -0.5 0.0 0.5 1.0

x / w0
P. Bruno, PRL 83, 2425 (1999)
20 nm X 20 nm

theory of tunneling
magnetoresistance
 θ
simple approach: Jullière model

E
assumptions: G = G↑ + G↓

Gσ ∝ ρ1σ (ε F ) ρ2σ (ε F )

GAP − GP
A≡ = P1 P2
GAP + GP

ρ ↑ (ε F ) − ρ ↓ (ε F )
with P≡
ρ ↑ (ε F ) + ρ ↓ (ε F )
DOS

measurement of the spin-polarization by

spin-injection into a superconductor
Soulen et al., Science 282, 85 (1998)

ab initio calculation of tunnel conductance

Ni / vacuum / Ni(001)

J. Henk (MPI Halle)

Fe / MgO / Fe(001)

MgO

Fe

J. Henk (MPI Halle)