Michel Viret Service de Physique de l’Etat Condensé CEA...
Transcript of Michel Viret Service de Physique de l’Etat Condensé CEA...
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Spin electronics at the nanoscale
Michel Viret
Service de Physique de l’Etat Condensé
CEA Saclay
France
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Principles of spin electronics:
ferromagnetic metalsspin accumulation
Resistivity of homogeneous materials:
AMRDWR
Spin torque in DWs
Reduced dimensions:
Mesoscopic transportAtomic MR
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Different DOS for upand down spins :
Spin dependent electrical transport in ferromagnetic metals
s electrons : low density of states + high mobility
d electrons : large density of states + low mobility
Transport is dominated by s electrons scattered into d bandsd bands split by the exchange energy→ diffusion is spin dependent
→ Two current model :Two conduction channels in parallel
with ρ↑≠ ρ↓
Resistivity :
or (with spin-flip) :
ρρρρρρρρ
↑↓↓↑
↓↑↑↓↓↑
++
++=ρ
4
)(
ρρρρ
↓↑
↓↑
+=ρ
E
d bands
s bands
Spin
down
spin
up
↑↑↑↑
↑↑↑↑↓↓↓↓
↓↓↓↓
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Current generated spin accumulation at a Ferro (Co) / Normal metal (Cu) interface:
Typically, at 4.2 K :lsf (Co) ≈ 60 nmlsf (Cu) ≈ 500 nm
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H (kOe)
80%
I
V
Multilayers
F metal / NM metal(ex : Fe / Cr, Co / Cu, etc )
4 K
Conf igurat ion P
M MNM
-
+
M MNM
+
-
Conf igurat ion AP
r r
r
r
R R R
RR+= r
R- = R
R+ = (r+R)/ 2
R- = (R+r)/ 2
P
PAP
R
RR −=GMR
rrR
RrRP ≈≈≈≈
++++====
4
rRRAP
++++====<
Introduction to spin electronics
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Domain wall resistance
Example of FePd:
MFM image 2 x 2 µm2 at zero field, in the virgin state and after saturation. The up domains are black andthe down ones are white
Resistive
measurements : on a nanostructure withstripe width = 300nm
0.5
7.992
8.016
8.040
8.064
8.088 ρ
CPW
ρCIW
ρ (µΩ
cm
)
H
∆R/R = 8 % within the DWs
Why is it so small?
(R. Danneau et al., Phys. Rev. Lett. 88, 157201 (2002))
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Spin transfer from the conduction electrons to the DW
Current
direction
Theory
Two kinds of electrons:
• Localised• Conduction electrons
→ s-d Hamiltonian
Action of a current:
Globally, the conduction electrons transfer gµB to the DW
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s-d Hamiltonian :
: localised spins
Precession equation :
s : conduction electrons
⇒⇒⇒⇒
Simple model : the particle approach
( )
⇒⇒⇒⇒
In the rotating frame:
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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exw
F
J
v
δφ
η=0
2wex
F
2
w 1
J
v
)p1(
p2
R
R
δ
−=
∆ η
Loc
a l M
omen
t
Electron spinφ 0
In the frame of the local moment direction :
Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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exw
F
J
v
δφ
η=0
2wex
F
2
w 1
J
v
)p1(
p2
R
R
δ
−=
∆ η
Loc
a l M
omen
t
Electron spinφ 0
In the frame of the local moment direction :
Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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exw
F
J
v
δφ
η=0
2wex
F
2
w 1
J
v
)p1(
p2
R
R
δ
−=
∆ η
Loc
a l M
omen
t
Electron spinφ 0
In the frame of the local moment direction :
Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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exw
F
J
v
δφ
η=0
2wex
F
2
w 1
J
v
)p1(
p2
R
R
δ
−=
∆ η
Loc
a l M
omen
t
Electron spinφ 0
In the frame of the local moment direction :
Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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Loc
a l M
omen
t
Electron spinφ0
In the frame of the local moment :
In the laboratory frame
Spin evolution during DW crossing
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For a long wall and
Precession around the effective field :
Rotating frameMagnetisation
Magnetic
moment
Direction of
electron
propagation
Laboratory frame
→ The mistracking angle is small (a few degrees) and theinduced spin scattering is weak
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The total moment is conserved →
Reaction on the wall
The torque can be decomposed into a constant and periodic partFor long walls, the periodic part averages to zero and the constant part reads:
distortion (steady state)
P = polarisation, j = current density pressure
• Torques: non-homogeneous within the walls + small ‘pressure’ term
• Importance of the magnetic structure of the DW
• Very thin DWs: Enhanced pressure oscillating with thickness
Conclusions :
Effect of the current : Globally, the conduction electrons transfer gµB to the DW→→→→ Spin torque
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Preliminary conclusions
Question: Can we build spin electronics devices with domain walls?
DW: topological soliton which can be moved by a current and which scatters electronsRussel Cowburn (Durham/London) : magnetic logic based on DWsStuart Parkin (IBM San Jose) : registery memory
Problems: DWs are not very resistive and cannot be pushed by small currents…
Solution : 1D structures
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Ohm’s law: I = G VG = σ S / L if L >>
• lF Fermi wavelength (quantum)
• ℓ mean free path (elastic)
• Lj coherence length (inelastic)
macroscopicdiffusiveatomic ballistic
Different transport regimes
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Magnetoresistance in reduced dimensions: the constriction
+ magnetism :
Spin degeneracy removed by the exchange energy
≠ Fermi wavelength for up and down electrons
→ the size of the constriction at which the
number of transmitted channels changes
is spin dependent
↓↑
↓↑
≠→
−±=
=
++∇−=
NN
kEEm
k
dnk
JrVm
H
perpexFlong
perp
ex
)(2
2.
.)(2
2
2
*,
22
η
η
π
σ
⇒ conductance quantized :
G = ΣΣΣΣTi↑↓↑↓↑↓↑↓G0 (G0 = e2/h = 1/26kOhm)
2D electron gases : σ quantized in units of 2G0 , but large H : quantization in G0
Perfect case: continuous materials of cross section close to λF (ex: 2DEG) : k⊥ quantized
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Closer to real life :
Metals : λF ≈ 2Å→ quantization requires atomic contacts !Conducting channels defined by overlap of atomic orbitals→ atomic calculation needed+ In the single atomic regime more than one conduction channels are opened for 3d elements. Ni: 4s2 3d8→ potentially 4↓ + 6↑ channels
Magnetic problems :DWs not infinitely thin: Micromagnetic configuration of the relevant atoms?
Experimental problems : Magnetostriction ??For Ni : λ ≈ -40 ppm → 100 µm wire shrinks by 4 nm !
Introduction of a DW in a constriction (ideal case) :DW width = size of constriction (P. Bruno, PRL83, 2425 (1999), Y. Labaye et al., J.A.P.91, 5341 (2002))
Constricted DW width ≈constriction diameter or length
+ Potential barrier of magnetic (exchange) origin (Imamura et al. PRL 84, 1003 (2000)) : large MR effects because a DW can close the conductance channel.
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Break junction technique :Samples : ferromagnetic bridges suspended with pads of different shapes made in polycrystalline Ni, Co, Fe :
MR in ferromagnetic atomic contacts
Micromagnetics:
Program OOMMF (NIST)
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Experimental setup
Bending system in a cryostatPulling ≈ 1 nm/turn
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H. Ohnishi, Y. Kondo and K. Takayanagi,
Nature 295, 780 (1998)
TEM pictures while pulling an Au tip from a Au film :
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Measurements : breaking
01234567
89
101112131415
-1 -0.8 -0.6 -0.4 -0.2 0 0.2
d (nm)
(e2/h)
Conductance steps : atomic reorganization (+ quantization)
Tunnelling : R = R0 exp(x/x0) , x0=0.045 nm
Tunneling regime - H=0.4T perp
3
4
5
6
7
8
9
10
11
0 0.01 0.02 0.03 0.04 0.05gap (nm)
ln(R)
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Two types of measurements
R(θ) → AMR:
0
0.2
0.4
0.6
0.8
1
1.2
-90 -60 -30 0 30 60 90 120 150 180 210 240 270
Angle (degree)
Resistance
R(Η) → ‘DWR’ :
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- 9 0 - 6 0 -3 0 0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0
6 9 8
7 0 0
7 0 2
7 0 4
7 0 6
A n g l e ( d e g r e e )
Atomic contact:
∆∆∆∆R/Rmin= 75%
9 0 0 0
1 0 0 0 0
1 1 0 0 0
1 2 0 0 0
1 3 0 0 0
1 4 0 0 0
1 5 0 0 0
1 6 0 0 0
1 7 0 0 0
1 8 0 0 0
Atomic contact:
∆∆∆∆R/Rmin= 21%
7 2 0 0
7 4 0 0
7 6 0 0
7 8 0 0
8 0 0 0
8 2 0 0
8 4 0 0
8 6 0 0
8 8 0 0
R (
Oh
m)
Nanostructure:
∆∆∆∆R/Rmin= 1.1%
Atomic contact regime (Fe, 4.2K)
R(θθθθ) curves :
• Significant effect• Clear departure from cos2(θ)
7000
7200
7400
7600
7800
8000
8200
8400
8600
8800
-100 -50 0 50 100 150 200
angle (°)
R (Ohm)
2T, Vdc=0mV
3e2/h
3.5e2/h
→ Channels closing?
Parallel with evolution of conductance with stretching
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Tentative explanation of the AMR effects :
Orbitals overlap responsible for the
opened channels
Distortion with field because of spin-orbit
coupling?
+ enhanced effects in reduced dimensions
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Ab-initio calculations
Pseudo potential plane wave method + spin-orbit coupling
Fe atomic chain: magnetisation parallel and perpendicular
Tight binding calculations
fcc (111)
bcc (001)
The exact geometry of the contact is
important, especially the coordination
number of the central atom.
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Tunnelling regime, Fe (4.2K) :
→AMR still large in tunnelling
Measurements quite ‘erratic’ because different configurations can give the same resistance
Tunnelling defined by the overlap of evanescent orbitals→ Spin-orbit coupling of the same nature but on the evanescent orbitals
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Summary of AMR measurements in Fe
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6.2
6.25
6.3
6.35
6.4
6.45
6.5
6.55
6.6
-60 -40 -20 0 20 40 60 80 100 120 140 160 180 200Angle(degrees)
R(kohms)
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
H(T)
R(kohms)
180°
90°
90°<--180°
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
-2.5 -1.5 -0.5 0.5 1.5 2.5H(T)
R(kohms)
← Fe (4.2K)‘Domain wall’ effects
12%
27
28
29
30
31
32
33
34
35
36
37
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
H(T)
R(kohms)
180°
90°
Co (4.2K)↓
DWR ≈ 10% – 20%
21%
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E-field efects
3700
3800
3900
4000
4100
4200
4300
4400
4500
4600
4700
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
H (T)
R (Ohm)
Vdc=100mV
Vdc=50mV
Vdc=0
field at 0°
Electric field effects, Fe (4.2K):
Effect of the electric field:
Evidence for spin torque?
At 50mV, j ≈≈≈≈ 5 108 A/cm2
differential conductance for two different magnetic configurations
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
Vbias (V)
dI/dV (Ohm)
H=0
H=1T
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Conclusions for the MR at the atomic scale
conductance depends on orbital overlapS-O coupling = atomic AMR effectIn reduced dimensions: large S + large O !
Contact:
AAMR : 50 %
DWR : 20%
AAMR>DWR
Tunnelling
TAMR : 100 %
TMR : 35%
TAMR>TMR
tunnelling AMR : same with evanescent orbitals
See: M. Viret et al., Eur. Phys. J. B 51, 1 (2006)
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Conclusions
Can DWs be used for spin electronics?
In the bulk :
DW resistance too small + current induced pressure too weak
In atomic constrictions:
Importance of orbital effects (AMR)
DW Resistance enhanced (20%)
Pushing with a current impossible (destruction of the contacts)
The ideal : 1D atomic chains…