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S. Maekawa(IMR, Tohoku University)
Spin Current vs. Charge Current Spin Current vs. Charge Current
in Magnetic Nanostructuresin Magnetic Nanostructures
Contents:(i) Spin current,(ii) Spin accumulation,(iii) Spin Hall effect,(iv) Spin current pumping.
(Charge current Spin Current)
YKIS2007 (November 20 ,2007)
FM current
normal metalsuperconductorhybrid device
charge current : cJ J J↑ ↓= +
sJ J J↑ ↓= −spin current :
Contents:(i) Spin accumulation,(ii) Spin current,(iii) Spin Hall effect,(iv) Spin current pumping.
What is a ferromagnet ?
Cu Fe,Co,Ni La1-xSrxMnO3CrO2
( )μ ↓ ↑= −BM N N
N N↑ ↓= N N↓ ↑> 0N N↓ ↑> =Electron number :
Atomic energy : i iε ε↑ ↓= i iε ε↓ ↑< i iε ε↓ ↑=
E
E E
EF
(half-metal)
Electric current :charge current :
cJ J J↑ ↓= + sJ J J↑ ↓= −spin current :J J↑ ↓≠ Magnetization :
Spin diffusion length(λN)
10 nm ~ 1 μm
λN
Ferromagnet MetalSemicond.Supercond.
λN
Spin Electronics Device !
Device size <
(Charge current usual electronics)
Tunnel magnetoresistance (TMR)
Parallel alignment Antiparallel alignment
(S. Maekawa and U. Gafvert: IEEE Mag. 18, 707 (1982))
Spin accumulation :
( ):
↑↓
Antiparallel alignment
( ):
↑↑
Parallel alignment
Antiparallel alignment
“Spin accumulation” “Spin current”
Parallel alignment
Spin accumulation in High-Tc superconductors :
(Z.W. Dong et al.: APL 71, 1718 (1997))
Critical current
Injection current
injI
injI
I I
V
Zeeman Effect Spin Accumulation
BHμ
BHμ
δμδμ
02 PeVΔ ≈
Magnetization( )BM n nμ ↑ ↓= −
Pair breaking :02 BHμΔ ≈
For Al,0 ~ 0.4 meVAlΔ
-3~ (10 V) ( ~ 1)bV O P~ (1 T)H O
Al AlB S(0) 4 (1Oe)M N PeV B M Oμ π→ =: :
For YBCO,0 0100 YBCO AlΔ Δ:
-1(10 V)bV O:
2(10 T)H O:
4(10 Oe)YBCOSB O:
2(0) 10 (0)YBCO AlN N⎡ ⎤⎣ ⎦:
Spin accumulation >> Zeeman effect
theory
Au
(S. Takahashi, H. Imamura, S.M., PRL. 82, 3911 (1999)
Spin accumulation signal:Spin accumulation signal:
P AP( ) /SR V V I= −
PP
APAP
650 nm10 mS
LR
== Ω
Non-Local Spin Accumulation Device, F. J. Jedema et. al., Nature 416, 713 (2002)
PP
Co-Al-Co
APAP
( )N xδμ μ μ↓↑
= −
spin
j j jj j j
↑ ↓
↑ ↓
= +⎧⎨ = −⎩
Spin accumulation:
Charge and Spin currents:
Non-local geometryfor measurement
NP AP
2 2 2 /S
V V eRI I
δμ−= =
2PeV+
AP2eV−
Spin accumulation signal:
xL0
x
Top view
Side view
F1 F2N
( )
( ) ( )
2
22s
0
1
σ μ σ μ
μ μ μ μλ
↑ ↑ ↓ ↓
↑ ↓ ↑ ↓
∇ + =
∇ − = −
Basic equations for Electro-chemical potential:
Charge conservation
Spin diffusion
, e e
σ σμ μ↑ ↓
↑ ↑ ↓ ↓= − ∇ = − ∇j j
Spin-dependent currents:
F FF
F F
p σ σσ σ
↓↑
↓↑
−=
+
N N N
F F F F F
12
,
( )
N :
F :
σ σ σ
σ σ σ σ σ
↓↑
↓ ↓↑ ↑
= =
≠ = +
s : spin diffusion lengthλ
8 μΩcm5 nm*Py14 μΩcm
6 μΩcm1.4 μΩcm
ρ
50 nm*
650 nm1000 nm
λS
Co
CuAl
( ) s/ exp xμ μ λ↑ ↓− ∝ −
(Py: Ni80Fe20)
Jedema et al.
←
←
Τ = 4.2Κ
*Bass and Pratt
Bulk spin polarizationof F:
F 50 70%*p = :
1 2
N
N N N
600 , 1200 , 100 A6 cm
250nm 50nm
R R I
A w d
μρ μ
= Ω = Ω =⎧⎪ = Ω⎨⎪ = = ×⎩
Co-Al-Co tunnel device
P AP N/2T N L
SV V
IR P R e λ−−
= =
N 650nmλ =
N 350nmλ =
N NN
N
3 RA
ρ λ= = Ω
NN
/N
12
( ) xx e eP R I λδμ −= ⋅
SR
L
15 eV
μ14 2 43
N Fitting parameter: , P λ
T 0.1P =
(F. J. Jedema et al., Nature 416, 713 (2002)S. Takahashi and S.M., PRB 67, 052409 (2003))
Hall effect
current
magneticfield
Spin Hall effect
Spin current ( )J J↑ ↓−
current
(Anomalous Hall effect)
J↓
J↑
spin current
spin current:
current:IInjection current:
J J↑ ↓−
J J↑ ↓+
Ferromagnet
Normal metal / semiconductor
Spin Hall effect :
Intrinsic Spin Hall Effect:Spin-Orbit Coupling in the Band Structure
Ballistic transport
Extrinsic Spin Hall Effect:Spin-Orbit Scattering of Electrons
Diffusive transport
Experiments:Valenzuela & Tinkham, Nature 442, 176 (2006).Saitoh et al., APL 88, 182509 (2006)Kimura et al., PRL 98,156601(2007),
metallic systems
Anomalous Hall effect in ferromagnets
side jump
Boltzman equation for AHE (Anomalous Hall Effect):
Hamiltonian:† †
, , k k k kk k k
k k ka a U a aσσ
σ σ σ σσ σ σ
ξ ′′ ′ ′
′ ′
= +∑ ∑ ∑H
( ) ( )ˆ ˆimp so ji k k r
kkj
U u i k k eσσσσ σσδ λ σ ′− ⋅′
′ ′ ′⎡ ⎤′= + ⋅ ×⎣ ⎦∑
Impurity potential:
Current density with spin σ :
spin-orbit scatt. 1 4 4 2 4 43
†ˆ k kk
kkj e a amσ σ σ
σ
σω⎡ ⎤= +⎢ ⎥⎣ ⎦∑ h
Anomalous velocity: ˆF imp
sok kk σσσ λ
ω τ σ⎡ ⎤= ×⎣ ⎦
Fermi distribution function:
0 0 0imp SS imp k k k k k
kf f v f fmσ σ σ σσ στ α τ σ⎡ ⎤= − ⋅∇ + × ⋅∇⎢ ⎥⎣ ⎦h
(2 ) (0)SS impso/3 N uα π λ=
skew scattering
q,x xN SH
s,y ySH N
J EJ eN
/δμ
σ σσ σ
−⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥ −∇⎣ ⎦⎣ ⎦ ⎣ ⎦
Spin Hall conductivity:
s,x xN SH
q,y ySH N
J eJ E
N/
δμσ σσ σ
−∇−⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥
⎣ ⎦⎣ ⎦ ⎣ ⎦
SH SH SHSS SJ σ σ σ= +
( )N
/q N
s N
j Ej e
σσ δμ
=⎧⎨ = − ∇⎩
spin // x[ ]⎧ = + ×⎪⎨ ⎡ ⎤= + ×⎪ ⎣ ⎦⎩
q q H
s s H q
sJ j x j
J j x j
α
α
σ αyq y
zj E x jN H spin⎡ ⎤= + ×⎣ ⎦
x
σ δμ αNzs
IJ xe z AN H
Pt
⎡ ⎤∂= − + ×⎢ ⎥∂ ⎣ ⎦
z
y
Spin current
Charge current
Charge current
Spin current
Room Temperature Spin Hall EffectT. Kimura (ISSP, RIKEN), Y. Otani (ISSP, RIKEN), T. Sato (ISSP)S. Takahashi (IMR, CREST), S. Maekawa (IMR, CREST)
( Phys. Rev. Lett. 98, 156601(2007))
Nonlocal Spin Hall device
``Conversion between charge-current and spin-current’’
スピン流
スピン流電荷蓄積
Py
Pt
Cu
IV
[ ]H =S Q
VRI
Δ→
Spin-current induced Spin Hall effect
PyPt
Cu
1 2 3
(Kimura et al.)
-200 -100 0 100 200
-0.1
-0.05
0
0.05
0.1
ΔΩ
V/I
C (
m)
ΔΩ
V/I
C (
m)
VC
IeM
H
ΔRSHE
a
b
-0.03
0
0.03
0.06
μ0H (mT)
RT
77 K
Nonlocal Spin Hall resistivity
スピン蓄積
Py
Pt
Cu
電流
IV
[ ] →Q S
VRISH = Δ
Charge-current induced Spin Hall effect
スピン蓄積
1 2 3
ΔΩ
V/I
S (
m)
ΔΩ
V/I
S (
m)
VS
IeM
H
a
b
-0.06
-0.03
0
0.03
0.06
-200 -100 0 100 200-0.2
-0.1
0
0.1
0.2
μ0H (mT)
RT
77 K
Nonlocal Spin Hall resistivity
IV I
V
[ ] →Q S
VRISH = Δ
Onsager Reciprocal Relation!!
[ ] →S Q
VRISH = Δ
Charge-current induced SHESpin-current induced SHE
Charge-current Spin-current
Valenzuela & Tinkham:
1.8 ×104
τsf / τ
Alb2 0.011λso
4.15 ×10−10 Ωcm2
ρNλN
5.88 μΩcm705 nm
ρNλN
◎ Side jump analysis:
kF=1. 5 ×108 cm−1 (Au)
41 10
0.011
SJSJ so
F imp
so
SHH
N k lσ λσ
λ
α −⎧= = ×⎪
⎨⎪⎩
:
:
( )110F imp imp so k l l λ: =
Spin-current induced Spin Hall effect:
(Nature 442, 176 (2006))
Spin pumping:
[ ] ∂⎛ ⎞∝ ×⎜ ⎟∂⎝ ⎠S j
SI St
α
α
x
z
IS
S
H
Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect E. Saitoh et al., APL88 (2006)
0.21502.2 ×10−11 Ωcm22.45 μΩcm90 nmAue
0.0111800041.5 ×10−11 Ωcm25.88 μΩcm705 nmAlc
0.074756.8 ×10−11 Ωcm23.50 μΩcm195 nmAgd
0.031230015.0 ×10−11 Ωcm21.00 μΩcm1500 nmCub
0.26331.8 ×10−11 Ωcm212.8 μΩcm14 nmPtf
2100
τsf / τ
0.03314.3 ×10−11 Ωcm21.43 μΩcm1000 nmCua
λsoρNλNρNλN
14 K2F N N
soRk
λρ λ
⎛ ⎞≈ ⎜ ⎟
⎝ ⎠24
9sfso
τ λτ
=
kF=1.5 ×108 cm−1T=4.2K
2
N sf
N
Dm
ne
λ τ
ρτ
⎫=⎪⎬
= ⎪⎭25.8K
2/ kR h e= ≈ Ω
2 2
32
sfN N
F
hk e
=τπρ λτ
a) Jedema et. al., b) Kimura et. al.(77K), c) Valenzuela&Tinkham, d) Godfrey&Johnsone) Seki et al..(RT), f) Kurt et. al.
Spin-orbit coupling : λso
Spin-orbit interaction strength in Pt and Auis about 30 times larger than that in Al.
( ) 30,( )
H
H
Pt Al
αα
=( ) 30,( )
so
so
PtAl
λλ
=
Pt, Au: Strong spin-orbit materialSpin absorberSpin generator
Takahashi, MaekawaPRL88, 116601 (2002)
S. Maekawa(IMR, Tohoku University)
Spin Current vs. Charge Current Spin Current vs. Charge Current
in Magnetic Nanostructuresin Magnetic Nanostructures
Contents:(i) Spin current,(ii) Spin accumulation,(iii) Spin Hall effect,(iv) Spin current pumping.
(Charge current Spin Current)
YKIS2007 (November 20 ,2007)