Introduction to spintronics
I.V. Bobkova
Institute of Solid State Physicsand
Moscow Institute of Physics and Technology
Outline
Spintronics: what is it about?
GMR and TMR
Spin injection into nonmagnetic metals and spin accumulation
Nonlocal measurements of the spin accumulation
Control of magnetization by spin-polarized currents: spin transter torques
Superconducting spintronics
Spintronics: what is it?
It is everything related to an active manipulation of the electron spins
According to Yaroslav Fabian: “it is an umbrella for electron spin phenomena in solids”
Review:
I. Zutic, J. Fabian, and S. Das Sarma,
Spintronics: Fundamentals and applications,
Rev. Mod. Phys. 76, 323 (2004)
Two groups of spintronics phenomena:
Influence of spins on electrical properties
Electrical control of spins
GMR, TMR,spin valves
Spin transfer, magnetic moments reversal,domain wall motion
A generic spintronic device: illustration
Datta-Das spin field-effect transistor (SFET)
Datta, S., and B. Das, 1990, ‘‘Electronic analog of the electrooptic modulator,’’
Appl. Phys. Lett. 56, 665–667.
The picture is from the review by I. Zutic, J. Fabian, and S. Das Sarma
The Nobel Prize in Physics 2007
Albert Fert Unité Mixte de Physique CNRS/THALES, Université Paris-Sud, Orsay, France
Peter Grünberg Forschungszentrum Jülich, Germany
"for the discovery of Giant Magnetoresistance".
GMR: discovery
Fe
Cr
0H
0H
Albert Fert’s experimental data (1988)
Basic mechanism of GMR
Electron spin and atom magnetic moments
in parallel → weak scattering
Antiparallel → strong scattering
More scattering = higher electrical resistance
Why is the scattering spin-dependent?
3d DOS at the Fermi level is
larger for minority-spin electrons
than majority-spin electrons
Higher DOS of 3d states → Stronger scattering
TMR
G
GG
R
RRTMR
2121 mmMM NNNNG
2121 MmmM NNNNG
,1
2
21
21
PP
PPTMR
whereii
ii
mM
mM
iNN
NNP
- is the degree of
polarization
First observations: Julliere 1975; Maekawa and Gafvert 1982 – small effectMoodera and Miyazaki groups 1995 – large effect (20%)
since 2004 – 200-1000% (at Tsukuba, IBM) – MgO as an insulator
Spin valves
It is a system where the resistance depends onthe mutual orientation of the layers’ magnetizations
Application: non-volatile MRAM –
grid of spin-valves
Stored bits encodedin magnetization direction of sensor layers
GMR hard disk read heads
From: IBM web site
Spin injection
jjj
jjjs
j
)()( 0 eeNnxn
e
Dn
DNe2
nnej
NN,2
sNN
NNej
where
s
The picture is from the review by I. Zutic, J. Fabian, and S. Das Sarma
𝑟𝑐 , 𝑟𝐹~𝐿𝑠𝐹𝜎𝐹
, 𝑟𝑁~𝐿𝑠𝑁𝜎𝑁
−𝑡ℎ𝑖𝑠 can be obtained from 𝑗𝜆 = 𝜎𝜆𝐸 + 𝑒𝐷𝜆∇𝑛𝜆 and
Spin injection
j
,2
sNN
NNej
22 / sss L
We introduce:
;2
2
s
;
jj
jjPj
;2
s
;ss DL
2/)(
DDD
ssj 2
The spin injection efficiency:
Pjj
P sss
j
)/)(/(22
∇𝜇= -𝑃𝜎∇𝜇𝑠 + 𝑗/2𝜎
𝑃𝜎 =𝜎↑ − 𝜎↓𝜎↑ + 𝜎↓
Spin injection
Boundary conditions:
22 / sss L
jjNjF PPP )0()0( -if no spin-flip at the interface
)),0()0(()0( FNj
-is the interface conductivity
jPPr jcsFsN )(2)0()0(
jPPr jcFN )1()0()0(
4cr - is the effective contact resistance
𝑃Σ =Σ↑ − Σ↓Σ↑ + Σ↓
Spin injection
Solving 22 / sss L and /2/ jP s
with the boundary conditionsjPPr jcsFsN )(2)0()0(
jPPr jcFN )1()0()0(
we find ;)0(/ sFLx
sFsF e ;)0(/ sNLx
sNsN e
;)(2)0( jPPr FjFsF jPr jNsN 2)0(
where ;4/ NsNN Lr FFFsFF Lr
4/
Spin injection
jPPr jcsFsN )(2)0()0(
;)(2)0( jPPr FjFsF
jPr jNsN 2)0(
)/()( NcFFFcj rrrPrPrP
)/()( NcFFFcj rrrPrPrP
Spin injection
Transparent junctions:FNc rrr , F
NF
Fj P
rr
rP
Injection into a semiconductor: FF
N
Fj PP
r
rP - the conductivity mismatch problem
Tunnel junctions: FNc rrr , PPj - spin injection efficiency is due to
the contact polarization
there is no conductivity mismatch problem
Nonlocal spin detection Johnson-Silsbee experiment
M. Johnson and R. H. Silsbee, Phys. Rev. Lett. 55, 1790 (1985)
spin injector
circuit
spin detector
circuit
Using the quasineutrality condition 0
nn
and the equations obtained earlier, one can show that
2/sNP
2/)0()0()1()0()0( sFNFjcFN PjPPr
<for a open circuit>
2/)0()0()0( sFNFsc PjPr
sNLx
sNsNsNsN e/
))()0(()(
spin flow
charge flow
Nonlocal spin detection
PjP sj
)/)(/(2sN
sNsNN
sF
sF
F
sLL
j)()0(
2)0(
2)0(
)0(2)0()0( scsFsN jr
;)(2
)()0(
FNc
sNs
rrrj
);()0(
sN
FNc
FsF
rrr
r )()0(
sN
FNc
FcsF
rrr
rr
taking into account that 0j we get )0()(2
1)0()0()()( sFNF
sFNFN P
Finally, 2/)()()(2
)()(
sNjsN
NcF
FFcFN P
rrr
rPrP
2/)()()( sNjDFN P
spin injector
circuitspin detector
circuit
sNsN Ld
IjIN
Ld
sIsDsN ejPre//
2)(
sNLd
NjIjD
I
FNnl erPP
jR
/)()(
Nonlocal spin detection
Spin relaxation
Elliott-Yafet mechanism:
the picture is from the presentation by Yaroslav Fabian
pVcm
Vso 224
rki
knknknerbrar
)()()(
rki
knknknerbrar
)()()( **
/1||||/122
''
22
''bVbV
nkiknnkikns
Spin relaxation
D’yakonov-Perel’ mechanism:
Time-reversal + space-inversion:
kk
Time-reversal symmetry only:
kk
kk
Effective spin-splitting magnetic field:
)(2
kH ckk R
ˆ)(
yxD kkk ,)(
Rashba Dresselhaus
1 -spin precession about fluctuating magnetic fields
at one step: k
/tt
2
s1/ 1 s
Spin torque: general theory
J. Grollier , A. Chanthbouala, R. Matsumoto, A. Anane, V. Cros, F. Nguyen van Dau, Albert Fert,C. R. Physique, 12 309 (2011)
s-d model:
,ˆˆˆˆ sSJHHHi
isdspd
i
effiB
d HSg
H
2ˆ
where spVcm
rUm
pH sp
ˆˆ4
)(2
ˆˆ22
2
;ˆ2
,2
sSJ
HSSi
g
t
S
isd
effiiB
i
sS
JspV
cmJ
t
si
sds
ˆ2
ˆˆ2
1ˆ22
svJ sˆˆ
Bg
s-d model
;),(
S
S
M
trM i
s
strm ˆ),(
effii HSS
, - depends on the detailed structure of )( ieff SH
It is usually approximated by the Landau-Lifshitz-Gilbert (LLG) equation:
mMJ
t
MM
MHM
t
M sd
s
eff
2
mMM
SJT
s
sdst
2
mMM
SJmspV
cmJ
t
m
s
sd
sf
s
2ˆˆ
2
122
s-d model
in the steady state 0
t
m
and with no spin-orbit coupling and no spin relaxation: s
s
sdst JmM
M
SJT
2
in general PMM
bPMM
M
aT
s
j
s
j
st
2
Torque in spin-valves
PMM
bPMM
M
aT
s
j
s
j
st
2
For metallic spin-valves typically 0 , jj baja
st
s
eff Tt
MM
MHM
t
M
cjj /
0T
Domain wall motion by spin transfer torque
J. Grollier , A. Chanthbouala, R. Matsumoto, A. Anane, V. Cros, F. Nguyen van Dau, Albert Fert,C. R. Physique, 12 309 (2011)
MuTst
)( - adiabatic spin transfer torque
)2/( sB eMPgju
MuHMt
Meff
)(
-has a solution )( utxMM
Domain wall motion by spin transfer torque
Problem: Gilbert damping
Mut
MM
MHM
t
M
s
eff
)(
-predicts large threshold current for DW motion, which is at least
one order of magnitude higher than observed experimentally
Solution: nonadiabatic spin-torque
MuMMut
MM
MHM
t
M
s
eff
)()(
Domain wall motion by spin transfer torque: applications
(a) Race-track memory; (b) DW-RAM
DW spintronic memristor
The more intense is the current through the structure, and the longer it is injected, the more the resistance changes.
Spin-transfer induced domain wall motion in a spin valve structure is intrinsically a memristive effect.
)/1(/ LxRLxRR PAP
qtxju )(
LqRRRR PAPP /)(
Superconducting spin valves
sdh
2/cos
P. G. de Gennes, PRL 23, 10 (1966).
B. Li, N. Roschewsky, B. A. Assaf, M. Eich, M. Epstein-Martin, D. Heiman,M. Munzenberg, and J. S. Moodera, PRL 110, 097001 (2013).
Superconducting spin valves
L.R. Tagirov, PRL 83, 2058 (1999)
J.Y. Gu, C.-Y. You, J. S. Jiang, J. Pearson, Ya. B. Bazaliy, and S. D. Bader, PRL 89
267001 (2002). Py/CuNi/Nb/CuNi/Py
P. V. Leksin, N. N. Garif’yanov, I. A. Garifullin, J. Schumann,H. Vinzelberg, V. Kataev, R. Klingeler, O. G. Schmidt, and B. Buchner,Appl. Phys. Lett. 97, 102505 (2010).
Superconducting spin valves:generation of equal-spin triplets
Linder, Robinson, Nat. Phys. 11, 307 (2015)
Superconducting spin valves based on equal-spin triplets
CoOx/Fe/Cu/Fe/Pb
P.V. Leksin,N. N. Garif’yanov, I. A. Garifullin, Ya.V. Fominov, J. Schumann,Y. Krupskaya,V. Kataev, O. G. Schmidt, and B. Buchner, PRL 109, 057005 (2012).