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).