Mesoscopic Spintronics - Université Paris-Saclay · Spin-dependent transport is a key phenomenon for the birth of spintronics. One representative example is the giant magnetoresistance

Mesoscopic Spintronics

Taro WAKAMURA (Université Paris-Sud)

Lecture 1

Today’s Topics

• 1.1 History of Spintronics

• 1.2 Fudamentals in Spintronics

Spin-dependent transport

GMR and TMR effect

Spin injection into diverse materials

Spin current and spin relaxation

Spin transfer torque

First of all... What is “spintronics”?

Electronics and Spintronics

Electron has: charge e Electronics

Electron has: spin 1/2 Spintronics

Spintronics in our daily lives

Magnetoresistive Random Access Memory

(MRAM)

Hard Disc Drive

(HDD)

How was spintronics born?

Spin polarized current

Ie ( = I↑ + I↓) ≠ 0

IS ( = I↑－I↓) ≠ 0

＝

Flow of charge and spin

Pure spin current

＝IS ( = I↑－I↓) ≠ 0

Flow of spin only

I↑： ↑spin current

I↓： ↓spin current

：Charge ：Spin

Spin-dependent transport

Currents

in ferromagnets

?

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

Peter Grunberg

Albert Fert

Nobel Prize in Physics in 2007

Nonmagnetic metal

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

Fert’s experiments

Fe/Cr/Fe structure Antiferromagnetic coupling depending on the thickness of Cr

Magnetoresistance (MR) ratio

Parallel ParallelAntiparallel

Inplane magnetization curves

MR(%) =𝑅𝐴𝑃 − 𝑅𝑃

𝑅𝑃x 100 ~ 50 % @ 4.2 K

M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

Grunberg’s experiments

Similar Fe/Cr/Fe structure, but measurements are at room temperature.

Small MR ratio: ~1.5 %

Fe/Cr/Fe trilayer structure

G. Binasch et al., Phys. Rev. B 39, 4828 (R) (1989).

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

How can we explain the gigantic magnetoresistance effect?

Electrical currents in ferromagnets are spin-polarized via s-d interaction

Most of carries can pass through in the parallel alignment of the ferromagnets

(= low R)

Most of carries are scattered at the interface in the antiparallel alignment

of the ferromagnets (= high R)

Birth of SpintronicsNote: Exchange coupling between ferromagnetic layers

Stuart Parkin (left)

Co/Ru/Co structure Fe/Cr/Fe structure

Coupling between

ferromagnetic layers

oscillates!

S. S. P. Parikin et al., Phys. Rev. Lett.

64, 2304 (1990).

Birth of SpintronicsNote: Exchange coupling between ferromagnetic layers

Rudermann, Kittel, Kasuya, Yoshida (RKKY) interaction between magnetic

moments via nonmagnetic layer can induce oscillating interaction.

S1S2

Conduction electron

Spin density wave of Cr might play a role as well (Wang, Levy and Fry, PRL 1990).

Birth of Spintronics

Tunneling Magneto-Resistance (TMR) effect

Breakthrough by magnetic tunnel junction (MTJ)

TMR in Fe/Al2O3/Fe multilayers MR ratio 18 % at room temperature

Thanks to high-quality amorphous Al2O3 tunnel barrier!

T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 (1995).

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

Julière’s model

Birth of Spintronics

Tunneling in a simple picture

Birth of SpintronicsTunneling in real materials

Importance of symmetries

of crystals

Birth of SpintronicsTunnel Magneto-Resistance (TMR) effect

There are many Bloch states in Fe, and they

have different spin polarization.

e.g. D1 state has high positive spin polarization,

and D2 state has negative spin polarization.

Amorphous Al2O3 mixes these states, thus

decrease of net spin polarization.

Decrease of MR ratio

Incoherent tunneling

Birth of SpintronicsTunnel Magneto-Resistance (TMR) effect

D1 state with high spin polarization coherently

couples D1 evanescent wave in MgO tunnel barrier.

High MR ratio is expected.

Coherent tunneling

Birth of SpintronicsTunnel Magneto-Resistance (GMR) effect

High tunneling probability of the D1 state for parallel alignment

High MR ratio

Tunnel Magneto-Resistance (GMR) effect

Birth of Spintronics

Tunnel Magneto-Resistance (GMR) effect

Birth of Spintronics

Small lattice mismatch (3%) between Fe and MgO

MgO with high crystallinity can be grown on Fe(001).

Birth of SpintronicsApplication of TMR to hard disk drives

Birth of SpintronicsApplication of TMR to hard disk drives

Brief Summary

Spin-dependent transport is a key phenomenon for the birth of spintronics.

One representative example is the giant magnetoresistance effect with metallic

insertion layer between two ferromagnets.

Giant magnetoresistance effect provoked intensive studies for systems

with higher MR ratio, and replacing metallic layer with tunnel barrier (insulator)

enables dramatically gigantic MR (TMR)

Then, is it possible to transfer spin angular momentum without charge

flow? If it is possible, Joule heating effects can be suppressed!

Spin polarized current

Ie ( = I↑ + I↓) ≠ 0

IS ( = I↑－I↓) ≠ 0

＝

Flow of charge and spin

Pure spin current

＝IS ( = I↑－I↓) ≠ 0

Flow of spin only

I↑： ↑spin current

I↓： ↓spin current

：Charge ：Spin

Pure spin currents

Currents

in ferromagnets

?

Nonlocal spin injection and detectionEasiest way: lateral spin valves

charge current

+ spin current

spin accumulation

spin current

F side N side

Spin Polarized CurrentPure Spin Current

Spin Current

Lateral Spin Valve (LSV) structure

↑

↓

N F

VP

VAP

DV

-500 0 500

-1

0

Magnetic field [Oe]

DV

/I [

m

]

DR

V

Nonlocal spin injection and detection

27

-500 0 500

-1

0

Magnetic field [Oe]

DV

/I [

m

]

DR

Fitting equation

where

PI: spin polarization of tunneling

junction

lX: spin diffusion length of X

T. Wakamura et al., Appl. Phys. Exp. 4, 063002 (2011).

Nonlocal spin injection and detectionData evaluation

L eB B

S

Larmor precession

NM

a 0 rotation

NM

B

b

B = 0

p/2 rotation

NM

B

c p rotation

V/I

B

0

0

VI

Hanle effectAnother way to estimate tsf and D: the Hanle effect

N

B=0V

Time t

t=0

44 46 48

P (

arb

.)

Time (ps)

DN

= 500 cm2/s

t = 40 ps

0

( )cosPV

dt tI

t

21( ) exp e p

4x

4 sfNN

LP t

D t

t

D t

p t

Diffusion Spin-flip

( )P t

F. J. Jedema et al, Nature 416, 713 (2002).

Hanle effectEstimation of tp and D by the Hanle effect

F. J. Jedema et al., Nature 416, 713 (2002).

B (G)

First experimental report

Information we can derive from the fitting of the Hanle curve:

Diffusion coefficient (D), Spin polarization of Co (P),

Spin diffusion length (lsf)

Many examples of the Hanle measurement for different materials:

n-GaAs (e.g. Lou et al., 2007), LaAlO3/SrTiO3 2DEG (Reyren et al., 2013).

Hanle effect

Key points of spin transport

Spin can transfer information

Spin transport in a long distance is preferable

However

Spins (to a certain quantized axis) are not conserved

Charges are conserved on the contrary.

Therefore, it is important to choose materials with long spin relaxation length or

spin relaxation time.

Then how does spin relaxation occur in materials?

Spin relaxation mechanismSpin relaxation mechanism

A: Elliot-Yafet mechanism

Periodic ion scattering containing

phonon contribution

B: D’yakonov-Perel’ mechanism

Spin precesses along an effective

magnetic field during momentum

scattering.J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

e.g. Metals, Graphene…

e.g. Semiconductors, Graphene…

Two mechanisms show different dependence of ts on tp.

ts: spin relaxation time, tp: momentum relaxation time

33

A: Elliot-Yafet mechanism

Basic idea: impurity or phonon scattering + spin-orbit interaction

B: D’yakonov-Perel mechanism

Spin tilts a little every time the electron

experiences momentum scattering.

ps tt

Basic idea: spin precession by random magnetic fields

The system lack of inversion symmetry:

kkEE

Kramer’s theorem: if Hamiltonian is time-reversal symmetric

J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

kkEE

Spin relaxation mechanism

34

From two equations

kkEE

This can be regarded as a spin split caused by an effective

k-dependent magnetic field (k):

)(2

1)( kΩk Η

J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

Electrons change their momentum after

each momentum scattering process

Random magnetic field between

the scattering processes

The smaller tp, the smaller the net magnetic field for spin becomes.

(motional narrowing)

Thusps tt 1

Spin relaxation mechanism

Spin relaxation from Hanle measurement

35

Example: single-layer graphene case

ts∝ D∝ tp

Single layer graphene

EY mechanism

Bilayer graphene

ts∝ D-1∝ tp-1

DP mechanism

H. Wei and R. K. Kawakami, Phys. Rev. Lett. 107, 047207 (2011).

Spin Transport in Materials

36

Spin Transport in Various Materials

Y. Fukuma et al., Nat. Mater. 10, 527 (2011).

Important issues in spintronics: efficient spin injection and detection

(spin impedance mismatch problem)

Search for materials with which long-range spin transport is possible

Examples in metals: Ag, Al, Cu etc.

(low spin-orbit materials)

B (Oe)S. P. Dash et al., Nature. 462, 491 (2009).

Spin Transport in MaterialsSpin Transport in Various Materials

Spin currents can also be transferred through semiconductors

(e.g. silicon, GaAs, LAO/STO)

Gate control of spin transport is possible

N. Reyren et al., Phys. Rev. Lett. 108, 186802 (2012).

N. Tombros et al., Nature 448, 571(2007).

Spin Transport in MaterialsSpin Transport in Various Materials

New materials

Carbon-based materials (graphene)

Graphene Small spin-orbit interaction

Good materials for transferring spin currents for a long distance (lsf ~ a few mm)

Brief summary

Spin angular momentum can be transferred with out any charge flow by means

of spin currents.

Spin currents can be easily generated by using ferromagnet-nonmagnet lateral

spin-valve structures.

The biggest difference between spin currents and charge currents is that spin

currents are not conserved.

Spin relaxation occurs by magnetic impurities or spin-orbit interaction. For the

latter, the EY and DP mechanisms can be considered.

Spin currents can be generated from ferromagnets. Then can spin currents

affect magnetization of ferromagnets?

Spin transfer torque (STT)

Concept of STT

When a current is passed

through magnetic junction as

shown in the right figure, spin-

polarized current is injected into

FM2 from FM1. If S1 and S2 is

not parallel, a net torque is

exerted on S2 by injected spin-

polarized current.

Magnetization can be

controlled by flowing a current.

Spin(-polarized) currents flow of spin angular momentum

Basics of spin dynamics

Landau-Lifsitz Equation

0: gyromagnetic constant

When a magnetic field is applied to a magnetic moment,

the magnetic field exerts a magnetic torque –0M x Heff

Magnetic moment continuously precesses around H

In real systems, there is relaxation, thus

phenomenological damping term

Basics of spin dynamics

phenomenological damping term

This equation implicitly assumes small damping (namely, the direction of M for

the second term does not depend on t).

Precisely speaking, damping is the force to prevent dM/dt. Gilbert

proposes the following equation:

Landau-Lifsitz-Gilbert (LLG) equation

These equations are equivalent by substituting

Basics of spin dynamics

For electrons from FM1 to FM2, three

situations can be considered.

(a) Reflection or spin scattering

at the interface

(b) Transmission (with

presession)

(c) Absorption of spin angular

momentum by FM2

Basics of spin dynamics

A spin points to (q ,f) can be expressed as

For example, in the case of (b), the phase shift for upspin and down spin

electrons is and , respectively.

Thus the spin function for the transmitted spin can be written as

Basics of spin dynamics

If , the electron’s spin

completely flips. This angular

momentum lost during the transmission

transfers to FM2.

In real materials, the phase shift should be random and averaged out for all

electrons. Therefore the net angular momentum change becomes

Spin-transfer-torque term proposed by Slonczewski

John Slonczewski

Spin transfer torque (STT)Theory of STT

Slonczewski’s STT term

Spin transfer torque (STT)

Magnetic domain wall motion driven by STT

Spin transfer from electrons to magnetic

moments move magnetic domail walls.

Magnetic force microscope images

A. Yamaguchi et al., Phys. Rev. Lett. 92, 077205 (2004).

Spin transfer torque (STT)

Magnetization switching by STT

AP

P

AP

P

Electrons with minority spin carrier from

nanomagnet scattered at the interface with Cu

Exert torque on magnetization of nanomagnet

A

B

A: Magnetic field driven magnetization switching

B: STT driven magnetization switching

F. J. Albert et al., Appl. Phys. Lett. 77, 3809 (2000).

Above the critical current, minor spin electrons

reflected back from the thick Co layer transfer

sufficient spin-angular momentum to the

nanomagnet to force it into antiparallel

alignment with the Co layer.P

AP

Brief summary

Spin(-polarized) currents are a flow of spin angular momentum, thus can

exert a torque on magnetization (spin-transfer torque, STT).

Magnetization dynamics can be described by Landau-Lifsitz-Gilbert (LLG)

equation, and STT is expressed as a Sloczewski term.

One can move magnetic domain walls by using STT with currents, and also

switch magnetization with STT larger than Gilbert damping.