spin dependent transport in nanostructures david halley, o. bengone and w. weber, institut de...

Spin dependent transport in nanostructures

David Halley, O. Bengone and W. Weber,

Institut de Physique et Chimie des Matériaux de Strasbourg

Seoul 2009

Plan

I Introduction: magneto-resistive effects

II Basis of spintronics• Principles of Giant Magneto-Resistance• Some typical metallic systems and applications• Technological requirements

III Tunnel Magneto-Resistance • Spin-conserving tunneling of electrons. Julliére’s

formula • Typical TMR systems• Electronic symmetry in monocristalline tunnel

junctions• Application to Fe/MgO/Fe systems• How can chromium become insulating?

IV Conclusion and perspectives• New materials• New effects: spin torque and resistive switching

Interplay between magnetism and electricalresistivity of a solid

Ordinary Magneto Resistance (OMR (Lord Kelvin, 1856: R/R < 5%) ):

the scalar resistivity is given by: xx=1/2)

where B is the magnetic field, the electron mobility,

Magneto-resistive effects:

The Lorentz force due to magnetic field modifies the trajectory

of electrons :

B

veF

B

vF

Bulk effect

Plan….






IV Conclusion and perspectives• new materials• new effects: spin torque and resistive switching

• Playing with the spin polarisation of electrons in

different ferro-magnetic materials.

• Devices mostly play with interface effects:

• Need of nanostructured devices:

Spintronics

Starting point : discovery of Giant Magneto-Resistance (P. Grünberg and A.Fert)

e-

lateral size: from a few microns to nanometers

a few nanometers

Giant Magneto Resistance ( GMR): injection through a

thin spacer layer into a second ferromagnetic layer:

e- Rp

Principle of Giant Magneto-Resistance

p

pap

R

)R-(R GMR

e-

-400 -200 0 200 400

2.70

2.75

In-p

lane

res

ista

nce

()

Magnetic Field (Oe)

D

Rp

Rapmagnetisation

Ni/Cu/Py system Rap

B

Spacer:

• metal (Fe/Cr/Fe for instance)

• or insulator: Tunnel Magneto Resistance

Electronic band structure and spin polarisation

Polarisation of the spin of the conducting electrons:

• majority electrons ( spin down relatively to the magnetisation)

• minority electrons (spin up)

Density of electronic states for majority

electrons (spin down)

EN

Fermi level

Energy

EN

Density of electronic states for minority

electrons (spin up)

Physical idea of GMR

The density of states is different for both spins.

It can lead to different mean free path for minority and majority spins.

Memories

• Magnetic Random Access Memories

(MRAM)

in competition with:

• Floatting gates (USB flash memories)

• Phase Change Random Access Memories

(PRAM)

• Ferro-electricity

• Resistive switching

• ….

Sensors….

• Sensors for magnetic field.

• Position sensors.

• Read heads in hard disks.

For which applications?

Magnetic recording: writing and reading magnetic bits

H

Inductive writting or reading:

Magnetic bits

Conventional memories:

Using GMR in read heads of hard disks

V

Reading:GMR system sensitive to the stray

field of magnetic bits

R( ) < R( )

Using GMR junctions as memories?

ireading

Soft layer

Hard layer

Magnetic Random Access Memorie (MRAM )

ir irir

Iwritting Iw Iw Iw

Stray field

Adressing each bit:ireading+Iwritting

Technological requirements for GMR

• Decoupling of the magnetic layers: parallel and antiparallel configurations in a low field.

• Making the resistance measurable : nanostructuration of devices.

• Obtaining high GMR values….

How to obtain two different coercitive fields?

• Different coercivities: one hard and one soft magnetic layers (NiFe and Co for instance)

• Interlayer Exchange Coupling

• Spin valves: magnetic pinning of one of the layers by antiferro-magnets (PtMn). Due to

interfacial exchange coupling.

Technologicaly important

Decoupling of the magnetic layers

From S. Yuasa et al., J. Phys. D., 40, R337, (2007)

Lithography of metallic GMR junctions

Lithography is required to have low lateral dimensions

… and measurable resistances

But the GMR does not exceed a few tens of percents…..except with magnetic tunnel junctions.

From Y. Jiang et al, Nature Materials 3, 361 - 364 (2004)

Reistivity of a metal:< 100 .cm

Assuming a 100 x 100 x 50 nm junction: R = .l/S# 1 …very low!!!

Plan….







Tunnel Magneto Resistance (TMR)

Bias voltage

Electron potential

Conservation of the spin of the electron during tunneling

e-Fermi level

metallic electrode metallic electrodeinsulator

Density of electronic states for majority

electrons (spin down)

EN

Fermi level

Energy

EN

Density of electronic states for minority

electrons (spin up)

e-Bias voltage

Electron potential

Fermi level

magnetisation magnetisationmagnetisation

Difference in resistivity between the parallel and anti-parallel magnetic configurations

Tunnel Magneto Resistance

One channel for each spin

Tunnel Magneto Resistance

« The tunneling current in each spin channel is proportionnal to the product of the effective density of states at the Fermi level. «

Juillère’s model:

Considering both electrodes as two isolated systems with different hamiltonians

gP D1D2 +D1D2

Cf Fermi golden rule

gAP D1D2+D1D2

So, the conductance in the parallel and anti parallel cases can be written:

Fermi level

Electrode 1 Electrode 2

Tunneling probability?

Julliére’s Formula

We define the spin polarisation in each electrode:

It yields (Juliére, 1975):

)(

)(P

11

111

DD

DD

)(

)(P

22

222

DD

DD

)PP-(1

P P 2

R

)R-(RTMR

21

21

p

pap

TMR = 2 P1 P2 /(1-P1P2)

Search for half-metals

If P1 = P2 = 1 the TMR can theoretically by infinite.

This 100% spin polarisation corresponds to:

thus: D = 0 for each electrode

Such materials are called half-metals:

• no transition metal

• some oxides are good candidates ( manganites). (cf N. Viart)

1)D(D

)D(D

P

Growth of TMR systems

Growth of continuous insulating layer with a low roughness.

Thickness between 1 and 3 nm.

* Images from wikipedia

*

*e-beam target

substrate

Deposition methods:Deposition methods:

• Sputtering ( Alumina barriers):

giving amorphous or polycristalline samples.

*

• Pulsed laser deposition (complex oxides, for instance SrTiO3)

• Molecular Beam epitaxy (MgO barriers).

http://upload.wikimedia.org/wikipedia/en/a/a4/PLD_Plume.png

Defects in TMR systems

• pinholes in the insulating layer = short circuit

• localised defects in the barrier

( oxygen vacancies, metallic impurities, dislocations ):

Can depolarise the current: the TMR drops

E. Fullerton et al, J. Appl.Phys., 81, (2) (1997)

SEM image of a 20 nm MgO grown on Fe (001)

e-

Localised defect

“hot spots” in TMR junctions

V. Da Costa et al, Eur. Phys. J. B., 13, 297, (2000)

Roughness of the barrier

Fluctuation of the barrier thickness t

Exponential dependency of the tunneling probability on t

Hot spots

Hot spot

AFM measurements on an Alumina barrier: Topography (left) current (right)

Lithography of tunnel junctions

Higher resistance: lateral sizes in the microns range

d #microns

12μm

Typical TMR systems

The TMR does not exceed 70% in polycristalline systems: due to defects in the barrier and to a non 100% spin polarisation in electrodes ( no real half metallic electrodes)

Co/Al2O3 barrier/ NiFe, with two different coercitive fields for both electrodes:

Co

NiFe

Al2O3

Magnetic field

Typical TMR measurements in a Ferro/insulator/Ferro junction

(C. Tiusan, Phys.Rev. B, 64, 104423 (2001))

TM

R (

%)

Polycristalline electrodes and amorphous insulating barrier

Plan….







When tunneling, electrons change their wave vector relatively to the cristalline directions

Intrinsic issues in polycrystalline junctions

Growth direction e-

electrode 1

insulator

electrode 2

the spin polarisation should be 100% on the whole Fermi surface

( for all electron wave vectors)

TMR in monocristalline systemsW.H. Butler (2001) introduced the concept of coherent tunneling in TMR epitaxial junctions:

The periodicity of the crystalline potential is same throughout the sample:

Tunnel barrier

Ferro 1

Ferro 2

Growth direction

The electron can be described by a Bloch wave function in both electrodes

and in the barrier.

Symmetry of Bloch functions

Bloch theorema: in a period crystaline potential the wave function of electrons can be written:

rik

kk erur )()(

These functions can be classified into different symmetries relatively to the normal to interfaces.

directionCf orbital wave function characterised by their symmetry: s, p, d….

Bloch wave function can be decomposed into these orbitals:

• The electron keeps its symmetry relatively to the normal to interfaces.

• For instance 1, 5, 2, 2’ states in [001] Fe is a label for the tunneling electron.

Tunnel barrier

Ferro 1

Ferro 2e-

The tunnelling of electrons is now determined by their spin and by the symmetry of their wave function

Coherent tunnelling

Symmetry of Bloch functions

Jullière model is no more valid

*Phys. Rev. B, 63, 054416, (2001)

This symmetry strongly determines the tunneling probability of electrons:

Density of states as a function of the insulator thickness for different symmetries in a Fe/MgO/Fe

monocristalline system (from W.H. Buttler *)

Symmetry dependent tunneling for Bloch functions

S. Yuasa et al., J. Phys. D., 40, R337, (2007)

Symmetry dependent tunneling for Bloch functions

From S. Yuasa et al., J. Phys. D., 40, R337, (2007)

Amorphous or polycristalline barriers

Monocristallinebarriers

Monocrystalline Fe/MgO/Fe systemsEpitaxial growth of Fe/MgO/Fe systems by Molecular Beam Epitaxy

Fe

MgO

Fe

CoHard layer

Soft layer

a MgO

aFe

Mg

O

Fe Transmission electron microscopy image of a MgO barrier

MgO

Fe/MgO/Fe (001) monocristalline junctions

Coherent tunnelling in Fe/MgO/Fe junctions

Regarding electrons dominating the tunnel transport (1 electrons), Fe is half-metallic!

Dispersion curves for 1 and 5 electrons in iron, ( k perpendicular to the barrier)

0 /aWave vector k

0 /aWave vector k

Majority electrons

Minority electrons

EF

-500 0 500

200

300

400

R(

)

Field (Oe)

65g 40µm

Best results:

up to 1000% at low temperature*

Very high TMR in MgO-based tunnel junctions

*Y.M. Lee et al., Appl. Phys. Lett.90, 212507 (2007)

Less defects in FeCoB/MgO/FeCoB systems:

Very high TMR in MgO-based tunnel junctions

Textured junctions grown by sputterring

industrial applications coming soon?


Plan….







How can Chromium become insulating?

Chromium is an insulating barrier in the parallel magnetic configuration

Fe

MgOCrFe

Insertion of a thin Cr epitaxial layerbelow the MgO barrier

Fe Cr MgO Fe

1 Electrons Potential

magnetisation magnetisation

e-

0 /aWave vector k

Regarding 1 electrons Chromium is an insulator ( no 1 states at the Fermi level)

Dispersion curve for electrons in chromium

The conductance in the parallel magnetic configuration drops with tCr:

The tunnel conductance of 1 states is filtered by Cr


Firt principle calculations of the conductanceFor majority electrons in the parallel magnetic configuration

For x=0 (no Cr), and x=6 monolayers Cr

1,0

2,0

3,0

Parallel Anti Parallel

1,0

2,0

3,0

d

I/d

V (

x10

-3 A

.V-1)

-1,0 -0,5 0,0 0,5 1,01,0

2,0

3,0

3 atomic layers Cr

2 atomic layers Cr

0 atomic layer Cr

Voltage (V)

The conductance in the parallel magnetic configuration drops with tCr:

The tunnel conductance of 1 states is filtered by Cr


F. Greullet, Phys. Rev. Lett., 99, 187202 (2007)

Symmetry-resolved quantum wells

Fe Cr Fe MgO Fe

1 electronspotential

Quantum well for 1 electrons only

Cr (2 nm)

Electrons Energy Loss SpectroscopyMap: section of a Fe/Cr/Fe/MgO/Fe junction

Coll. G. Bertoni EMAT Anvers

oxygen chromiumiron

Fe (20 nm)

Fe (1.5 nm)

Fe (5 nm)MgO (2 nm)

MgOsubstrate

20 nm

e-magnetisationmagnetisation

Fe

Fe

FeCr

MgO

Symmetry-resolved quantum wellsFe/Cr/Fe/MgO/Fe systems

F. Greuillet et al., Phys. Rev. Lett. 99 , 187202 (2007)

Oscillations of the differential conductance:

modulations of the density of 1 electronic

states in the quantum well

-1.0 -0.5 0.0 0.5 1.0

1 nm Fe quantum well

Parallel Anti Parallel

d2 I

/dV

2 (

a.u

)

Voltage (V)

Peaks

….and resonant tunnel diodes

Changing the voltage selects the resonant condition that is spin-dependantvery large TMR expected.

From T. Niizeki et al.1

1 T. Niizeki et al., Phys. Rev. Lett. 100, 047207 (2008)

Ab initio calculation of the position of the peaks as a function of Fe thickness.

Cr/Fe/MgO/Fe stacking

The amplitude and the energy position of the peaks depends on the width of

the Fe quantum well.

Plan….







Conclusion

• new concept of « symmetry-tronics » : artificial way to make half metals.

• observed in metals, oxides, and …..semi-conductors?

• MgO based tunnel junctions very promising for spintronics.

• industrial ways of deposition are studied by IBM.

Could we combine both aspects: electronic symmetry

in organic stacks?

What about organic materials?

Conclusion: much work to do concerning the growth of epitaxial organics…

From ref. [2] : GMR device based on an Alq3 spacer. The measured GMR reaches 40%

2 Z.H. Xiong, Nature. 427, 821 (2004)

From ref [3] : STM observation of ZnPcF8

( fluorated Phtalocyanine molecules) grown on Ag (111)

3 V. Oison, Phys. Rev. B,75, 35428 (2007)

Perspective: organic materials

(High spin diffusion length)

Perspective: resistive switching and TMR?

Can we play with defects in the barrier ?

Tunneling via defects in the insulator

High electric field across the barrier

Electro-migration of defects:change in the tunneling probability

Perspective: resistive switching and TMR

0 10 20 305

10

15

20

R(M

)

n° cycle

-1,0 -0,5 0,0 0,5 1,0-3

-2

-1

0

1

2

I (m

A)

bias voltage (V)

-500 0 500012

TM

R (

%)

H (Oe)

-500 0 500012

TM

R (

%)

H (Oe)

Fe/Cr/MgO/Fe junctions

Defining an off and on states…

D. Halley et al, Appl. Phys. Lett. 92, 212115 (2008)

Writting bits with a high spin-polarised current density

V

e-

e-

Spin polarised of electrons along M1M1

Magnetic switching of M2

Reading: GMR measured with a low current density

Iwritting

Perspective: spin torque

E.B. Myers, et al., Science, 285,868

Injecting the current through small nano-pilars:

Perspective: experimental spin torque

Also through thin tunnel barriers…..


Spin torque and magnetic domain walls:

Perspective: spin torque

Phys. Rev. Lett., 96, 197207 (2006)

spin dependent transport in nanostructures david halley, o. bengone and w. weber, institut de...

Documents

magnetoresistive effects

spin torque

spin polarisationpolarisation

spin polarisation of

magnetic field

magnetic pinning

magnetic recording

resistance measurable