spin dependent transport in nanostructures david halley, o. bengone and w. weber, institut de...
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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….
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
• 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….
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
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).
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….
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
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?
S. Yuasa et al., J. Phys. D., 40, R337, (2007)
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
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
How can Chromium become insulating?
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
How can Chromium become insulating?
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….
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
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…..
S. Yuasa et al., J. Phys. D., 40, R337, (2007)
Spin torque and magnetic domain walls:
Perspective: spin torque
Phys. Rev. Lett., 96, 197207 (2006)
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