1. Spin dependent transport in nanostructures
David Halley, O. Bengone and W. Weber,
Institut de Physique et Chimie des Matériaux de Strasbourg
Seoul 2009

2. 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

3. Interplay between magnetism and electrical resistivity of a solid
Magneto-resistive effects:
The Lorentz force due to magnetic field modifies the trajectory
of electrons :
Ordinary Magneto Resistance (OMR (Lord Kelvin, 1856: DR/R < 5%) ):
the scalar resistivity is given by: rxx=1/s0 (1+(mB)2)
where B is the magnetic field, m the electron mobility,
Bulk effect

4. 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

5. from a few microns to nanometers
Spintronics
Playing with the spin polarisation of electrons in
different ferro-magnetic materials.
Devices mostly play with interface effects:
Need of nanostructured devices: e-
a few nanometers
lateral size:
from a few microns to nanometers
Starting point : discovery of Giant Magneto-Resistance (P. Grünberg and A.Fert)

6. Principle of Giant Magneto-Resistance
Giant Magneto Resistance ( GMR): injection through a thin spacer layer into a second ferromagnetic layer:
Rap Rp e- e- Rp
Rap
Ni/Cu/Py system
magnetisation
Spacer:
metal (Fe/Cr/Fe for instance)
or insulator: Tunnel Magneto Resistance

7. The density of states is different for both spins.
Physical idea of GMR
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)
Fermi level
Energy
states for minority
electrons (spin up)
The density of states is different for both spins.
It can lead to different mean free path for minority and majority spins.

8. For which applications?
Sensors….
Sensors for magnetic field.
Position sensors.
Read heads in hard disks.
Memories
Magnetic Random Access Memories
(MRAM)
in competition with:
Floatting gates (USB flash memories)
Phase Change Random Access Memories
(PRAM)
Ferro-electricity
Resistive switching ….

9. Magnetic recording: writing and reading magnetic bits
Conventional memories: H
Inductive writting or reading:
Magnetic bits

10. GMR system sensitive to the stray
Using GMR in read heads of hard disks V
Reading:
GMR system sensitive to the stray
field of magnetic bits
R( ) < R( )

11. Using GMR junctions as memories?
Magnetic Random Access Memorie (MRAM )
Stray field
Iwritting Iw Iw Iw
ireading ir ir ir
Soft layer
Hard layer
Adressing each bit:ireading+Iwritting

12. 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….

13. Technologicaly important
Decoupling of the magnetic layers
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
From S. Yuasa et al., J. Phys. D., 40, R337, (2007)

14. Lithography of metallic GMR junctions
Reistivity of a metal: r < 100 mW.cm
Assuming a 100 x 100 x 50 nm junction: R = r.l/S# 1 W …..very low!!!
Lithography is required to have low lateral dimensions
… and measurable resistances
From Y. Jiang et al, Nature Materials 3, (2004)
But the GMR does not exceed a few tens of percents…..except with magnetic tunnel junctions.

15. 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

16. Conservation of the spin of the electron
Tunnel Magneto Resistance (TMR)
metallic electrode
insulator
metallic electrode
Electron
potential
Bias voltage
Conservation of the spin of the electron
during tunneling e-
Fermi level

17. One channel for each spin
Tunnel Magneto Resistance e-
Bias voltage
Electron
potential
Fermi level
magnetisation
magnetisation
magnetisation
Density of electronic
states for majority
electrons (spin down)
Fermi level
Energy
One channel for each spin
Density of electronic
states for minority
electrons (spin up)
Difference in resistivity between the parallel and anti-parallel magnetic configurations

18. Tunneling probability?
Tunnel Magneto Resistance
Fermi level
Electrode 1
Electrode 2
Tunneling probability?
Juillère’s model:
Considering both electrodes as two isolated systems with different hamiltonians
« The tunneling current in each spin channel is proportionnal to
the product of the effective density of states at the Fermi level. « 
Cf Fermi golden rule
So, the conductance in the parallel and anti parallel cases can be written:
gP  D1D2 +D1D2
gAP  D1D2+D1D2 

19. We define the spin polarisation in each electrode:
Julliére’s Formula
We define the spin polarisation in each electrode:
It yields (Juliére, 1975):

20. Search for half-metals
TMR = 2 P1 P2 /(1-P1P2)
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)

21. Growth of TMR systems
Growth of continuous insulating layer with a low roughness.
Thickness between 1 and 3 nm.
Deposition methods:
Sputtering ( Alumina barriers):
giving amorphous or polycristalline samples. * *
Pulsed laser deposition
(complex oxides, for instance SrTiO3)
e-beam
target
substrate
Molecular Beam epitaxy (MgO barriers). *
* Images from wikipedia

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

23. “hot spots” in TMR junctions
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)
V. Da Costa et al, Eur. Phys. J. B., 13, 297, (2000)

24. Higher resistance: lateral sizes in the microns range
Lithography of tunnel junctions
Higher resistance: lateral sizes in the microns range
d #microns
12μm

25. Typical TMR systems
Polycristalline electrodes and amorphous insulating barrier
Co/Al2O3 barrier/ NiFe, with two different coercitive fields for both electrodes:
Typical TMR measurements in
a Ferro/insulator/Ferro junction
(C. Tiusan, Phys.Rev. B, 64, (2001))
TMR (%) Co
NiFe
Al2O3
Magnetic field
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)

26. 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

27. e- Intrinsic issues in polycrystalline junctions
electrode 1
insulator
electrode 2
Growth
direction
When tunneling, electrons change their wave vector relatively to the cristalline directions
the spin polarisation should be 100% on the whole Fermi surface
( for all electron wave vectors)

28. TMR in monocristalline systems
W.H. Butler (2001) introduced the concept of coherent tunneling in TMR epitaxial junctions:
Tunnel barrier
Ferro 1
Ferro 2
Growth
direction
The periodicity of the crystalline potential is same throughout the sample:
The electron can be described by a Bloch wave function in both electrodes
and in the barrier.

29. Symmetry of Bloch functions
Bloch theorema: in a period crystaline potential the wave function of electrons can be written:
These functions can be classified into different symmetries relatively to the normal to interfaces.
Cf orbital wave function characterised by their symmetry: s, p, d….
Bloch wave function can be decomposed into these orbitals:
D direction

30. Symmetry of Bloch functions
Ferro 2
Tunnel barrier
Coherent tunnelling
Ferro 1
The electron keeps its symmetry relatively to the normal to interfaces.
For instance D1, D5, D2, D2’ states in [001] Fe is a label for the tunneling electron.
The tunnelling of electrons is now determined by their spin
and by the symmetry of their wave function
Jullière model is no more valid

31. Symmetry dependent tunneling for Bloch functions
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 *)
S. Yuasa et al., J. Phys. D., 40, R337, (2007)
*Phys. Rev. B, 63, , (2001)

32. Amorphous or polycristalline
Symmetry dependent tunneling for
Bloch functions
Amorphous or polycristalline
barriers
Monocristalline
barriers
From S. Yuasa et al., J. Phys. D., 40, R337, (2007)

33. Transmission electron microscopy
Monocrystalline Fe/MgO/Fe systems
Epitaxial growth of Fe/MgO/Fe systems by Molecular Beam Epitaxy Fe
MgO Co
Hard layer
Soft layer
Transmission electron microscopy
image of a MgO barrier
MgO
aMgO
aFe Mg O Fe

34. Coherent tunnelling in Fe/MgO/Fe junctions
Fe/MgO/Fe (001) monocristalline junctions
Dispersion curves for D1 and D5
electrons in iron, ( k perpendicular to the barrier)
p /a
Wave vector k
Majority
electrons
Minority EF
Regarding electrons dominating the tunnel transport
(D1 electrons), Fe is half-metallic!

35. Very high TMR in MgO-based tunnel junctions
Less defects in FeCoB/MgO/FeCoB systems:
Best results:
up to 1000% at low temperature*
*Y.M. Lee et al., Appl. Phys. Lett.90, (2007)

36. 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)

37. 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

38. Insertion of a thin Cr epitaxial layer
How can Chromium become insulating?
p /a
Wave vector k
Regarding D1 electrons Chromium is an
insulator ( no D1 states at the Fermi level)
Dispersion curve for
electrons in chromium Fe
MgO Cr
Insertion of a thin Cr epitaxial layer
below the MgO barrier Fe Cr
MgO
D1 Electrons
Potential
magnetisation e-
Chromium is an insulating barrier in the parallel magnetic configuration

39. How can Chromium become insulating?
Firt principle calculations of the conductance
For majority electrons in the parallel magnetic configuration
For x=0 (no Cr), and x=6 monolayers Cr
The conductance in the parallel magnetic configuration drops with tCr:
The tunnel conductance of D1 states is filtered by Cr

40. How can Chromium become insulating?
Voltage (V)
The conductance in the parallel magnetic configuration drops with tCr:
The tunnel conductance of D1 states is filtered by Cr
F. Greullet, Phys. Rev. Lett., 99, (2007)

41. Symmetry-resolved quantum wells
Cr (2 nm)
Electrons Energy Loss Spectroscopy
Map: section of a Fe/Cr/Fe/MgO/Fe junction
Coll. G. Bertoni EMAT Anvers
oxygen
chromium
iron
Fe (20 nm)
Fe (1.5 nm)
Fe (5 nm)
MgO (2 nm)
MgO
substrate
20 nm
Fe Cr Fe MgO Fe
D1 electrons
potential e-
magnetisation
Quantum well for D1 electrons only

42. Symmetry-resolved quantum wells Fe/Cr/Fe/MgO/Fe systems
 F. Greuillet et al., Phys. Rev. Lett. 99 , (2007)
Oscillations of the differential conductance:
modulations of the density of D1 electronic
states in the quantum well
Peaks

43. ….and resonant tunnel diodes
From T. Niizeki et al.1
1 T. Niizeki et al., Phys. Rev. Lett. 100, (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.
Changing the voltage selects the resonant condition that is spin-dependant
very large TMR expected.

44. 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

45. Conclusion MgO based tunnel junctions very promising for spintronics.
industrial ways of deposition are studied by IBM.
new concept of «  symmetry-tronics » : artificial way to make half metals.
observed in metals, oxides, and …..semi-conductors?

46. Perspective: organic materials
What about organic materials?
(High spin diffusion length)
Could we combine both aspects:
electronic symmetry
in organic stacks?
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, (2007)
Conclusion: much work to do concerning the
growth of epitaxial organics…

47. Perspective: resistive switching and TMR?
Can we play with defects in the barrier ?
High electric field
across the barrier
Tunneling via defects in the insulator
Electro-migration of defects:
change in the tunneling probability

48. Fe/Cr/MgO/Fe junctions
Perspective: resistive switching and TMR
Fe/Cr/MgO/Fe junctions
Defining an off and on states…
D. Halley et al, Appl. Phys. Lett. 92, (2008)

49. Perspective: spin torque
Writting bits with a high spin-polarised current density e- M1
Spin polarised of electrons along M1 V e-
Magnetic switching of M2
Iwritting
Reading: GMR measured with a low current density

50. Also through thin tunnel barriers…..
Perspective: experimental spin torque
Injecting the current through small nano-pilars:
Also through thin tunnel barriers…..
E.B. Myers, et al., Science, 285,868
S. Yuasa et al., J. Phys. D., 40, R337, (2007)

51. Spin torque and magnetic domain walls:
Perspective: spin torque
Spin torque and magnetic domain walls:
Phys. Rev. Lett., 96, (2006)