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Nanomagnetism Part III Atomic-scale properties Olivier Fruchart Institut Nel (CNRS-UJF-INPG) Grenoble - France http://neel.cnrs.fr Institut Nel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/

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Institut Néel, Grenoble, France

Nanomagnetism – Part III Atomic-scale properties

Olivier Fruchart

Institut Néel (CNRS-UJF-INPG) Grenoble - France

http://neel.cnrs.fr

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.2

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Institut Néel, Grenoble, France

SKETCH OF THE LECTURES Part I – Magnetization reversal Part II – Techniques Part III – Atomic-scale properties

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.3

http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

Institut Néel, Grenoble, France

MOTIVATING THE LECTURE – The need for nanomagnetism (reminder)

Fundamental issues for nanomagnetism

Is a small grain (ferro)magnetic?

kBT 300 K≈4×10

−21 J≈25 meV

Is a small grain stable against

thermal fluctuations? Count number of surface atoms Derive from macroscopic arguments

Decades-old (yet still modern) topic

100kBT 300 K≈2.5 eV

Magnetic grain media of current hard disks

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.4

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Institut Néel, Grenoble, France

TABLE OF CONTENTS

  • 1. Ferromagnetic order in low dimensions
  • 2. Magnetic energy anisotropy
  • 3. Interfacial effects

Structure and magnetic order Magnetic moments (surfaces etc.) Magnetic ordering (thermal effects)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.5

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Institut Néel, Grenoble, France

Robustness of ferromagnetic orders

  • 1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe)
  • V. L. Moruzzi et al., PRB39, 6957 (1989)

See also: O.K. Andersen, Physica B 86, 249 (1977)

High Spin Anti-Ferro Non-Magn. Low Spin & Low Spin

Theory: phase diagram of fcc iron (Fe)

Properties of bulk Fe

(P,T) ambiant conditions Body-Centered Cubic (bcc) Ferromagnetic ≈2.2B atom

−1

T>1185 K Face-Centered Cubic (fcc, -Fe) No magnetic order T C=1043 K

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.6

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe)

Effect of strain on the crystalline structure

  • P. Ohresser et al., PRB59, 3696 (1999)

300K growth with MBE: fcc>bcc

Fe/Cu(001)

300K growth with PLD: fcc

Magnetism of fcc Fe

High-spin and low-spin fcc phases?

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.7

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Metastable phases (fcc Fe)
  • D. Qian et al., PRL87, 227204(2001)

See also:

  • H. L. Meyerheim et al.,
  • Phys. Rev. Lett. 103,

267202 (2009)

Ferro. SDW - AF

Spin-density wave antiferromagnetism

Fe/Cu(001)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.8

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Surface magnetism – Naive views

Surface techniques at OK

  • Mossbauer with probe layers

Plot m(t) at 0K:

  • Magnetometry
  • XMCD
  • Fe/W(110) : 0.14ml(+0.35µB)
  • UHV/Fe(110); Ag/Fe(110): 0.26ml(+0.65µB)
  • Cu/Ni(111): -0.5ml
  • Overlayers: Pd/Ni(111)/Re(0001)

Probing surface magnetization Some results

s-p d k E s-p d k E

(Too) simple picture: band narrowing at surfaces

Bulk picture Surface picture

Enhanced moment at surfaces

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.9

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Surface magnetism – Towards single atoms

Conclusions

  • From bulk to atoms:

considerable increase of orbital moment

  • 2 atoms closer to wire than 1 atom
  • bi-atomic wire closer to surface than wire

Conclusions

  • Bulk: mL=0.14µB/at.
  • Surface: mL=0.31µB/at.
  • Bi-atomic wire: mL=0.37µB/at.
  • Mono-atomic wire: mL=0.68µB/at.
  • bi-atom: mL=0.78µB/at.
  • atom: mL=1.13µB/at.
  • A. Dallmeyer et al., Phys.Rev.B 61(8), R5153 (2000)

Co/Pt(997)

  • P. Gambardella et al., Science 300, 1130 (2003)
  • P. Gambardella et al., Nature 416, 301 (2002)

Co/Pt(111)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.10

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Surface magnetism – Polarizability and Stoner criterium
  • J. Vogel et al., PRB55, 3663 (1997)

Fe/Pd multilayers

  • U. Gradmann, Handbook…

Pd(D)/Ni(111)/Re(0001)

Conclusion: Pd sigifnicantly polarized over several layers

XMCD

Exchange polarization at interfaces

TOM

Spontaneous polarization – Stoner criterieum

  • A. J. Cox et al., PRL71, 923 (1993)
  • A. J. Cox et al., PRB49, 12295 (1994)

Small Rh(4d) clusters studied in flight (Stern-Gerlach experiment) I ,F1 Handwavy explanation based on Stoner criterium

Conclusion: recuced bandwidth may even drive ferromagnetism

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.11

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Magnetic ordering

Elements of theory

  • Ising (1925). No magnetic order at T>0K in 1D Ising chain.
  • Bloch (1930). No magnetic order at T>OK in 2D Heisenberg.

(spin-waves; isotropic Heisenberg)

  • → N. D. Mermin, H. Wagner, PRL17, 1133 (1966)
  • Onsager (1944) + Yang (1951).

2D Ising model: Tc>0K Magnetic anisotropy stabilizes ordering

  • R. Bergholz and
  • U. Gradmann,

JMMM45, 389 (1984)

Ni(111)/Re(0001)

Tc interpreted with molecular field

Experiments

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.12

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Magnetic ordering

Naïve model

Molecular field z neighbors

zb zs

  • 1

c

~ ) ( t t T

∆

Less naïve…

λ

  • c

~ ) ( t t T

∆

1

= λ

G.A.T. Allan, PRB1, 352 (1970)

Thickness-dependant molecular field

Experiments

  • U. Gradmann,

Handbook of Magn. Mater. Vol.7, ch.1 (1993)

Conclusion: Naïve views are roughly correct

T C=0 z nW,1ngJ

2 B 2 J J1

3kB 〈z〉=z b−2z b−zs N

N atomic layers

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.13

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Institut Néel, Grenoble, France

  • 1. FERROMAGNETIC ORDER – Magnetic ordering

Effect of lateral size

H.J.Elmers et al., Phys.Rev.Lett.73, 898(94)

  • U. Gradmann, Handbook of Magn. Mater. 7 (1993)

Conclusion Tc also depends on size of islands (lateral dimensions)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.14

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Institut Néel, Grenoble, France

  • 3. Magnetic anisotropy
  • 1. Ferromagnetic order in low dimensions
  • 2. Magnetic energy anisotropy
  • 3. Interfacial effects

Microscopic origins of Magnetic Anisotropy Energy (MAE) Surface versus magneto-elastic anisotropy From surfaces (2D) to atoms (0D)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.15

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Basics

1 2

‘Cone’ of alignment Let us assume two magnetic dipoles with vertical direction, either ‘up’ or ‘down’ :

θ

      − =

) . ).( . ( 3 . 4

2 1 2 2 1 3 1,2

r μ r μ μ μ r r E

π µ

Mutual energy of two magnetic dipoles : Parallel alignment is favored for Antiparallel alignment is favored for

° ≈ <

74 . 54

C θ θ ° ≈ >

74 . 54

C θ θ

3 / 1 ) ( cos2

= C θ

[ ]

θ µ µ π µ θ 2 2 1 3 1,2

cos 3 1 4 ) (

− =

r E

Conclusions

  • Nanostructures: long axis favored
  • Films: in-plane favored

2 Z d

2 1 M ez

µ =

Dipolar energy

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.16

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Basics

(Derived from slide of A. Thiaville – CNRS/Orsay)

Electronic cloud Atom nucleus (crystal structure) Spin-orbit coupling  the energy of both spin and orbital moment depends on orientation Series development on an angular basis:

...

4 2 2 1 mc + + = z z

m K m K E

Uniaxial

... ) (

2 2 2 2 2 2 4 mc + + + = x z z y y x

m m m m m m K E

Cubic

…

Anisotropy energy Alignement of magnetization is favored along given axes of the crystal Normalized magnetization components

Magnetocrystalline anisotropy energy

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.17

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Basics

+ + =>

... ) ( cos2

1 mel, mel + = θ

K E

ε i i

K B ~

mel, Result Origin Distortion of orbitals & crystal field Correction to the magneto-crystalline energy

Magneto-elastic anisotropy

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.18

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Basics
  • L. Néel,
  • J. Phys. Radium 15,

15 (1954)

« This surface energy, of the order of 0.1 to 1 erg/cm2, is liable to play a significant role in the properties of ferromagnetic materials spread in elements of dimensions smaller than 100Å »

« Superficial magnetic anisotropy and orientational superstructures »

Overview Breaking of symmetry for surface/interface atoms Correction to the magneto-crystalline energy Pair model of Néel:

  • Ks estimated from magneto-elastic constants
  • Does not depend on interface material
  • Yields order of magnitude only: correct value

from experiments or calculations (precision !)

... ) ( cos ) ( cos

4 2 S, 2 1 S, s + + = θ θ

K K E

Surface anisotropy

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.19

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Surface anisotropy

Magnetic Anisotropy Energy (MAE): Link with anisotropy of orbital moment

L B µ µ ξ α ∆ =

4 MAE Theory

  • P. Bruno,

PRB39, 865 (1989)

Perturbation theory for 3d metals:

Experiments atom / 10 4

B L µ µ

−

≈ ∆

Bulk (Fe, Ni, …)

eV 1 MAE

µ ≤

Ab initio calculations

High precision needed:

eV 10 eV 1

< < µ

  • O. Hjortstam et al., PRB55, 15026 (1997)

Conclusions

  • Origin of MAE = anisotropy of orbital moment
  • No strict linearity
  •  may also depend on thickness in thin films (band structure)

 Direct measurement of MAE preferable

L µ

does not rotate in 3d metals

  • > MAE reflects cost in ξ

Covers magnetocrystalline, magnetoelastic and surface anisotropy

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.20

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Surface anisotropy

History of surface anisotropy : STEP 1 (1/t plot)

S V tot

2 ) ( k t k t E

+ =

t 2 ) (

S V

k k t e

+ = 1/t e(t) Bulk S l

  • p

e

  • >

S u r f a c e s

First example of perpendicular anisotropy

  • U. Gradmann and J. Müller,
  • Phys. Status Solidi 27, 313 (1968)

Bulk T=2AL

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.21

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Surface anisotropy

Structural relaxation

t 2 ) (

S V

k k t e

+ =

  • W. A. Jesser et al., Phys. Stat. Sol. 19, 95 (1967)

tc

Pseudomorphic range Relaxation range (introduction of dislocation)

t t a a t

c bulk substrate

) ( ~ ) (

− ε

Effect on anisotropy

  • C. Chappert and P. Bruno., JAP64, 5736 (1988)

ε mel mel ~ B

k

Conclusion: Mixing of surface and magneto-elastic contributions

t / ) (

mel bulk

B k t k

α + = Magneto-elastic anisotropy: Strain relaxation regime:

  • U. Gradmann, Appl. Phys.3, 161 (1974)

Co/Cu(111)

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.22

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Interface anisotropy – What use?

Main use in applications : perpendicular magnetic anisotropy

Materials and geometry

Interfacial elements with large spin-orbit: Pt, Au, Pd Often: multilayers Co/Au film

  • A. Fert et al., J. Magn. Magn. Mater. 200, 338 (1999)
  • M. T. Johnson et al.,
  • Rep. Prog. Phys. 59,

1409 (1996)

Magneto-optical recording

Why: large magneto-optical response Material: 3D-Rare-Earth based

  • S. Tsunashima, J. Phys. D 34, R87 (2001)
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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.23

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Institut Néel, Grenoble, France

  • 2. Magnetic anisotropy – Interface anisotropy – What use?

Main use in applications : perpendicular magnetic anisotropy

Decreased dipolar coupling in HDD media

Longitudinal recording (1956 - ) Perpendicular recording (2005 -)

High anisotropy with low spread angle Reduced intra- and inter-grain dipolar

coupling

See lecture: Laurent RANNO

Enhanced anisotropy for solid-state memories

Concerns MRAM: Magnetic Random Access Memories

  • S. N. Piramanayagam, J. Appl. Phys. 102,

011301 (2007)

  • C. Chappert et al., The emergence of spin

electronics in data storage, Nat. Mater. 6, 813 (2007)

Hc= 2 K 0 M S1− 25kBT KV  Reminder for the thermal stability fo small flat elements:

In-plane magnetization

K=N × 1 2 0 M S

2

Issue: N is small with flat elements

Perpendicular magnetization

K≈ 1 2 0 MS

2

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.24

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Institut Néel, Grenoble, France

Views of the model systems

  • 2. Magnetic anisotropy – Interface anisotropy – from 2D to atoms

From surfaces (2D) to wires (1D) and atoms (0D)

Conclusions:

  • Model systems to highlight

trends in applied materials

  • Anisotropy per atom increases

in low dimensions

  • The TOTAL anisotropy

decreases Not thermally stable →

  • XMCD
  • Fit magnetization curves

Method Magnetic Anisotropy Energy STM, 8.5nm, 5.5K

  • P. Gambardella et al., Science 300, 1130 (2003)
  • P. Gambardella et al., Nature 416, 301 (2002)
  • Bulk Co: 40eV/atom
  • Co ML: 140eV/atom
  • Co bi-wire: 0.34meV/atom
  • Co wire: 2meV/atom
  • Co bi-atom: 3.4meV/atom
  • Co atom: 9.2meV/atom
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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.25

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Institut Néel, Grenoble, France

TABLE OF CONTENTS

  • 1. Ferromagnetic order in low dimensions
  • 2. Magnetic energy anisotropy
  • 3. Interfacial effects

Exchange bias RKKY coupling Dipolar effects

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.26

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Institut Néel, Grenoble, France

  • 3. INTERFACIAL EFFECTS – Exchange-bias

AFM FM

Meiklejohn and Bean,

  • Phys. Rev. 102, 1413 (1956),
  • Phys. Rev. 105, 904, (1957)

FC ZFC µ0HE ≈ 0.2 T

Exchange bias

  • J. Nogués and Ivan K. Schuller
  • J. Magn. Magn. Mater. 192 (1999) 203

Exchange anisotropy—a review A E Berkowitz and K Takano

  • J. Magn. Magn. Mater. 200 (1999)

Seminal studies

Oxidized Co nanoparticles

Field-cooled hysteresis loops:

  • Increased coercivity
  • Shifted in field
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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.27

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  • 3. INTERFACIAL EFFECTS – Exchange-bias: what use?

Increase coercivity of layers

AF F2 HF−AF≈HF1 K AFt AF K FtF  Crude approximation for thin layers:

Application

Concept of spin-valve in magneto- resistive elements

  • B. Diény et al., Phys. Rev. B 43, 1297 (1991)

Sensors Memory cells Etc.

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.28

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Institut Néel, Grenoble, France

  • 3. INTERFACIAL EFFECTS – RKKY interlayer coupling

J t= A t

2 sinqt

Coupling strength: ES=J tcos with: J/m

2

in

The physics

Spin-dependent quantum confinement in the spacer layer =〈m1,m2〉 =qtAB Forth & back phase shift q=k

+−k

  • r A ,A

rB,B Spin-independent Spin-dependent r A ,A ,rB,B

Figures

Constructive and destructive interferences

Maxima and minima of n

  • P. Bruno, J. Phys. Condens. Matter 11, 9403 (1999)
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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.29

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Illustration of coupling strength

  • 3. INTERFACIAL EFFECTS – RKKY interlayer coupling

J t= A t

2 sin

2t P  Note: J(t) extrapolated for t=3Å

  • S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991)
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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.30

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What use? Synthetic Ferrimagnets (SyF) – Crude description

  • 3. INTERFACIAL EFFECTS – RKKY interlayer coupling – What use? What constraints?

F2 F1 Hc=e1 M 1 Hc ,1e2 M2 H c ,2

∣e1 M 1−e2 M2∣

K=e1 K 1e2K 2 e1e2 M=∣e1 M 1−e2 M 2∣ e1e2 Hypothesis:

Two layers rigidly coupled Reversal modes unchanged Neglect dipolar coupling Increase coercivity of pinned layers Decrease intra- and inter- dot

dipolar coupling AF F1 F21 F22 Reference layer Free layer

Practical aspects

Ru spacer layer (largest effect)  Control thickness within a few

Angströms !

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Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.31

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Institut Néel, Grenoble, France

Stacked dots : orange-peel coupling

  • 3. INTERFACIAL EFFECTS – Collective effects: bilayers

Stacked dots : dipolar

In-plane magnetization Out-of-plane magnetization

Hint: An upper bound for the dipolar coupling is the self demagnetizing field

Notice: similar situation as for RKKY coupling

+ + + + +

  • +

+ + + +

In-plane magnetization Always parallel coupling Out-of-plane magnetization May be parallel or antiparallel

  • L. Néel, C. R. Acad. Sci. 255, 1676 (1962)
  • J. C. S. Kools et al., J. Appl. Phys. 85, 4466 (1999)
  • J. Moritz et al., Europhys. Lett. 65, 123 (2004)

(valid only for thick films) (valid for any films)

slide-32
SLIDE 32

Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.32

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Institut Néel, Grenoble, France

  • 3. INTERFACIAL EFFECTS – Collective effects: range of interaction

∫

≤

3 d

d 2 ) ( r r r R

π

H

Position (a.u.) Average Real

Estimation of an upper range of dipolar field in a 2D system R Local dipole: 1/r3 Integration

R R / 1 Cte ) (

d

+ ≤

H

Convergence with finite radius (typically thickness) Dipolar fields are weak and short-ranged in 2D or even lower-dimensionality systems Dipolar fields can be highly non-homogeneous in anisotropic systems like 2D Consequences on dot’s non-homogenous state, magnetization reversal, collective effects etc.

Upper bound for dipolar fields in 2D Non-homogeneity of dipolar fields in 2D

Example: flat stripe with thickness/height = 0.0125

slide-33
SLIDE 33

Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.33

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Institut Néel, Grenoble, France

Some literature

Moment and anisotropy of ultrathin films

  • U. Gradmann, Handbook of magnetic materials vol. 7,
  • K. H.K. Buschow Ed., Elsevier, Magnetism of transition

metal films, 1 (1993)

  • M. Farle, Ferromagnetic resonance of ultrathin

metallic layers, Rep. Prog. Phys. 61, 755 (1998)

  • P. Poulopoulos et al., K. Baberschke, Magnetism in

thin films, J. Phys.: Condens. Matter 11, 9495 (1999)

  • H. J. Elmers, Ferromagnetic Monolayers, Int. J. Mod.
  • Phys. B 9 (24), 3115 (1995)
  • O. Fruchart, Epitaxial self-organization: from surfaces

to magnetic materials, C. R. Phys. 6, 61 (2005)

  • O. Fruchart et al., Magnetism in reduced dimensions,
  • C. R. Phys. 6, 921 (2005)
  • M. T. Johnson et al., Magnetic anisotropy in metallic

multilayers, Rep. Prog. Phys. 59, 1409 (1996)

Perpendicular anisotropy Magneto-elasticity in thin films

  • D. Sander, The correlation between mechanical

stress and magnetic anisotropy in ultrathin films, Rep. Prog. Phys. 62, 809 (1999)

Theory (misc)

  • T. Asada et al., G. Bihlmayer, S. Handschuh, S.

Heinze, P. Kurz, S. Blügel, First-principles theory of ultrathin magnetic films, J. Phys.:

  • Condens. Matter 11, 9347 (1999)
  • F. J. Himpsel et al., Magnetic Nanostructures,
  • Adv. Phys. 47 (4), 511 (1998)
  • P. Bruno, Theory of interlayer exchange

interactions in magnetic multilayers, J. Phys.:

  • Condens. Matter 11, 9403 (1999)
  • F. E. Gabaly et al., Noble metal capping effects
  • n the spin-reorientation transitions of

Co/Ru(0001), N. J. Phys. 10, 073024 (2008)

  • J. Nogues et al., I. K. Schuller, Exchange bias, J.
  • Magn. Magn. Mater 192 (2), 203 (1999).

Exchange-bias

slide-34
SLIDE 34

Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.34

http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

Institut Néel, Grenoble, France

Online literature: http://esm.neel.cnrs.fr

slide-35
SLIDE 35

Olivier Fruchart – IWOS MASENA – Hanoi, Vietnam, Nov.2010 – p.35

http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/

Institut Néel, Grenoble, France

Charte graphique ToC →

  • 1. Introduction
  • 2. Self-assembled epitaxial growth
  • 3. Self-organized epitaxial growth
  • 4. Engineered and 3D self-organization
  • 5. Perspectives of self-organization
  • 6. X-ray investigation of SO systems
  • I. Overview of self-organization processes