Basic concepts on magnetization reversal (1) Static properties : - - PowerPoint PPT Presentation

SLIDE 1

Basic concepts

• n magnetization reversal (1)

Static properties : coherent reversal and beyond

Stanislas ROHART Laboratoire de Physique des Solides Université Paris Sud and CNRS Orsay, France

SLIDE 2

Introduction: Hysteresis loop

Manipulation of a magnetization : Application of a magnetic field

Zeeman energy : Ez=-µ0 H.MS H M Remanent Magnetization MR Coercive field HC Spontaneous Magnetization MS

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 3

Introduction: Soft and Hard materials

H M H M Hard Materials SoftMaterials Applications : Permanent magnets, motors, magnetic recording Ex: Cobalt, NdFeB, CoSm, Garnets Applications : Transformer, flux guide (for electromagnets…), magnetic shielding Ex : Iron, FeCo, Permalloy (Fe20Ni80)

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 4

Introduction: Energies in magnetic systems

Exchange energy Magnetocrystalline anisotropy energy Zeeman energy Dipolar energy

( )

2

θ ∇ = − = A S S J E

j i ex

r r

≠

( )

2

.e m K EMC r r =

(simplest form, may be more complicated) reflects the cristal symmetry

H M EZ r r . µ − =

j ij i ij ij ij i D

m r m r r r m E r r r r r . ) . ( 3 4

3 5

        − − = π µ

For practical use : shape anisotropy

M N M H M E

d D

r r r r ] .[ 2 1 . 2 1 µ µ − = − =

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 5

Introduction: Micromagnetism: Typical Length Scales

Bloch wall

• > Anisotropy vs. Exchange

( )

θ θ

2 2

sin K dx d A E + =

Bloch wall parameter Bloch wall width Bloch wall energy

K A

B =

δ K A dB π = AK

B

4 = σ

Typical value : 2-3 nm (hard)

• > 100-1000 nm (soft)

Exchange length

• > Dipolar coupling vs. Exchange

Λ 6 . 2 ~

2

2

S

M A µ = Λ

Typical value : 5-10 nm Ex : Magnetic vortex

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

Quality factor ( )

2 2

2 δ µ Λ = =

S

M K Q

1 1 << > Q Q

hard soft

SLIDE 6

Introduction: Magnetic Domains

Bulk materials Mesoscopic scale Nanometric scale Complex magnetic paterns Self organization of domains Small number of possible configuration. Well defined states Magnetic single domain but non collinearities are still possible True collinear state at very reduced dimensions (< few Λ)

Cowburn et al. PRL 81, 5414 (1998) Cowburn J.Phys.D: Appl. Phys. 33, R1 (2000)

(square dots – 500 nm)

• Except at very small scales, dipolar energy plays an

essential role [competition between dipolar energy (long range) and domain wall energy (local)].

• Single domain state is observed well below 1 µm or for

hard material .

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

120 µm 130 µm

SLIDE 7

Contents

I. Coherent reversal

• II. Magnetization reversal in nanostructures
• III. Domain nucleation and domain wall

propagation

• IV. Conclusion
• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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SLIDE 8

Coherent reversal: Macrospin hypothesis

Hypothesis : m(r)=cte=M (strong approximation)

H M M G E r r r . ) ( µ − =

Exchange energy is constant Dipolar energy equivalent to anisotropy energy Simplest model : Stoner and Wohlfarth

) cos( sin

2 H S eff

H M K E θ θ µ θ + − =

d mc eff

k K K + =

Anisotropy field :

S eff K

M K H / 2 µ =

Dimensionless equation :

) cos( 2 sin2

H

h e θ θ θ + − =

Easy axis

M

H θ θ θ θ θ θ θ θΗ

Η Η Η

Different names : Uniform rotation, coherent rotation, macrospin, Stoner and Wohlfarth model…

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 9

• 4
• 2

2 4

e

θ

−π/2 π/2 π 3π/2

• 4
• 2

2 4

e

θ

−π/2 π/2 π 3π/2

• 4
• 2

2 4

e

θ

−π/2 π/2 π 3π/2

• 4
• 2

2 4

e

θ

−π/2 π/2 π 3π/2

• 4
• 2

2 4

e

ϕ

−π/2 π/2 π 3π/2

• 4
• 2

2 4

e

θ

−π/2 π/2 π 3π/2

>0

Coherent reversal: Equilibrium states and switching

=

H

θ

(Field aligned with the anisotropy axis)

) (cos sin 2 cos 2 sin2 h e h e + = ∂ ∂ − = θ θ θ θ θ π θ θ θ θ θ θ

• r

h e

m

: sin : cos = = = − = ⇒ = ∂ ∂

Stability

θ θ θ θ θ θ cos 2 2 cos 4 cos 2 cos 2 sin 2

2 2 2 2 2

h h e + − = + + − = ∂ ∂ ) 1 ( 2 ) ( ) 1 ( 2 ) ( ) 1 ( 2 ) (

2 2 2 2 2 2 2

h e h e h e

m

− = ∂ ∂ > − = ∂ ∂ + = ∂ ∂ π θ θ θ θ

h = 2 h = 1 h = 0 h = -0.5 h = -1 h = -2 >0 >0 <0

• 2
• 1

1 2

• 1.0
• 0.5

0.0 0.5 1.0

m=M/MS h

Square hysteresis loop Hswitch = HK

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 10

Coherent reversal: Equilibrium states

θ θ cos 2 sin2 h e − =

• 2
• 1

1 2

• 1.0
• 0.5

0.0 0.5 1.0

m=M/MS h

• Square hysteresis loop
• >Hswitch = HK

Energy barrier

( ) (

) ( )

2 2 2

1 2 2 1 ) ( ) ( h h h h e e e

m

+ = − − + − = − = ∆ ϕ

For arbitrary angle :

• no analytical solution
• HK/2<Hswitch<HK
• ∆e=(1-h)α with α=1.5

Important for thermally activated switching

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 11

Coherent reversal: Hysteresis Loops

) cos( 2 sin2

H

h e θ θ θ + − =

• 2
• 1

1 2

• 1.0
• 0.5

0.0 0.5 1.0

m h

θ = 0

• 2.0 -1.5 -1.0 -0.5

0.0 0.5 1.0 1.5 2.0

• 1.0
• 0.5

0.0 0.5 1.0

m

h

θΗ = π/3

• 4
• 2

2 4

e

ϕ

−π/2 0

π/2 π 3π/2

• 4
• 2

2 4

e

ϕ

−π/2 0

π/2 π 3π/2

• 4
• 2

2 4

e

ϕ

−π/2 0 π/2 π 3π/2

• 4
• 2

2 4

e

ϕ

−π/2 π/2 π 3π/2

HC Hswitch Switching field (or reversal field)

• > abrupt jump of magnetization angle

Coercive field : M.H = 0

• > may not be equal to the switching field

Hswitch=HC

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 12

0.0 0.5 1.0 30 60 90 120 150 180 210 240 270 300 330 0.0 0.5 1.0 0.0 0.5 1.0 30 60 90 120 150 180 210 240 270 300 330 0.0 0.5 1.0

Coherent reversal: Switching field plot : astroids

Astroid curve : Polar plot of Hswitch

( )

2 / 3 3 / 2 3 / 2

cos sin

H H K switch

H H θ θ + =

] [ @ 4 3 ; 4 2 sin 2 1 ] [ @ 4 ; 4 π π π θ θ π π π θ       ∈      − ∈ =

H H H switch C

if if H H

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

J.C. Slonczewski (1956)

SLIDE 13

Coherent reversal: Switching field plot : astroids

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.5

0.0 0.5 1.0

hy hx

( )

θ θ sin , cos . 2 ) ( = − = m m h m G e r r r r

Equilibrim condition

. 2 ) ( ' = − = e h m G d de r r r θ

with

( )

θ θ cos , sin − = e v

• > For given m : Straight line in the field space, tangente

to the critial astroid curve, directed along m Stability condition

. 2 ) ( " ² ² > + = m h m G d e d r r r θ

• >For given m : Only one part of the line is stable

2 stable states 1 stable state

J.C. Slonczewski Research Memo RM 003.111.224, IBM Research Center (1956)

• A. Thiaville JMMM 182, 5, (1998)

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

Easy axis Hard axis

SLIDE 14

Coherent reversal: Switching field plot : astroids

• > To go further :
• Complex type of anisotropy

θ θ ² cos ² sin = G ) 6 / ²( sin ² cos ² sin π θ θ θ + + = G

(Cubic anisotropy) (Cubic anisotropy + uniaxial)

• Three dimensionnal extension

Thiaville PRB 61, 12221 (2000) Thiaville JMMM 182, 5, (1998)

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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SLIDE 15

Coherent reversal: Experimental relevance

First observation (2D) : Co (D = 25 nm) cluster Wernsdorder et al. PRL 78, 1791 (1997) In 3 D: (same Co cluster) E. Bonnet et al PRL 83, 4188 (1999) 3 nm Co cluster : M. Jamet et al PRL 86, 4676 (2001)

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 16

Coherent reversal: Experimental relevance

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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In technological application : memory cells Measurements of the astroids of elliptical M-RAM cells

(Dimensions in µm)

Conclusion : Good agreement with coherent rotation only for smallest elements. ⇒Apply coherent reversal with great care! ⇒In most systems Hswitch<<HK «Brown’s paradox» Sun et al. APL 78, 4004 (2001)

SLIDE 17

Magnetization reversal in nanoparticles

• Is the coherent reversal model applicable to

nanoparticles?

• Is a uniform magnetized ground state

sufficient for coherent magnetization reversal?

• Can we go further than coherent

magnetization reversal?

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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SLIDE 18

Nanoparticles: Phase diagram of nanostructures

• 1. Single domain ground-state criterion
• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Single domain state

• Exchange energy is minimum
• Anisotropy energy is minimum

(magnetization along easy axis)

• Dipolar energy :

3 2 2

3 4 6 1 2 R M M NV E

S S SD d

π µ µ × = =

DW DW d SD d SD

E E E R + = ⇔

2

36

S SD

M AK R µ =

• Bloch domain wall at the

centre -> exchange and anisotropy cost :

• Dipolar energy gain : magnetic flux

is closed in two domains:

AK R R E

BW DW 2 2

4π σ π = = 2 /

SD d DW d

E E =

Non uniform state : 1 domain wall

!

Domain wall width is neglected

• > calculation adapted for high

anisotropy materials

SLIDE 19

θa θb θa θb

Nanoparticles: Phase diagram of nanostructures

• 2. Coherent/Incoherent rotation criterion
• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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• Schematic calculation : coherent rotation vs. 2 domain rotation

Hypothesis : 2 localized moments at

2 /

/

R x

b a

± = 2 /

/

V M m

S b a

=

( ) ( )(

)

b a S b a S

H M K M R A V E

2 2 2 2 2

2 4 1 24 1 θ θ µ θ θ µ + − + −       − =

Stability analysis : diagonalize the 2x2 matrix and find H that changes the sign of one eigenvalue

        ∂ ∂ ∂

j i

E θ θ

2

The two eigenmodes are :

K coh b a

H H = ⇒ =θ θ

2

8 3 R M A M H H

S S K incoh b a

µ θ θ + − = ⇒ − =

(coherent rotation)

incoh incoh H

H <

if

2

24

S

M A R µ >

Remarks :

SD coh R

R <

for real materials anisotropy does not enter in the criterion

SLIDE 20

Nanoparticles: Phase diagram of nanostructures

• 2. Coherent rotation criterion
• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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( ) ( )(

)

b a S b a S

H M K M R A V E

2 2 2 2 2

2 4 1 24 1 θ θ µ θ θ µ + − + −       − =

Exchange : the two moments are distant of R and the angle variation is ∆=θa-θb. The exchange energy density is A(dm/dx)²~A(θa-θb)²/R² Dipolar energy : if θa=θb, the dipolar energy is µ0MS²/6. If the two angles are different, the total magnetization is lower so that Ed decreases by

• [µ0MS²/6]cos(θa-θb)/2~ -[µ0MS²/24](θa-θb)²

Anisotropy energy : each hemisphere of volume V/2 has the anisotropy energy K[sin²θ]*V/2~2Kθ²V/4 Zeeman energy : each hemisphere of volume V/2 has the Zeeman energy

• µ0MSH[cosθ]*V/2~ -µ0MSHθ²*V/4

SLIDE 21

Real reversal mechanisms : Coherent Curling, Buckling

Nanoparticles: Phase diagram of nanostructures

• 2. Coherent/Incoherent rotation criterion
• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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For curling :

2

67 . 8 3 R M A M H H

S S K sw

µ + − =

2

26

S crit

M A R µ =

See: Aharoni Introduction to the theory of Ferromagnetism (1996) Skomski and Coey Permanent Magnetism (1999)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

HSW/HK R/Rcoh

Incoherent Reversal Coherent Reversal

SLIDE 22

Nanoparticles: Phase diagram of nanostructures

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Phase diagram for a flat disk with surface anisotropy Keff = KS/t Skomski et al. PRB 58, 3223 (1998)

SLIDE 23

Nanoparticles : Influence of nanostructure inhomogeneity

Dipolar field effect

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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• > Soft elements: flux closure domains faciliate magnetic reversal

Uhlig and Shi APL 84, 759 (2004)

cte W t M H Oe H

S C K

+ = = 3 5000

Shape anisotropy ~ MS L/W but switching field intependant of L

SLIDE 24

Nanoparticles : Influence of nanostructure inhomogeneity

Dipolar field effect

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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• > Soft elements

SLIDE 25

Nanoparticles : Influence of nanostructure inhomogeneity

Edge and surface anisotropy in very small elements

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Origin : enhanced magnetic anisotropy at low coordinated atoms Gambardella et al. Science 300, 1130 (2003) Jamet et al. PRL 86, 4676 (2001) Co islands on Pt(111) Nearly spherical Co cluster Néel pair anisotropy model

∑

> <

=

. . , 2

) . (

n n j i ij a

u m L E r r

On spherical clusters, atom anisotropy axis are perpendicular to the local surface

• > Hedgehog like orientation of anisotropy axis

Kachkachi and Dimian PRB 66,174419 (2002) Néel J. Phys. Radium 15, 225 (1954)

SLIDE 26

Nanoparticles : Influence of nanostructure inhomogeneity

Edge and surface anisotropy in very small elements

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Consequence of surface anisotropy axis distribution Non colinear magnetic configuration Atomic simulation : L/J=2 (unphysically strong surface anisotropy!) 1 particle assembly of many coupled spins h mz J ~ Ksurface >> Kvolume h mz J >> Ksurface = Kvolume 1 particle 1 macrospin Kachkachi and Dimian PRB 66,174419 (2002) Garanin and Kachkachi PRL 90 065504 (2003)

SLIDE 27

Nanoparticles : Influence of nanostructure inhomogeneity

Edge and surface anisotropy in very small elements

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.5

0.0 0.5 1.0

HZ/HK HX/HK

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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0.7155 0.7500 0.7845 0.8190 0.8535

mZ Y (u.a.) X (u.a.)

Typical astroid with a 4th order anisotropy

Rohart et al. PRB 76, 104401 (2007) Garanin and Kachkachi PRL 90 065504 (2003)

Example: flat disk with edge anisotropy

Twisted inhomogeneous configuration

Exchange Shape anisotropy (in plane) Edge anisotropy (out of plane)

Effective anisotropy model

SLIDE 28

Nanoparticles: Vortices

⇒Strongly inhomogeneous magnetic state Cowburn et al. PRL 83, 1042 (1999) Wachowiak et al. Science 298 577 (2002) Four degenerated states :

• vortex cirulation (clock wise vs. Counter clock wise)
• > difficult to manipulate with magnetic field
• Vortex core (up vs. Down) -> easily coupled to magnetic field

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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SLIDE 29

Nanoparticles: Vortices

Cowburn et al. PRL 83, 1042 (1999) Guslienko and Metlov PRB 63, 100403R (2001)

Stable vortex state Stable uniform state

The energy cost to expell the vortex core

• ut of the disk creates an hysteresis

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Hysteresis loop with IN PLANE magnetic field

SLIDE 30

Nanoparticles: Vortices

Shinjo et al. Science 289, 930 (2000)

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Normal vortex state : magnetization is perpendicular to minimize exchange energy Vortex with Bloch point: magnetic moment are all almost in plane, mean magnetization is zero at the core

AR d drd r r E E r A r E

ex BP ex

π ϕ θ θ 8 sin ) ( / 2 ) (

2

∫∫∫

= = =

Beyond micromagnetism

Thiaville et al. PRB 67, 094410 (2003) Images from R. Dittrich http://magnet.atp.tuwien.ac.at/gallery/bloch_point/index.html

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

Vortex core magnetization reversal Magnetic field is coupled to the vortex core only but coherent reversal of vortex core magnetization is topologically impossible

SLIDE 31

Nanoparticles: Vortices

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Thiaville et al. PRB 67, 094410 (2003) Images from R. Dittrich http://magnet.atp.tuwien.ac.at/gallery/bloch_point/index.html Experiments : Okuno et al. JMMM 240, 1 (2006)

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

Vortex core magnetization reversal

SLIDE 32

Magnetization reversal in thin films

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Is the macrospin model relevant for thin films ?

• Lateral dimension >> Micromagnetic lengthes
• Experimental observation : HC<<HK in most systems

⇒Coherent reversal is unreallistic : need for micromagnetic modelling. ⇒Defect (even at very low density) may drive the switching field if domain wall propagation is involved

Brown’s paradox

SLIDE 33

Thin Films: Hard axis hysteresis loops

In some cases, coherent reversal can be applied to hard axis hysteresis loops H M H M 2K/µ0MS MS

• In hard axis loop, domain nucleation is

prevented (the two orientation energies are the same) and coherent rotation is possible. => Application: determination of magnetic anisotropy and MS Example1: Soft magnetic film Permalloy thin film

• no magnetocristalline anisotropy
• in plane magnetization due to the shape

anisotropy => Loop with perpendicular field yields a saturation field of MS

2 2 1 S d

M E µ =

Example2: « Anisometry » Ga(Mn)As thin film (with perpendicular magnetization)

• Polar Kerr effect measurment

with quasi in plane field (α)

( )

θ α θ θ cos ; cos 2 sin

s S eff

M M M K H = + =

MScos(α) MS -> Keff = 272 mT

J.P. Adam PhD. Thesis 2008

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Principle/Application: Grolier et al. J. Appl. Phys. 73, 5939 (1993)

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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SLIDE 34

Thin Films: Brown’s paradox

Origin of the lower coercivity : magnetic defects, temperature

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 35

Thin Films: Nucleation vs. Propagation

First magnetization curve indicates the type of coercivity H M Nucleation limited reversal

• > Need few nucleation event

followed by domain wall propagation

• > Provides generally square

loops Pinning center Propagation limited reversal

• > Need many nucleation events
• > Provides generally rounded loops

Ex : Recording media Magnetization reversal is controlled by the micro/nanostructure

• >Soft inclusion, misoriented grains…

create nucleation centers

• >Hard inclusion,crystalline defect…

create pinning centers

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• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

European School on Magnetism - Targosite 2011

SLIDE 36

Switching field of a Co(1 nm) film grown on Au(233)

• > In plane magnetization with

well defined in plane anisotropy (step edges)

• G. Baudot PhD. Thesis,

unpublished (2003)

Thin Films: Nucleation – « 1/cos θΗ law »

36

Nucleation of a reversed domain on defect -> Nucleation volume Nucleation cost (domain wall, anisotropy energy ) is compensated by Zeeman energy gain (plus thermal energy)

E

If : M is aligned with easy axis

H S z

vH M E θ µ cos 2 − = ∆

K c

H H <<

( )

H C H C z

H

H H kT E E θ θ

θ

cos 25

, =

= ⇒ − = ∆

Magnetization reversal if

Kondorsky, J. Exp. Theor. Fiz. 10, 420 (1940) See also : Givord JMMM 72, 247 (1988)

M H θH

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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3

δ ≈ v

• for bulk hard magnets Givord et al. JMMM 258, 1 (2003)
• Droplet theory for thin films Barbara JMMM 129, 79 (1994)

SLIDE 37

Thin Films: Nucleation vs. DW propagation Importance of dynamics

• S. ROHART : Basic Concepts on Magnetization Reversal : Static Properties

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Key ingredient :

• > Nucleation rate
• > Domain wall propagation dynamics

Coercive field may not be an intrinsic property (ie. only linked to micromagnetic parameters)

• > depend on temperature
• > depend on sweeping rate

See second part of the lecture

• n temperature activation and

slow dynamics Pt/Co/Pt (From J. Vogel)

SLIDE 38

Some readings

• Fruchart and Thiaville Magnetism in reduced dimensions CR Physique 6 921 (2005)

Some readings

• Skomski and Coey Permanent magnetism (Taylor & Francis Group 1999)
• Hubert and Schäfer Magnetic domains (Springer 1999)
• Aharoni Introduction to the theory of ferromagnetism (Oxford 1996)
• Skomski Nanomagnetics J. Phys. Cond. Mat. 15, R841 (2003)
• Fiorani Surface effects in Magnetic Nanoparticles (Springer 2005)
• Fruchart and Thiaville Magnetism in reduced dimensions CR Physique 6 921 (2005)

To go further

• Temperature influence and slow dynamics
• Precessionnal magnetization reversal (ns time scale, need loweer magnetic fields)
• Ultra fast magnetization reversal (beyond micromagnetism hypothesis M=cte)
• New driving forces for magnetization reversal (spin polarized currents, electrical field…)

Take home messages

• Coherent (uniform) magnetization reversal only takes place in very small particles
• Micromagnetism is powerfull to determine the switching mode in nanoparticles
• In thin films: Importance of micro/nano structure of magnetic films to determine the

reversal mechanism

• Coercive field may be ambiguous (different from switching field, not intrinsic…)

Conclusion

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