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Simple concepts of magnetization reversal --------------- II. - - PowerPoint PPT Presentation

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Simple concepts of magnetization reversal --------------- II. Non-single-domain effects: Interactions, nanostructures and domain walls Olivier Fruchart Institut Nel (CNRS-UJF-INPG) Grenoble - France http://neel.cnrs.fr Institut Nel,

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SLIDE 1

Institut Néel, Grenoble Institut Néel, Grenoble, France , France. .

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

Simple concepts of magnetization reversal

  • II. Non-single-domain effects:

Interactions, nanostructures and domain walls

Olivier Fruchart

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

http://neel.cnrs.fr

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SLIDE 2

Institut Néel, Grenoble Institut Néel, Grenoble, France , France. .

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

Was your head whirling?

Recas, Sep7th 2009

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SLIDE 3

Institut Néel, Grenoble Institut Néel, Grenoble, France , France. .

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

Chamois, nearby Grenoble

June 1st, 2008

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SLIDE 4

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.4

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – General table of content

  • 1. Dipolar energy
  • 2. Coercivity in patterned elements
  • 3. Manipulation of domain walls
  • 4. Interfacial effects
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SLIDE 5

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.5

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Dipolar energy

  • 1. Treatment of dipolar energy
  • 2. Some consequences of dipolar energy on hysteresis loops
  • 3. Dipolar energy and collective effcts in assemblies

I.1. Dipolar energy

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SLIDE 6

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.6

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Origins of magnetic energy

2 2 1 2 , 1 Ech

) ( .      A J E S S ) ( sin 2

mc

 K E 

H M .

S Z

   E

1 2 d S d

. 2 1 H M    E

Zeeman energy (enthalpy) Magnetocrystalline anisotropy energy Dipolar energy Echange energy

Hext M

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SLIDE 7

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.7

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Magnetization NON-SINGLE DOMAIN EFFECTS – Notations

                     

z y x z y x

m m m M M M M

s

M 1

2 2 2

  

z y x

m m m

Magnetization vector M Can vary in time and space. Mean-field approach possible: Ms=Ms(T) Modulus is constant (hypothesis in micromagnetism)

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Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.8

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Treatment of dipolar energy (1/3)

) ( ). ( ) (

d 2 1 d

r H r M r    E

Density of dipolar energy



   

space 3 3 s d

' d ' 4 ) ' )].( ' ( [ div ) ( r M r r r r r m r H  H curl  ) (

d

) ( div ) ( div

d

M H  

By definition . As we have (analogy with electrostatics):

] ) ( div[

  • )

(

s

r m r M  

is called the volume density of magnetic charges To lift the divergence that may arise at sample boundaries a volume integration around the boundaries yields:

              

 

sample 2 3 space 3 3 s d

' d ' 4 ) ' )].( ' ( ). ' ( [ ' d ' 4 ) ' )].( ' ( [ div ) ( r r M r r r r r n r m r r r r r m r H   ) ( . ) ( ) (

s

r n r m r M  

is called the surface density of magnetic charges, where n(r) is the outgoing unit vector at boundaries Do not forget boundaries between samples with different Ms

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Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.9

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Treatment of dipolar energy (2/3) Some ways to handle dipolar energy



 

sample d 2 1

d . V M.H  E

 

  

space 2 d 2 1 sample d 2 1

d . d . V V H M.H   E

Notice: six-fold integral over space: non-linear, long-range, time-consuming. Bottle-neck of micromagnetic calculations Integrated dipolar energy: Usefull theorem for finite samples:

E is always positive Significance of (BHmax) for permanent magnets

  

    

sample \ space 2 d 2 1 sample d 2 1 sample d d 2 1

d . d . d . ) ( V V V H B.H .H H M   

Energy available outside the sample, ie usefull for devices Cf: M. Coey

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SLIDE 10

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.10

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Treatment of dipolar energy (3/3)

+ + + +

  • -

+ + + + + + + + + + + + + + + + + + + + + +

  • + + +

x

Examples of magnetic charges

Notice: no charges and E=0 for infinite cylinder + + + + + + + + +

  • Charges on

surfaces Surface and volume charges

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SLIDE 11

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.11

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Demagnetizing coefficients (1/3)

 

     

sample 2 3 s sample 2 3 s d

' d ' 4 ) ' ).( ' ( ' d ' 4 ) ' )].( ' ( . [ ) ( r n m M r M

i i

r r r r r r r r r r n m r H  

 

i i z y x

m M m m m M r u z y x M M

s s

) (     

    

         

sample 2 3 sample 3 d sample 2 3 sample 3 2 s 2 1 sample 3 d 2 1 d

' d ' 4 ) ' ).( ' ( d ' d ' 4 )] ' .( ).[ ' ( d d . ). ( r r r r r r r r r r m r r r M r H    

j j i j i i i

r r n m m K n m M E m N m . .

d d d

V K m m VN K

j i ij

  E

Assume uniform magnetization

See more detailed approach: M. Beleggia and M. De Graef, J. Magn. Magn. Mater. 263, L1-9 (2003)

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SLIDE 12

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.12

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Demagnetizing coefficients (2/3)

m N m . .

d d d t j i ij

K m m N K   E

N is a positive second-order tensor

          

z y x

N N N N m N r H . ) (

s d

M   

i

N M H

s i d,

) (    r 1   

z y x

N N N ) (

2 2 2 d d z z y y x x

m N m N m N K    E

What with ellipsoids???

Self-consistency: the magnetization must be at equilibrium and therefore fulfill m//Heff Assuming Happlied and Ha are uniform, this requires Hd(r) is uniform. This is satisfied

  • nly in volumes limited by polynomial surfaces of order 2 or less:

slabs, cylinders, ellisoids (+paraboloïds and hyperboloïds).

  • J. C. Maxwell, Clarendon 2, 66-73 (1872)

…and can be defined and diagonalized for any sample shape

Valid along main axes only!

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SLIDE 13

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.13

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Demagnetizing coefficients (3/3)

     d ) )( )( ( ) (

1 2 2 2 2 2 1  

           c b a a abc Nx                      1 1 sinh A 1 1 1

2 2 2 2

    

x

N

For prolate revolution ellipsoid: (a,c,c) with =c/a<1

                          1 sin A 1 1 1 1

2 2 2 2 x

N

For oblate revolution ellipsoid: (a,c,c) with =c/a>1

  • J. A. Osborn, Phys. Rev. 67, 351 (1945).

General ellipsoid: main axes (a,c,c)

) 1 (

2 1 x z y

N N N    ) /( ); /( ; c b b N c b c N N

z y x

    

For a cylinder along x For prisms, see: More general forms, FFT approach:

  • A. Aharoni, J. Appl. Phys. 83, 3432 (1998)
  • M. Beleggia et al., J. Magn. Magn. Mater. 263, L1-9 (2003)

Ellipsoids Cylinders

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SLIDE 14

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.14

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Dipolar energy and hard-axis loops (1/2) Magnetization loop of a macrospin along a hard axis

) sin( 2 ) ( sin2   h e  

d s a a

/ 2 . K N K M K H H h H

i

   

H  M H

) cos( 2 ) ( sin2

H

h e       2 /   

H

 

h e        sin cos 2

h

u m. ) cos( sin    

H

h    Hard axis: Dipolar energy: Equilibrium position

Ha

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SLIDE 15

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.15

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Dipolar energy and hard-axis loops (2/2) Case of a bulk soft magnetic material

Hypotheses:

  • 1. Use an ellipsoid, cylinder or slab along a main direction

so that the demagnetizing field may be homogeneous.

  • 2. Domains can be created to yield a uniform and effective magnetization Meff

ext eff 2 eff 2 1 Z d tot

H N E E E M M      

ext eff eff tot

H N E       M M

ext eff

1 H N   M

Density of energy: Minimization:

Ha

Susceptibility is constant and equal to 1/N Conclusion for soft magnetic materials

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SLIDE 16

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.16

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Easy axis, coercitive Ideally soft NON-SINGLE DOMAIN EFFECTS – Compensation of dipolar energy in loops (1/4)

Ha

N=0 (slab, infinite cylinder) N>0 (here N=1: slab, perpendicular) N=0 (slab, infinite cylinder) N>0 (here N=1: slab, perpendicular)

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SLIDE 17

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.17

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Compensation of dipolar energy in loops (2/4)

1. Measure a hysteresis loop M1(Happl) 2. Internal field during loop: Hd=-Ni.M1 (must be corrected to access intrinsic properties) 3. Plot M1(Happl-NiM1) M2(Htot)

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SLIDE 18

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.18

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Compensation of dipolar energy in loops (3/4)

+

  • +

+ +

+ + + + + +

  • Ha=Ms

M +

  • Ha=Ms/3
  • 1. The concept of effective magnetization fails, because grains are either up or down.
  • 2. Individual grains have a shape, implying a demagnetizing field that must be taken

into account

  • 3. In heteromaterials (ex: hard-soft; magnetic/non-magnetic etc.) the magnetization of

both phases has to be taken into account. Depends also on grain size…

Specific aspects in hard magnetic materials

Lorentz cavity

Example with cubic grains The field felt in the grain if it tries to reverse is -2Ms/3, not –Ms. The loop is overcompensated if N=1 is used.

See: D. Givord et al.

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SLIDE 19

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.19

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Compensation of dipolar energy in loops (4/4) Specific aspects to systems with non-ellipsoidal shapes

  • +

+ +

M

In a non-ellipsoidal (or cylindrical, slab) system the demagnetizing field is not homogeneous in magnitude nor direction

Ha

2 s 2 1 ext d

s

d NM M H E

M

    

  • 1. Initial slope higher than 1/N

(demag field smaller than average)

  • 2. Late slope smaller than 1/N

(demag field larger than average) Demagnetizing energy (thus area above loop) is identical

In a non-ellipsoidal sample (or cylinder, slab) the loop is overcompensated at low magnetization and undercompensated at high field, even for soft magnetic materials. This effect adds up to the previous effect of grain shape

  • P. O. Jubert, O. Fruchart et al., Europhys. Lett. 63, 102-108 (2003)

Cf: O. Chubykalo

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SLIDE 20

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.20

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: range of interaction

3 d

d 2 ) ( r r r R  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

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SLIDE 21

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.21

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Stacked dots : orange-peel coupling NON-SINGLE DOMAIN 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)

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SLIDE 22

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.22

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models of dipolar energy

  • R. Álvarez-SÁnchez at el., Analytical model for shape anisotropy in thin-film

nanostructured arrays: Interaction effects, J. Magn. Magn. Mater. 307, 171-177 (2006)

Models for arrays of single-domain planar rectangular dots

  • E. Y. Tsymbal, Theory of magnetostatic coupling in thin-film rectangular magnetic

elements, Appl. Phys. Lett. 77, 2740 (2000)

Models for arrays of elements of arbitrary shapes

  • N. Mikuszeit, E. Y. Vedmedenko & H. P. Oepen, Multipole interaction of polarized single-

domain particles, J. Phys. Condens. Matter 16, 9037-9045 (2005) E.Y. Vedmedenko, N. Mikuszeit, H. P. Oepen and R. Wiesendanger, Multipolar Ordering and Magnetization Reversal in Two-Dimensional Nanomagnet Arrays, Phys. Rev. Lett. 95, 207202 (2005)

  • M. Beleggia and M. De Graef, On the computation of the demagnetization tensor field for

an arbitrary particle shape using a Fourier space approach, J. Magn. Magn. Mater. 263, L1-9 (2003)

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SLIDE 23

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.23

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops

Hext M

Expected hysteresis loop for macrospins

M Hext

Hysteresis for assemblies of dots

Possible effects that may arise

  • Distribution of coercive fields
  • (Dipolar) interactions
  • The loops of the macrospins are slanted
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SLIDE 24

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.24

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops Distribution of properties

le irreversib r)

( dH dm H  

Hext M Reversible Irreversible

Effect of distributions and dipolar interactions are sometimes difficult to disentangle

Hc(T) for a given population of the distribution can be studied at a given stage of the reversal (10%, 20% etc.)

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SLIDE 25

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.25

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 B (T)

  • 185 mT
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 B (T)

  • 15 mT

Minor loops: negative interactions Minor loops: negligible interactions

  • 0.1
  • 0.05

0.05 0.1 B (T)

  • 50 mT
  • 0.1
  • 0.05

0.05 0.1 B (T)

  • 17 mT
  • O. Fruchart et al., unpublished

Example: dipolar interactions in arrays of Co/Au(111) pillars

  • Faster than Henkel and Preisach
  • Other applications:

characterization of exchange bias

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SLIDE 26

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.26

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 50 100 150 200 250 300 y = 0.042584 + 0.00030788x R= 0.96311 T(K)

 

kT NH μ μ m / B

eff. Co ½

 m M r H H

s eff.

 

T N μ k r M μ χ dm H μ d

Co

S

1 ) (    

a + b . T

  • Brillouin 1/2 function
  • Effective field
  • First order expansion:

susceptibility

1/χ

(T)

(Demagnetizing dipolar interactions)

  • O. Fruchart et al., PRL 23, 2769 (1999)

Superparamagnetic regime: plot of inverse susceptibility

  • No need of hysteresis
  • Analogy with Curie-Weiss law
slide-27
SLIDE 27

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.27

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops Henkel plots

  • O. Henkel,
  • Phys. Stat. Sol. 7, 919 (1964)
  • S. Thamm et al.,

JMMM184, 245 (1998)

 

) ( 2 1 ) ( ) (

r d

x M x M x M H    

Measure of dipolar interactions

  • The analysis of interactions on qualitative
  • Long experiments (ac demagnetization)
slide-28
SLIDE 28

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.28

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Solving NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops Preisach model

  • G. Biorci et al., Il Nuov. Cim. VII, 829 (1958)
  • I. D. Mayergoyz, Mathematical models of

hysteresis, Springer (1991)

b a

 Distribution function  No true link between real particles and 

      with ) , ( ' ' 2 1 ) ' , ' (

' , ' 2

    

 

    f

Hext M

b’ a’

  • Long experiments (1D set of hysteresis curves)
  • Better suited to bulk materials

with strong interactions

slide-29
SLIDE 29

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.29

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Archetype for AF coupling NON-SINGLE DOMAIN EFFECTS – Collective effects: models based on loops

  • S. Bedanta & W. Kleemann,

Supermagnetism, J. Phys. D: Appl. Phys., 013001 (2009)

Interactions between (suparamagnetic) particles

Cf O. Chubykalo: 'Negative' or 'Positive' interactions? Smaller or larger energy barriers? Archetype for ferro coupling

  • R. P. Cowburn, PRB65, 092409 (2002)
  • R. P. Cowburn et al., New J. Phys. 1, 1-9 (1999)

Conclusion: Interactions may decrease or increase the switching field, as well as increase energy barriers

slide-30
SLIDE 30

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.30

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Patterned elements TOC

  • 1. Near-single domain structures
  • 2. Flux-closure domains
  • 3. Conclusion on characteristic length scales

II.2. Coercivity in patterned elements

slide-31
SLIDE 31

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.31

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Configurational anisotropy (1/2)

 

2 2 2 d

2 1

z z y y x x

M N M N M N E     Strictly speaking, ‘shape anisotropy’ is of second order:

2 d tot

sin VK E 

2D: In real samples magnetization is never perfectly uniform: competition between exchange and dipolar

Num.Calc. (100nm)

 Higher order contributions to the anisotropy

Configurational anisotropy: deviations from single-domain

Flower state Leaf state c/a>2.7 c/a<2.7

  • M. A. Schabes et al., JAP 64, 1347 (1988)

R.P. Cowburn et al., APL 72, 2041 (1998)

Configurational anisotropy may be used to stabilize configurations against switching

slide-32
SLIDE 32

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.32

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Configurational anisotropy (2/2)

500 Oe 400 Oe 300 Oe 200 Oe

Color code: strength of anisotropy in a given direction Radius: size of measured pattern Direction: direction of measurement

R.P. Cowburn, J.Phys.D:Appl.Phys.33, R1–R16 (2000)

Polar plot of experimental configurational anisotropy with various symmetry

4-fold 6-fold 10-fold

Théorie, expérience, et implications sur Hc

2 10 4 6 

slide-33
SLIDE 33

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.33

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – C and S states (1/2)

’

 At least 8 nearly-equivalent ground-states for a rectangular dot  Issue for the reproductibility of magnetization reversal ‘C’ state ‘S’ state

slide-34
SLIDE 34

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.34

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Preparation of ‘C’ state NON-SINGLE DOMAIN EFFECTS – C and S states (2/2) Preparation of ‘S’ state

Longitudinal field to reverse the magnetization Transverse field to keep end domains aligned parallel to each other End domains aligned mainly antiparallel owing to a dipolar shape effect

Avoid the formation of 180° domain walls during magnetization reversal Purpose

slide-35
SLIDE 35

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.35

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Hc ~Ms * Thickness Hc ~1/Width NON-SINGLE DOMAIN EFFECTS – Coercivity of stripes

  • W. C. Uhlig & J. Shi,
  • Appl. Phys. Lett. 84, 759 (2004)

W t M a H

S c

3  

Hypotheses  Soft magnetic material

 Not too small neither too large nanostructures

~Lateral demagnetizing coefficient of the stripe t W

slide-36
SLIDE 36

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.36

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Effect of end shapes (1/2)

Experiments

K.J. Kirk et al., J. Magn. Soc. Jap., 21 (7), (1997)

Permalloy (soft)

Similar

Magnetization is pinned at sharp ends

slide-37
SLIDE 37

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.37

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Effect of end shapes (2/2)

}

J.G. Zhu

Numerical micromagnetic calculation

Two ground-states each Eight ground-states

GOOD: Better reproducibility BAD: Higher switching field

(Images courtesy of J. Miltat – CNRS, Orsay, France)

Magnetization is pinned at sharp ends

slide-38
SLIDE 38

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.38

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

FLUX-CLOSURE – reminder about domain walls in thin films (1/2)

  • L. Néel, Énergie des parois de Bloch dans les couches minces,
  • C. R. Acad. Sci. 241, 533-536 (1955)

Thickness t Wall width W

W t

K E

2 d d  t W

K E

2 d d 

Bloch wall Néel wall

Bloch versus Néel wall

Crude model: wall is a uniformly-magnetized cylinder with an ellipsoid base

At low thickness (roughly t W) Bloch domain walls are expected to turn their magnetization in-plane > Néel wall Model needs to be refined Domain walls not changed for films with perpendicular magnetization Conclusion

slide-39
SLIDE 39

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.39

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

FLUX-CLOSURE – reminder about domain walls in thin films (2/2)

y z

z M y M x M

z y x

     

    M div

  • Néel caps occur atop Bloch walls to reduce

surface and volume magnetic charges

 M.n

  • A. Hubert and R. Schäfer,

Magnetic domains, Springer (1999)

Refined phase diagram of domain walls

From Néel walls to cross-tie walls

slide-40
SLIDE 40

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.40

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Theory / Simulation FLUX-CLOSURE – Disk-shaped dots: vortex state at remanence

5 10 15 20 100 200 300 400 500

Thickness (nm)

Vortex state Single domain state

R.P. Cowburn, J.Phys.D:Appl.Phys.33, R1–R16 (2000)

Experiments

P.-O. Jubert & R. Allenspach, PRB 70, 144402/1-5 (2004)

 Vortex state (flux-closure) dominates at large thickness and/or diameter  The size limit for single-domain is much larger than the exchange length Experimentally the vortex may be difficult to reach close to the transition (hysteresis)

2 ex

20 .   D t

Zero-field cross-over

slide-41
SLIDE 41

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.41

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

FLUX-CLOSURE – Vortex state under field

300nm/10nm 100nm/10nm

Experiments

R.P. Cowburn, J.Phys.D:Appl.Phys.33, R1–R16 (2000)

Theory / Simulations

Displaced vortex model Calculation of the equilibrium line and the annihilation line

  • K. Y. Guslienko & K. L. Metlov,

PRB 63, 100403(R) (2001)

 Typical loops for flux-closure states  Energy of the vortex state can be computed from the anhysteretic above-loop area.

slide-42
SLIDE 42

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.42

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Solution

NON-SINGLE DOMAIN EFFECTS – Van den Berg model (1/2)

  • div

 M

.  n M

  • H. A. M. Van den Berg, J. Magn. Magn. Mater. 44, 207 (1984)

Infinitely soft material (K=0) Zero external magnetic field (no volume charges) (no surface charges)

Z 

e

mc 

e

ex 

 e

d 

e

Looking for a solution with : « Flux closure » 2D geometry (neglect thickness) Size >> all magnetic length scales (wall width)

Hypothesis

x y

y M x M

y x

   

  M div

Van den Berg model

slide-43
SLIDE 43

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.43

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Van den Berg model (2/2) Sandpiles for simulating flux-closure patterns

slide-44
SLIDE 44

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.44

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Large dots many degres of freedom many possible states history is important even slight perturbations can influence the dot (anisotropy, defects, etc.).

NON-SINGLE DOMAIN EFFECTS – Van den Berg model and anisotropy

Easy axis of weak magnetocrystalline anisotropy Easy axis of weak magnetocrystalline anisotropy

slide-45
SLIDE 45

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.45

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Van den Berg model in field (1/3)

The domains with magnetization parallel to the applied field are favored

  • P. Bryant et al., Appl. Phys. Lett. 54, 78 (1989)

Generalization for non-zero field

See further extension to field arbitrarily-close to the saturation field:

  • A. DeSimone, R. V. Kohn, S. Müller, F. Otto & R.

Schäfer, Two-dimensional modeling of soft ferromagnetic films, Proc. Roy. Soc. Lond. A457, 2983-2991 (2001)

  • A. DeSimone, R. V. Kohn, S. Müller & F. Otto, A

reduced theory for thin-film micromagnetics,

  • Comm. Pure Appl. Math. 55, 1408-1460 (2002)
slide-46
SLIDE 46

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.46

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Van den Berg model in field (2/3)

Zero field : agreement with Van den Berg’s model View details Longitudinal applied field The domains with magnetization parallel to the applied field are favored

In the following, many pictures taken from Hubert’s book

Material : Ni80Fe20 ‘Permalloy’, Py.

slide-47
SLIDE 47

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.47

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetic length scales Typical length scale: Bloch wall width B

 

 

2 2

sin / K dx d A e  

Exchange Anisotropy

J/m

3

J/m

Numerical values

K A/

B

  

nm 3 2

B

   nm 100

B 

Hard Soft

=A/K is often called

the Bloch wall parameter. Notice also that several definitions of Bloch wall width have been proposed, e.g. with  or 2 as prefactor

slide-48
SLIDE 48

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.48

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetic length scales Typical length scale: Exchange length ex

 

 

2 d 2

sin / K dx d A e   Exchange Dipolar energy J/m

3

J/m

2 d ex

/ 2 /

s

M A K A     nm 10 3

ex

   Critical size relevant for nanoparticules made of soft magnetic material

ex c

3   D

2 s c

) /( 6 M N A D    Generalization for various shapes

Quality factor Q

 

2 d 2

sin sin K K e    m.c. Dipolar energy J/m

3

J/m

d

/K K Q  Relevant e.g. for stripe domains in thin films with perpendicular magnetocristalline anisotropy

Critical size for hard magnets

for hard magnetic materials

B d w c

5 . 2 / 6  Q K E D   AK E 4

w 

Notice: Other length scales: with field etc.

slide-49
SLIDE 49

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.49

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetic length scales

  • E. F. Kneller & F. E. Luborsky,

Particle size dependence of coercivity and remanence of single-domain particles,

  • J. Appl. Phys. 34, 656 (1963)

Towards suparamagnetism Towards nucleation-propagation and multidomain

slide-50
SLIDE 50

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.50

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Domain walls TOC

1. Details and use of domain walls in stripes 2. Magnetization processes inside domain walls

II.3. Manipulating domain walls

slide-51
SLIDE 51

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.51

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Pinning in stripes: notches NON-SINGLE DOMAIN EFFECTS – Preparation of states (2/4)

Nucleation Propagation Nucleation Pinning/depinning Propagation Reservoir for nucleation Pinning/depinning Propagation

Nucleation in in-plane magnetized stripes Nucleation in out-of-plane magnetized stripes

slide-52
SLIDE 52

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.52

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Geometrical pinning NON-SINGLE DOMAIN EFFECTS – Preparation of states (3/4) Preparation for in-plane anisotropy

Step 1: transverse field Remanent state H

  • T. Taniyama et al., APL76, 613 (2000)
slide-53
SLIDE 53

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.53

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Preparation of states (4/4) Disks

Vortex state Near single-domain (leaf state) Aspect ratio D/t Large diameter D

Rings

Vortex state Onion state Stability less dependent on geometry (no vortex energy)

Control of ring states

H H Notch

Ex: M. Klaüi et al., APL78, 3268 (2001)

Hx Hy Hx Hy

slide-54
SLIDE 54

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.54

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Use of domain walls

  • S. S. P. Parkin, IBM-Almaden

U.S. patents 6834005, 6898132, 6920062

  • D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson,
  • D. Petit & R. P. Cowburn,

Magnetic domain-wall logic, Science 309, 1688 (2005)

slide-55
SLIDE 55

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.55

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetization processes inside vortices

Closure domains (flat)

  • T. Shinjo et al., Science 289, 930 (2000)
  • T. Okuno et al., JMMM240, 1 (2002)

The central magnetic vortex can be magnetized up or down using a perpendicular field

  • A. Thiaville et al., Phys. Rev. B 67,

094410 (2003)

UP DOWN UP UP UP UP DOWN DOWN DOWN

Theory and simulation

Micromagnetic simulation

Require a Bloch point: Not well described in micromagnetism

  • W. Döring, J. Appl. Phys. 39, 1006 (1968)

First theoretical insight in Bloch points

slide-56
SLIDE 56

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.56

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetization processes inside vortices

Magnetic vortex core reversal by excitation with short bursts of an alternating field

  • B. Van Waeyenberg et al.,

Nature 444, 461 (2007)

  • R. Hertel et al.,
  • Phys. Rev. Lett. 98, 117201 (2007)

Resonant phenomenon Non-resonant phenomenon

slide-57
SLIDE 57

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.57

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Magnetization processes inside vortices

  • K. Yamada et al., Nat. Mater. 6 (2007)

Electrical switching of the vortex core in a magnetic disk

Experiment 2.4x1011A/m2 Experiment 3.5x1011A/m2 Simulation 3.88x1011A/m2 (resonant phenomenon)

slide-58
SLIDE 58

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.58

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Interfacial effects II.4. Interfacial effects on magnetization reversal

slide-59
SLIDE 59

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.59

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

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)

NON-SINGLE DOMAIN EFFECTS – Interfacial effects (F/AF 1/3) Seminal studies

Oxidized Co nanoparticles

Field-cooled hysteresis loops:

  • Increased coercivity
  • Shifted in field
slide-60
SLIDE 60

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.60

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Dependence of the blocking temperature

  • n the nature of the matrix

AFM matrix TB  TN CoO

100 200 300 2 4 6 8 m, J/T x10

  • 8

TN CoCORECoOSHELL in Al2O3 matrix ZFC FC CoCORECoOSHELL in CoO matrix T, K

Non-magnetic matrix : TB  30K

NON-SINGLE DOMAIN EFFECTS – Interfacial effects (F/AF 2/3)

Problems remain:

 Not all features understood  Very sensitive on fabrication

V.Skumryev, et al., Nature 423, 850 (2003)

slide-61
SLIDE 61

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.61

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Astroids of single particles with Ferro/Antiferro exchange NON-SINGLE DOMAIN EFFECTS – Interfacial effects (F/AF 3/3)

  • A. Brenac et al., CEA-Grenoble,
  • W. Wernsdorfer, Institut Néel

Core-shell CoO cluster on CoO

slide-62
SLIDE 62

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.62

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

Experiments NON-SINGLE DOMAIN EFFECTS – Edge anisotropy

  • S. Rohart, PhD Thesis (2005)
  • S. Rohart, A. Thiaville, unpublished
  • S. Rusponi et al., Nature Mater. (2003):

« The remarkable difference between surface and step atoms in the magnetic anisotropy

  • f two-dimensional nanostructures”

Co/Pt(111)

Simulation/Theory

slide-63
SLIDE 63

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.63

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

NON-SINGLE DOMAIN EFFECTS – Electrical control

  • M. Weisheit et al., Science 315, 349 (2007)

Electric modification of intrinsic properties

See also: magnetic semiconductors, multiferroics etc.

slide-64
SLIDE 64

Olivier Fruchart – Simple concepts of magnetization reversal – European School on Magnetism – Timisoara Sept 2009 – p.64

Institut Néel, Grenoble Institut Néel, Grenoble, France , France

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

[1] Magnetic domains, A. Hubert, R. Schäfer, Springer (1999, reed. 2001) [2] R. Skomski, Simple models of Magnetism, Oxford (2008). [3] R. Skomski, Nanomagnetics, J. Phys.: Cond. Mat. 15, R841–896 (2003). [4] O. Fruchart, A. Thiaville, Magnetism in reduced dimensions,

  • C. R. Physique 6, 921 (2005) [Topical issue, Spintronics].

[5] O. Fruchart, Couches minces et nanostructures magnétiques, Techniques de l’Ingénieur, E2-150-151 (2007) [6] Lecture notes from undergraduate lectures, plus various slides: http://perso.neel.cnrs.fr/olivier.fruchart/slides/ [7] G. Chaboussant, Nanostructures magnétiques, Techniques de l’Ingénieur, revue 10-9 (RE51) (2005) [8] D. Givord, Q. Lu, M. F. Rossignol, P. Tenaud, T. Viadieu, Experimental approach to coercivity analysis in hard magnetic materials, J. Magn. Magn. Mater. 83, 183-188 (1990). [9] D. Givord, M. Rossignol, V. M. T. S. Barthem, The physics of coercivity, J. Magn. Magn. Mater. 258, 1 (2003). [10] J.I. Martin et coll., Ordered magnetic nanostructures: fabrication and properties,

  • J. Magn. Magn. Mater. 256, 449-501 (2003).

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