Bielefeld University

D2 PHYSICS

Ferromagnetic

materials for MEMS-

and NEMS-devices Towards the design of

novel spintronic devices

A. Weddemann,* J. Jadidian, Y.S. Kim,

S.R. Khushrushahi, M. Zahn

Presented at the 2011 COMSOL Conference

Boston, MA

* *email: weddeman@mit.edu

Motivation 2

Arrays of thin magnetic layers:

Ferromagnetic materials in spintronic devices

10/13/2011 A. Weddemann

0

0

XMR PR R

R

Good understanding of the dynamics

of ferromagnetic materials necessary.

Applications:

- data storage

- magnetic field sensors

How to describe ferromagnetism? 3

Governing equation is Landau-Lifshitz Gilbert:

Ferromagnetism

10/13/2011 A. Weddemann

efft t

m mm H mγ α

damping

precession

demagnetization

demag mag H

mag SM m

anieff demag ext

0 S 0 S

( )2 1 fA

µ M µ M

mH m H H

m

δ

δ

exchange

cubic

anisotropy

linear

non-local

contribution

SMM m

| | 1m

Magnetic beads

Magnetic nanoparticles 4 Superparamagnetic multi-core beads

10/13/2011 A. Weddemann

eff( )Id A

tα γ

mHM

1 0

0 N

MM

M

,n ijk n jmεM

T,1 ,1 ,1 ,2( , , , ,...)

x y z xm m m mm

Teff eff, ,1 eff, ,1 eff, ,1 eff, ,2( , , , ,...)x y z xH H H HH

anieff demag ext

0 S 0 S

( )2 1 fA

µ M µ M

mH m H H

m

δ

δ

( , , )x y z m m

simplifies to set

of ODEs

effLLG~m H

~ 1 µm Even without

consideration of

temperature effects,

dipolar coupling results

in a vanishing magnetic

moment in the

equilibrium state and a

superparamagnetic

behaviour.

polymer

matrix

nano-

particles

Wide range of parameters allows for

adjustment of ensemble properties.

Magnetic nanoparticles 5 From clusters to monolayers

10/13/2011 A. Weddemann

Assemblies of magnetic nanoparticles

minimize their magnetic moment

globally and locally.

Probe particle:

- R = 8 nm

- MS = 1000 kA/m

2D-approach

should look like will look like magφ

m

full 3D FEM-BEM

magΩ

= mφ f dx

Magnetic multilayers 6 Thin magnetic films

10/13/2011 A. Weddemann

Thin films Néel S,1 S,2 1 2~ ,J M M m m

stray field

coupling

System matrix not sparse

combined 2D/3D

anieff demag ex

0 S 0 S

( )2 1 fA

µ M µ M

mH m H H

m

δ

δ

( , , ) ( , )x y z x ym m

iΦ

Stray field too strong System matrix too large

Magnetic multilayers 7 Weak equations for finite element discretization

10/13/2011 A. Weddemann

Layer stray field

Mmag Sφ m

mag S, 0M dxψ φ mΩ

Weak form

H1( )ψ Ω

dxt t

1 ,magΩ

αγ

m mmψ

x y z i i

Adx

M x x, ,0 S

2 ,magΩ

μ

mm

ψ

K

dxM1

0 S

2 , ,magΩ

μm e m eψ

dxext, ( )mag

mag

Ω

φm Hψ

Projections: imag mag Φφ φ

i

1Φmm

Next step?

10 nm

Magnetic multilayers 8 Micromagnetics – A trilayer system

10/13/2011 A. Weddemann

Strongest limitation (also for

analysis of additional effects such

as magnetostriction, spin-torque … )

is the model size together with the

high aspect ratio.

FEM-BEM allows for a two-

dimensional formulation

for magnetic field of thin

films

Hybrid FEM-BEM approch

to open boundary

electromagnetic problems

6:15pm Magnetic and

Electric Fields

www.spinelectronics.de Bielefeld University

D2 PHYSICS

Conclusion & Outlook

We implemented the LLG-equations for:

thin films

ensembles of magnetic nanoparticles

We designed novel magnetic field sensor based on highly ordered monolayers.

easy to control magnetic properties

increased sensitivity at the cost of inherent device noise

four different measurement regimes

Implementation of FEM-BEM frame

Integration of physical phenomena:

magnetostriction

spin-torque effects

moving objects

10/13/2011

9

A. Weddemann

Conclusion Outlook

Suspension of magnetic particles

exposed to a magnetic field

See posters:

→ Ferromagnetic materials for MEMS- and NEMS-devices

→ Magnetic nanoparticles for novel spintronic devices