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: [email protected]
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