Actuation and control of motion in micro mechanical systems are technological challenges, since they are accompanied by mechanical friction and wear, principal and well known sources of device lifetime reduction. In this theoretical work we propose a non-contact motion control technique based on the introduction of a tunable magnetic interaction. The latter is realized by coating two non-touching sliding bodies with ferromagnetic films. The resulting dynamics is determined by shape, size and ordering of magnetic domains arising in the films below the Curie temperature. We demonstrate that the domain behavior can be tailored by acting on handles like ferromagnetic coating preparation, external magnetic fields and the finite distance between the plates. In this way, motion control can be achieved without mechanical contact. Moreover, we discuss how such handles can disclose a variety of sliding regimes. Finally, we propose how to practically implement the proposed model sliding system.

1. A.
Benassi
Sliding
mo*on
and
Adhesion
control
through
magne*c
domains
EMPA
Materials
Science
&
Technology,
Zürich
(Switzerland)
SINERGIA
project
CRSII2
136287/1

2. Micro
and
nano
scale
fric*on
control
Geometrical
control
exploi=ng
the
surface
geometry
and
interac=on
poten=al
periodicity
• Superlubricity
• Commensurability
• Nano
paDerning
Chemical
control
exploi=ng
chemical
reac=on
and
molecular
proper=es
• Coa=ng
and
surface
func=onaliza=on
• Lubricant
design
• Ionic
liquids
based
lubrica=on
Dynamical
control
ac=ng
on
the
system
with
an
external
parameter
• Mechanical
vibra=ons
• Suppressing/promo=ng
a
phase
transi=on
• Termolubricity
Lantz
et
al.
Nat.
Nanotech.
4
586
(2009)
Socoliuc
et
al.
Science
313
207
(2006)
Benassi
et
al.
PRL
106
256102
(2011)
Urbakh
et
al.
Nature
430
525
(2004)…
Dienwiebel
et
al.
PRL
92
126101
(2004)
Park
et
al.
Science
309
1354
(2005)
CoJn-­‐Bizonne
et
al.
Nat.
Mater.
2
237
(2003)
…
Perkin,
Mistura,
Drummond,
Bennewitz,
Spencer,
Szlufarska
talks

3. Magne*c
domains
and
sliding
mo*on
New
ways
of
actua=ng
and
controlling
mo=on
in
MEMS
If
we
coat
two
nearby
bodies
with
ferromagne=c
films,
below
the
Curie
temperature
magne=c
domains
will
appear
Magne=c
domains
behave
like
micro-­‐scale
magnets
and
they
will
interact
via
magne=c
field
The
magne=c
domain
paDern
can
be
controlled
with
a
magne=c
field
crea=ng
disordered,
ordered
and
even
periodic
structures
If
the
magne=c
interac=on
is
strong
enough
we
can
thus
control
sliding
and
adhesion
dynamically
and
reversibly
by
a
magne=c
field.
Domains
can
be
ordered
into
periodic
paDerns
mimicking
the
atomic
periodicity
at
the
nanoscale.
Similar
aDempts
of
crea=ng
a
mesoscale
fric=on
lab
have
been
recently
proposed
exploi=ng
ion
traps
and
colloidal
suspensions.
Benassi
et
al.
Nat.
Comm.
2
236
(2011)
Mandelli
et
al.
PRB
87
195418
(2013)
(see
POSTER)
Bohlein
et
al.
Nat.
Mater.
11
126
(2012)
Vanossi
et
al.
PNAS
109
16429
(2012)
(see
POSTER)

4. Why
magne*c
domains?
The
domain
width
ranges
over
many
order
of
magnitude
depending
on
the
film
thickness:
The
domain
shape
can
be
controlled
very
easily
applying
an
external
magne=c
field
perpendicular
to
the
film
surface,
maze
paDerns
can
be
formed
as
well
as
bubble
laQces:
2
µm
t
=
23
nm
60
µm
t
=
9
nm
110
µm
t
=
12
nm

5. Why
magne*c
domains?
Maze-­‐like
domains
can
be
ordered
in
metastable
periodic
structures
like
stripes
whose
width
can
be
controlled
by
a
field
parallel
to
the
film
surface:
Defects,
impuri=es
and
inhomogenei=es
act
as
pinning
sites
for
the
domains,
determining
the
domain
mobility.
The
density
of
inhomogenei=s
can
be
controlled
changing
the
film
growing
condi=ons:
thickness
deposi=on
rate

6. Modeling
the
magne*za*on
dynamics
Our
Simplified
scalar
model:
• Less
accurate
than
Micro-­‐Magne=c
simula=ons
• Allows
to
treat
large
system
sizes
(few
µm2
up
to
hundreds
of
µm2)
• Quan=ta=ve
agreement
with
experiments
• Ad-­‐hoc
for
perpendicular
anisotropy
ferromagne=c
films
E.
Jagla
PRB
72
094406
(2005)
E.
Jagla
PRB
70
046204
(2004)
A.
Benassi
et
al.
PRB
84
214441
(2011)
p
hKuiA
p
A/hKuiDomain
width
Wall
thickness
Boundaries
and
mobility
⌘
The
Landau-­‐Lifshtz-­‐Gilbert
equa=on
contains
3
material
parameters:
• Anisotropy
constant
Ku
• Exchange
s=ffness
A
• Anisotropy
and
inhomogenei=es
strength
η
They
set
all
the
domain
proper=es
(size,
walls,
regularity,
mobility…)

7. Modeling
the
magne*za*on
dynamics
Our
Simplified
scalar
model:
• Less
accurate
than
Micro-­‐Magne=c
simula=ons
• Allows
to
treat
large
system
sizes
(few
µm2
up
to
hundreds
of
µm2)
• Quan=ta=ve
agreement
with
experiments
• Ad-­‐hoc
for
perpendicular
anisotropy
ferromagne=c
films
E.
Jagla
PRB
72
094406
(2005)
E.
Jagla
PRB
70
046204
(2004)
A.
Benassi
et
al.
PRB
84
214441
(2011)
Each
dipole
moment
associated
to
the
infinitesimal
volume
elements
experiences
a
magne=c
field
due
to
the
rest
of
the
medium,
its
precession
mo=on
is
described
by
a
Landau-­‐Lifshitz-­‐Gilbert
equa=on:
The
local
field
is
determined
by
the
Hamiltonian
containing
the
material
proper=es
and
the
physics
of
the
medium.
⇤m
⇤t
=
1 + ⇥2
m ⇥

B + ⇥
✓
m ⇥ B
◆
B =
1
Ms
H[m]
m
+ Q(R, t)
hQ(R, t)i = 0
hQ(R, t)Q(R0
, t0
)i = ⇥(t t0
)⇥(R R0
)2KBT⇤/Ms
Bm
precession
term
Bm
damping
term
dissipa=on
by
microscopic
degrees
of
freedom
Bm
stochas=c
term
thermal
fluctua=ons

8. Modeling
the
magne*za*on
dynamics
Our
Simplified
scalar
model:
• Less
accurate
than
Micro-­‐Magne=c
simula=ons
• Allows
to
treat
large
system
sizes
(few
µm2
up
to
hundreds
of
µm2)
• Quan=ta=ve
agreement
with
experiments
• Ad-­‐hoc
for
perpendicular
anisotropy
ferromagne=c
films
External
field:
uniform
but
=me
dependent
Anisotropy
energy:
1)
Energy
gain
if
the
dipole
is
aligned
to
the
easy-­‐axis.
2)
Its
fluctua=ons
around
an
average
value
provides
strong
pinning
points
for
the
domain
walls.
Ku(R) = hKui(1 P(x, y))
Exchange
energy:
It
represents
the
energy
cost
for
the
magne=za=on
misalignment
in
the
walls
We
do
not
have
real
Block
or
Neel
walls,
just
their
projec=on
along
z.
Stray
field
energy:
Interac=on
energy
of
a
dipole
moment
field
with
the
rest
of
the
medium
This
is
a
non
local
term
to
be
treated
in
reciprocal
space
H =
Z
d3
R

Ku(R)
m2
2
+
A
2
(⇥Rm)2
+
µ0M2
s d
8
Z
d2
R0 m(R0
)m(R)
|R R0|3
µ0Msm(Hext HUCS(R))=
Z
d3
R

Ku(R)
m2
2
+
A
2
(⇥Rm)2
+
µ0M2
s d
8
Z
d2
R0 m(R0
)m(R)
|R R0|3
µ0Msm(Hext HUCS(R))

9. Modeling
the
film-­‐film
interac*on
Two
interac*ng
films:
• The
domains
feel
the
presence
of
the
other
film
through
a
new
magne=c
field
and
they
can
mutually
modify
their
shape
• The
boDom
film
exert
a
force
on
the
upper
one,
i.e.
to
the
slider
• The
slider
is
driven
at
constant
velocity
through
a
spring.
Whit
2
LLG
equa=ons
+
one
Newton’s
equa=on
we
can
simultaneously
simulate
the
slider
mo=on
and
the
dynamics
of
the
magne=c
domains
and
study
how
the
influence
each
other
The
work
done
by
the
driving
force
is
dissipated
exci=ng
the
microscopic
degrees
of
freedom,
i.e.
phonons,
magnons
and
eddy
currents.
Dissipa=on
is
included
in
the
model
through
a
viscous
damping
term
in
the
domains
equa=ons
(Gilbert
damping)
For
the
moment
we
use
the
same
thickness
and
the
same
material
for
both
the
films
and
we
drive
the
slider
at
constant
height
d.

10. S*ck-­‐slip
dynamics
Orien=ng
the
domains
into
parallel
stripes
we
can
obtain
a
periodic
magne=c
field
resul=ng
in
a
periodic
effec=ve
interac=on
poten=al
between
the
two
films.
With
an
effec=ve
periodic
poten=al
we
can
reach
a
s=ck-­‐slip
regime
if
we
drive
the
system
perpendicularly
to
the
stripe
direc=on.
N
N
S
S
N
S
S
N

11. Controlling
magne*c
fric*on
-­‐
When
a
ferromagne=c
film
has
uniform
magne=za=on
it
behaves
like
a
plane
capacitor:
the
inner
field
is
constant,
the
outer
field
is
0.
No
domains,
no
field
à
zero
fric=on!
-­‐
Sliding
parallel
to
the
stripes
the
fric=on
force
is
almost
zero
except
when
the
stripes
brake.
Very
anisotropic
response!
-­‐
Changing
the
homogeneity
of
the
sample
the
fric=on
does
not
change
that
much.
S=ck-­‐slip
is
independent
of
the
regularity
and
perfect
periodicity
of
the
stripes:
top
film
boDom
film
sliding
direc=on

12. Controlling
magne*c
fric*on
E(Hext=0)
E
>
E(Hext=0)
Hext

13. Magne*c
fric*on
and
domain
proper*es
The
magne=c
fric=on
is
also
sensi=ve
to
the
material
proper=es
and
growing
condi=ons:
Larger
domain
width
results
in
a
larger
fric=on
force,
this
is
not
always
true:
• larger
domains
à
smaller
repulsion
• larger
domains
à
less
interac=ng
wall
per
unit
area
a
non
monotonic
behavior
rises,
and
depends
on
the
film
separa=on
d.
Thinner
domain
walls
give
rise
to
a
larger
fric=on
force,
the
force
between
the
films
goes
as
the
field
deriva=ve:
The
stripes
break
down
when
their
width
is
comparable
with
the
domain
wall
thickness.
Thinner
walls
resist
to
higher
external
field
before
breaking
down.
-1
+1mU
x
HU
x
F
-1
+1mU
x
HU
x
F

14. Playing
with
commensurability
Non
trivial
behaviors
can
arise
from
the
domain
relaxa=on
that
can
some=mes
reduce
the
incommensurablity.
S=ll
under
inves=ga=on…

15. Controlling
magne*c
adhesion
When
the
two
films
are
kept
in
close
contact
their
interac=on
is
so
strong
that
the
domain
paDern
on
both
of
them
is
exactly
the
same.
The
adhesion
force
is
propor=onal
to
the
total
domain
wall
length
(domain
perimeter)
per
unit
area.
Changing
the
domain
morphology
with
an
external
field
we
can
control
the
adhesion
between
the
plates!

16. Magnet
fric*on
and
film
separa*on
mixed
state
pure
sliding
domain
plas=city
pure
s=ck-­‐slip
Decreasing
the
separa=on
between
films
makes
the
domain
interac=on
Stronger,
this
results
in
a
variety
of
non
trivial
sliding
regimes:
At
fixed
driving
condi=ons
and
material
proper=es,
a
“phase
diagram”
of
the
different
regimes
can
be
drown:

17. Possible
experimental
setups
Several
geometries
and
devices
can
be
exploited
to
measure
the
magne=c
contribu=on
of
fric=on…
non-­‐contact
AFM
with
colloidal
probe
=p
contact
AFM
or
MFT
spacing
layer
planar
geometry
non
magne=c
coa=ng
when
in
contact…
Ftot = Fk
mag + Fmec =
= Fk
mag + µ(F?
mag + L + A)
L = vertical load
A = Adhesion force
F?
mag ' Fk
mag
µ 0.8 ÷ 0.002
Fmag and A / plate area
with:
Wang
et
al.
Experiment.
Mech.
47
123
(2007)
Tang
et
al.
Rev.
Sci.
Instrum.
84
013702
(2013)
Forces
à
1
nN
÷
10
µN
Periodicty
à
50
nm
÷
10
µm