sliding motion and adhesion control through magnetic domamins
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A. Benassi
Sliding mo*on and Adhesion control through magne*c domains
EMPA Materials Science & Technology, Zürich (Switzerland)
SINERGIA project CRSII2 136287/1
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
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)
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
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
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)
phKuiA
pA/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…)
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 + ⇥2m⇥
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
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 =
Zd3R
�K
u
(R)m2
2+
A
2(⇥Rm)2 +
µ0M2s
d
8�
Zd2R0m(R0)m(R)
|R�R0|3 � µ0Ms
m(Hext
�HUCS
(R))
�H =
Zd3R
�K
u
(R)m2
2+
A
2(⇥Rm)2 +
µ0M2s
d
8�
Zd2R0m(R0)m(R)
|R�R0|3 � µ0Ms
m(Hext
�HUCS
(R))
�
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.
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
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
Controlling magne*c fric*on
E(Hext=0)
E > E(Hext=0) Hext
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
HUx
F
-1+1mU
x
HUx
F
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…
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!
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:
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
= F kmag
+ Fmec
=
= F kmag
+ µ(F?mag
+ L+A)
L = vertical load
A = Adhesion force
F?mag ' F k
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
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