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Magnetic ordering in two-dimensional
nanoparticle assemblies
Pedro Zeijlmans van EmmichovenFaculty of Science, Utrecht University
Leiden, June 18th, 2007
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Collaborators
• Mirela Georgescu• Mark Klokkenburg• Ben Erné• Daniël Vanmaekelbergh• Peter Liljeroth
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Outline
• Introduction• Experiments and simulations
- Magnetite- Cobalt ferrite
• Conclusions
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Introduction
Goal: understand fundamental interactions in 2D assemblies ofmagnetic nanoparticles
Two systems:I. 21-nm magnetite (Fe3O4) particles
- Single domain with large magnetic moment- Superparamagnetic
II. 21-nm cobalt ferrite (CoFe2O4) particles- Single domain- Cubic anisotropy- Anisotropy energy small
at room temperature, large at low temperature (related to kBT )
6.7-nm CoFe2O4
Liu et al., Pure Appl. Chem. 72 (2000) 37
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I. Superparamagnetic magnetite
Edd ~ -500 meV
Dipole-dipole interactions
II. Cobalt ferrite (cubic anisotropy)
Room temperature Low temperature
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Experiments and simulations
Sample preparation- Wet chemical preparation of nanoparticles- Particles capped with oleic acid- Drop casting on graphite (HOPG)- 2D islands of nanoparticles
Measurements- Scanning probe methods- Ultra high vacuum < 10-10 torr- Temp. 25 K – 1000 K
Simulations- Monte Carlo
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Detector LASER
Sample
Scanner tube
Az V
Non-contact Atomic Force Microscopy
• Oscillate tip at resonance frequency f0• Close to sample: force field shifts f0 by df• Keep df constant and scan sample:
Topography
z
dfPrinciples Forces
Van der WaalsRepulsive magneticAttractive magneticVdW + repulsive magn.
• Scan at large distance:Magnetic image
• Force spectroscopy
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Topography
1x1 µm2; Inset 170x130 nm2
Room temperature
Dark: 0 nmBright: 25 nm
Magnetic image
Tip-substrate distance: 70 nm
Dark: -5 HzBright: 0 Hz
Results for magnetite
• Large islands (10-200 particles)• Single monolayer
• Substrate: force ~ 0• Attraction with small contrast
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Force spectroscopy (Force vs. distance)
Observations:• Above substrate: weak attraction (1; VanderWaals)• Above island: strong attraction (6; magnetic)• At edge of island: repulsion (2-3-4; magnetic)
0.5x1 µm2; Room temperature1234
65
0 10 20 30 40 50 60 70
-10
-8
-6
-4
-2
0
2
df (H
z)
z (nm)
1 2 3 4 5 6
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• On top of island: strong attraction - Tip very close (large field)- Dipoles reoriented
• Edge of island: repulsion- Tip-particle distance large (small field)- Strong dipole-dipole interactions:
minimum energy configuration (blocking)
Interpretation
tip
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• Nanoparticles fixed on substrate• Calculate minimum energy
- Start with arbitrary configurationof dipoles and vary them while minimizing energy
- Energy = sum of all dipole-dipole energies
- Stop when minimum is found
Experiment
Simulation
Monte-Carlo simulations
• Results: - Dipoles in plane- Flux-closure configuration- E = -650 meV/particle
M. Georgescu et al., Phys. Rev. B 73, 184415 (2006)
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Experiment Simulation
Experimental and calculated Force
• Image D shows, for comparison, flux closure in hexagonal arrangement of particles
• Solutions not unique
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Results for cobalt ferrite
Experiments at room temperature
Topography
Magnetic image
Dark: 0 nmBright: 25 nm500x500nm2
Force spectroscopy
Tip-substr. dist. 40 nmDark: -2 HzBright: 0.2 Hz
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Topography Magnetic image
700x400nm2
Temperature 100 K
Bright: repulsion; dark: attraction
Experiments at low temperature
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100nm
100nm
0 10 20 30 40 50 60 70-12
-10
-8
-6
-4
-2
0
2
df [H
z]
z [nm]
1 2 3 4
Experiments on small islands (~25 nanoparticles)
Topography
Magnetic image
Spectroscopy
Temperature 100 K
Bright: repulsion; dark: attraction
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Monte-Carlo simulations
• Minimize energy• Room temperature: - anisotropy energy small
- dipole-dipole interactions
• Calculate arrangements of dipoles and MFM images
• Low temperature: - large cubic anisotropy- Dipole-dipole interactions and
anisotropy energy
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Edd = -14.9 eV Edd = -14.3 eV Edd = -14.5 eV
Simulations at room temperature
• Flux-closure arrangements• Large contrast at edges (‘escaping’ field lines)
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Simulations at low temperatures
Room temperature Room temperature
Edd = -14.9 eV Edd = -14.5 eV
Edd = -8.8 eV
Temp. 100 K
Edd = -7.9 eV
Edd = -8.8 eV
Temp. 100 K
Temp. 100 K
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100nm
Comparison with experiments
Experiments, above islands:• Areas with small contrast• Areas with repulsion/attraction
Simulations, above islands:• Areas with flux-closure type
arrangements• Areas where moments point
‘away’ from flux closure
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Conclusions
• Superparamagnetic nanoparticles: moments arrange in flux-closure structures
• Nanoparticles with large anisotropy: only partial flux closure