Magnetic ordering in two-dimensional

nanoparticle assemblies

Pedro Zeijlmans van EmmichovenFaculty of Science, Utrecht University

Leiden, June 18th, 2007

Collaborators

• Mirela Georgescu• Mark Klokkenburg• Ben Erné• Daniël Vanmaekelbergh• Peter Liljeroth

Outline

• Introduction• Experiments and simulations

- Magnetite- Cobalt ferrite

• Conclusions

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

I. Superparamagnetic magnetite

Edd ~ -500 meV

Dipole-dipole interactions

II. Cobalt ferrite (cubic anisotropy)

Room temperature Low temperature

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

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

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

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

• 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

• 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)

Experiment Simulation

Experimental and calculated Force

• Image D shows, for comparison, flux closure in hexagonal arrangement of particles

• Solutions not unique

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

Topography Magnetic image

700x400nm2

Temperature 100 K

Bright: repulsion; dark: attraction

Experiments at low temperature

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

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

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)

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

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

Conclusions

• Superparamagnetic nanoparticles: moments arrange in flux-closure structures

• Nanoparticles with large anisotropy: only partial flux closure