Thin layers (2D) of nanoparticles are formed by evaporating dispersions of nanoparticles on a solid substrate

Three-dimensional assemblies are prepared by slowly diffusing a poorly coordinating solvent into the liquid dispersion of nanoparticles

With Fe nanoparticles the 2D and 3D assemblies have different structural and magnetic behavior

2D Nanoparticle Arrays and 3D Nanoparticle Crystals

Simulated phase contrastTEM image

Layer Stacking

Found for hexagonal close packed arrays of larger Fe nanoparticles

Not seen with nonmagnetic particles

S. Yamamuro, D. Farrell, and S. A. Majetich, Phys. Rev. B65, 224431 (2002)

Preference for an Odd Number of Layers

Dilute solutions form hexagonal monolayers

Concentrated solutions form thicker cubic or hexagonal arrays

BCC structure entropically stabilized for small diameters

Slower formation increases the coherence length

Evaporating droplet

2D Array Structure Summary

Use very slow precipitation (hours, weeks, months) by diffusion of “bad” solvent

Can make 3D array crystals up to 10 microns in size

Particles dispersed in toluene

Ethanol

Propanol

3D Nanoparticle Arrays

For standard surfactants, edge-to-edge interparticle separation

≥ 2.5 nm

Expect magnetostatic interactions to dominate

Learn about interactions from Mr(H), Mrelax(t), MZFC(T)

Dipolar Interactions

-60

-40

-20

0

20

40

60

σr

(emu/g)

-4000 -2000 0 2000 4000

H (Oe)

T = 10 K

6.7 nm Fe cores, OA/OY

Arrays, H parallel

Arrays, H perpendicular

Magnetization with H perpendicular harder to saturate, decays faster

Interactions shape anisotropy in 2D arrays

1.00

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

Normalized M

6543210

ln(t/t0

)

H = 0 Oe

T = 10 K

6.7 nm Fe cores

2.5 nm separation

H parallel to substrate

H perpendicular

H

H=0

Field Orientation Mr(H)

€

Φmag =μ0

4πr3

r μ •

r μ [ ]

€

Φmag =1.4kT

€

Φmag=2.4kT

Dipolar energy

per pair of particles

At T = 10 K

Vary the Particle Size

1.0

0.8

0.6

0.4

0.2

Normalized M

zfc

30025020015010050

T (K)

H= 100 Oe

2.5 nm spacing

6.7 nm Fe cores

8.5 nm cores

-1.0

-0.5

0.0

0.5

1.0

Normalized M

r

-4000 -2000 0 2000 4000

H (Oe)

T = 10 K

OA/OY

6.7 nm Fe cores

8.5 nm Fe cores

1.00

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

Normalized M

6543210

ln(t/t0

)

H = 0

T = 10 K

OA/OY

6.7 nm Fe cores

8.5 nm Fe cores

Larger particles have:

• slightly faster approach to saturation

• slower decay in M(t)

• higher TB and broader M ZFC(T)

Particle Size Effects

Same batch of 6.7 nm Fe particles with different surfactants

Oleic Acid/Oleyl Amine Hexanoic Acid/Hexyl AmineAvg. spacing 2.5±0.3 nm 1.2±0.3 nm

€

Φmag=2.8kT

€

Φmag=1.4kTAt T = 10 K

Varying the Particle Spacing

1.0

0.8

0.6

0.4

0.2

Normalized M

zfc

30025020015010050

T (K)

H = 100 Oe

6.7 nm Fe cores

OA/OY (2.5 nm spacing)

HA/HY (1.2 nm spacing)

1.00

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

Normalized M

543210

ln (t/t0

)

H = 0

T = 10 K

6.7 nm Fe

OA/OY (2.5 nm spacing)

HA/HY (1.2 nm spacing)

-1.0

-0.5

0.0

0.5

1.0

Mr

/Ms

-20000 -10000 0 10000 20000

H (Oe)

Surfactants Spacing

Oleic Acid/Oleyl Amine 2.5 nm

Heanoic Acid/Hexyl Amine 1.2 nm

Smaller spacing leads to:

• more gradual saturation

• slower decay in M(t)

• a slightly higher Blocking T

Interparticle Spacing Effect

3D arrays have:

• slower approach to saturation

•higher TB and broader M ZFC(T)

• faster decay in M(t) not explained by demagnetization field due to different shape

-1.0

-0.5

0.0

0.5

1.0

M/Ms

-40x103

-20 0 20 40H (Oe)

T = 10 K 3D arrays, 8.5 nm Fe 2D arrays, 8.2 nm Fe

1.00

0.98

0.96

0.94

0.92

0.90

M/M(t

0)

6543210ln (t/t0)

H = 0T = 10 K

2D arrays, 8.2 nm Fe 3D arrays, 8.5 nm Fe

1.4

1.2

1.0

0.8

0.6

0.4

0.2

M/M(T

B)

30025020015010050T (K)

solvent melting

H = 200 Oe 3D arrays, 8.5 nm Fe 2D arrays, 8.2 nm Fe

2D and 3D Arrays

-1.0

-0.5

0.0

0.5

1.0

M/M (50 kOe)

-30 -20 -10 0 10 20 30

H (kOe)

5 minutes; x = -0.672 weeks: x = -1.174 weeks: x = -1.89

€

ΔM(H)∝H x

x = -2 Ferromagnet

x = -1/2 amorphous magnet (spin glass-like)

Remanent magnetization 10 K

Small Lcoh like spin glass

Large Lcoh FM

Approach to Saturation

• Both the strength of dipolar forces and the structural coherence length Lcoh affect the magnetic properties of nanoparticle arrays

• When Lcoh is long, magnetic relaxation is much faster, suggesting the presence of domain walls within coherent regions

• Stronger dipolar interactions slow the magnetic relaxation when Lcoh is short, and the arrays are spin glass-like

D. Farrell, Y. Ding, S. A. Majetich, C. Sanchez-Hanke, and C.-C. Kao, J. Appl. Phys. 95, 6636 (2004).

D. Farrell, Y. Cheng, Y. Ding, S. Yamamuro, C. Sanchez-Hanke, C.-C. Kao,and S. A. Majetich, J. Magn. Magn. Mater. 282, 1-5 (2004).

Magnetics Summary

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