Magnetic Force Microscopy - uh.edukbyung/Mfmappl.pdf · Magnetic Force Microscopy June 10, 1998 Kim Byung-Il Dept. of Physics Seoul National Univ. BIK Seoul National University _____

Seoul National University BIK _______________________________________________________________________

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6/19/2001 1 Superconductivity Lab.

Magnetic Force Microscopy

June 10, 1998

Kim Byung-Il

Dept. of Physics Seoul National Univ.


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Development of MFM l Noncontact mode ²weak interaction ümagnetic, electric and attr. VdW force ²resonance frequency shift: ∆ω ω0 0 2~ ( / ).′F k üamplitude change ülock-in technique ²tip-sample spacing dependence l Principle of noncontact mode

²One dimentional harmonic osicillator F z F F z

mz

tzt

k z u F z

( ) ( )

( ) ( )

= +

+ + − =

0 1 0

2

2

ζ

∂∂

γ∂∂

The positions of the bimorph and the lever


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u u a i t

z z

= += +

0

0

e x p ( )ωζ respectively.

then

mt t

k a i t F∂ ζ∂

γ∂ζ∂

ζ ω ζ2

2 + + − =[ exp( )] '

The amplitude of vibration is given by

A Fak i

k m ib ( , ' )exp( )

'ω

θω ωγ

=− +

2

where k k F' '= −

The motion of the lever is now influenced by the force derivative(resonance frequency shift).

∆ω ω0 0 2~ ( / ).′F k

Frequency

Amp

interaction

withoutinteraction

Driving frequency

Amp change


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At the frequency with maximum sensitivity,

ω ωm Q≅ ′ +0 1

1

2 2( )

The amplitude change is given by

∆AA Qk

F=

′2

3 30

l contrast mechanism of MFM ²point dipole model

ρ ρ ρ ρF m H= ∇ ⋅( )

m : magnetic moment of the tip H : stray field from sample

′ =⋅

FF zz

∂∂

( ∃)ρ

= + +mHz

mHz

mHzx

xy

yz

z∂∂

∂∂

∂∂

2

2

2

2

2

2

forρm m zz= ∃, ′ =F m

Hzz

z∂∂

2

2


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l bimorph driven system

l feedback in MFM


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l operating condition ²oscillation freq:ω∼ω0 üresonance frequency shift ²tip-sample distance:10-100nm ü long range magnetic interaction ²bias between tip and sample: 0V-10V üelectrostatic force

l servo force ²attractive or repusive magnetic force ütip crash due to polarity change üneed of servo force for feedback ²addition of overall attractive force ücontrol of the spacing between tip and

sample üadditional electrostatic force

² ( )∆ ∆AA Qk

F Fm c=

′ + ′2

3 30

²under feedback: ∆A = 0

ü∆

∆z

FF z

m

servo z z

=′

′

=∂ ∂/

0


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üdata 2: contours of constant force gradient

Force(F)

Distance(z)

Attractive magnetic force(Fm)

Repulsive magnetic force(F m)

Electrostatic force(Fc)


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Repulsive Magnetic Force(F m)

Attractive Magnetic Force(Fm)

Capacitive force(Fc)

Distance(z)

Force gradient(F')

l Co-Pd multilayer film ²sample preparation ü total thickness is about 300A ü (4.0Co+13.2Pd)17 layer ü glass substrate ²image ü earth’s magnetic field ü observation of natural magnetic domain


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(1.8µm× 1.8µm)

(1.8µm× 1.8µm)

Summary

l MFM using resonnce frequency shift was constructed. l The contrast mechanism of MFM was discussed by using one dimensional harmonic oscillator model. l The role of electrostatic force as servo force under feedback was discussed.


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l MFM was applied for the observation of magnetic domain of the magnetic multilayer films

MFM using Electrostatic Force Modulation

l drawback of bimorph driven system ²indirect modulation ²uncontrolled vertical deflection ⇒unstable feedback


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²complex amplitude vs. frequency ⇒restriction in op. frequency range

l electrostatic force modulation ²direct modulation

²ac voltage between tip and sample : V V tac= sin ω

²driving force: ( )f VCz

tc ac= −14

1 22 ∂∂

ωcos

²mzt

zt

k z u∂∂

γ∂∂

2

2 0+ + − =( ) F F Fm c vdW+ + l block schematics


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l rms amplitude-frequencycurve ²electrostatic modulation system ü well-defined amp.-freq. spectrum ²bimorph driven system ü unwanted peak around the main peak

25 50 75 100

bimorph drivenelectrostatic modulation

RM

S A

mpl

itude

(Arb

. uni

t)

Frequency(kHz)


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l 2ω component m

zt

zt

k z u∂∂

γ∂∂

2

2 0+ + −( ) = + +F Fm vdW ( )1

41 22V

Cz

tac∂∂

ω− cos Near average position z0, z z= + +0

1ζ ( ) ... then ζ ω φ

ω ω γωω21 0

1

02 2 2 2

2

4 16

( )( )( ) sin( )

( ) ( )= − +

′ − +

Φ z t,φ

ω ωγω

( ) arctan1 02 244

=′ −

where ω0

2 =km

, γ = 2b/m, Φ( )( )

zC z

m zVtip

ac021

40

=∂

∂, ′ = −

′−ω0

2 00

km

F zm

zm ( )( )(1)Φ

In-phase output Xz

20

202 2 2

4

4 16ω

γωω ω γω

= −− ′ +

Φ( )( ) ( )

In-quadrature output Yz

20

202

202 2 2

4

4 16ω

ω ωω ω γω

=− ′

− ′ +Φ( )( )

( ) ( ) l in-phase component for different distances ü d5=20µm, d4 =10µm, d3=5µm, d2=2µm, d1=1µm.


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25 50 75 100

d5

d4

d3

d2

d1

In-p

ha

se

2ω

co

mp

on

en

t(A

rb.

un

it)

Frequency(kHz)

lrms amplitude-frequency curve ²various tip-sample distances: ²subharmonic peaks ü m z

tzt

k z u∂∂

γ∂∂

2

2 + + − =( ) F F F Fm c vdW rep+ + + ü nonlinear characteristics of capacitance ²truncated peaked near 100nm ü electrostatic tapping interaction.

25 50 75 100 125

2ω component

ω component

Electrostatic Force Modulation 450nm 300nm 150nm 100nm 70nm 0nm

RM

S A

mpl

itude

(Arb

. uni

t.)


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²resonance frequency in noncontact regime

0 100 200 300 400 50050

51

52

53

Frequency Shift

Fre

qm

ax

Tip sample distance

2ω Amplitude-Distance Curve ²cantilever :Co coating(∼40nm), k=2.1N/m,

fres=65kHz ²Vac=14V, fop=33.43kHz ²sample: CoCr thin film( t ∼ 300nm)


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1.5 2.0 2.5

(b)

Def

lect

ion(

Arb

. uni

t)

tapping noncontact

200nm

Relative tip position to sample(µm)

(a)

2ω c

ompo

nent

(Arb

. uni

t)

Am

plitu

de(A

rb. u

nit)

² good amplitude vs. frequency curve(cf.bimorph) ² long range electrostatic capacitive modulation ⇒stable imaging condition ² 2ω increases as tip approaches surface(cf. inset) ⇒high signal to noise ratio

Results ²noncontact regime(vibration∼80nm) ⇒labyrinthine domain(period 4.5∼5µm) ²tapping regime(vibration∼85nm, d∼90nm)


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⇒elongated grains(∼300nm×600nm)

(10µm×10µm)

²noncontact regime(vibration amp.∼80nm) ²contrast increase for larger distance


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(20µm×20µm)

C

B

A

0 4 8 1 2 1 60

1 0 0

2 0 0

3 0 0

4 0 0

p o s i t i o n (µ m )

Dis

tanc

e(nm

)


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-100 0 1 0 0 200 3 0 0 4 0 0

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

On the Positive Domain On the Negative Domain

82nm

87nm91nm

86nm

T

CB

A

2ω C

om

po

nen

t(n

m)

t ip posi t ion f rom sample(nm)

⇒long range magnetic interaction

100 1000-20

0

2 0

4 0

6 0

8 0

100

120

s lope = -54.6

slope = -56.5

On the Pos i t ive Domain On the Negat ive Domain

2ω C

ompo

nent

(nm

)

t ip position from sample(nm)

1000 2000 3 0 0 0

0

50

100

² ∂∂C zz( )0 ≈a D zln( / )0

⇒conical tip model ⇒electrostatic long range order interaction ⇒stable feedback condition


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Summary ²development of MFM using electroststic force

modulation ²good amplitude vs. frequency curve(cf. bimorph) ²long range electrostatic capacitive modulation

⇒stable imaging condition ²increase of 2ω as tip approaches surface ⇒high signal to noise ratio ²conical tip model in the noncontact regime ²labyrinthine domain(period 4.5∼5µm) on

CoCr thin film ²elongated grains(∼300nm×600nm) ²promising tool for studying magnetic sample

Documents

Magnetic Force Microscopy - uh.edukbyung/Mfmappl.pdf · Magnetic Force Microscopy June 10, 1998 Kim Byung-Il Dept. of Physics Seoul National Univ. BIK Seoul National University _____