Magnetic Force Microscopy Techniques and Applications · MFM Workshop: Cargese, France, June 3-7...

Magnetic Force MicroscopyTechniques and Applications

Bruce MoskowitzInstitute for Rock MagnetismDepartment of Geology and GeophysicsUniversity of MinnesotaWorkshop presented at 2008 International Conference on Rock Magnetism and itsEarth Science ApplicationsInstitut d'Études Scientifiques de Cargèse, France June 2-7 2008

The IRM is made possible through the Instrumentation and Facilities program of the

National Science Foundation, Earth Science Division and by funding from the University of Minnesota

MFM Workshop: Cargese, France, June 3-7

Magnetic Force Microscopy (MFM)

Topics Covered

• Brief introduction to SPM• Fundamental principles of MFM• Tips, scanning, and images• Applications

Gary Larson, 1984

domain

Magnetic Force Microscopy (MFM)• Noncontact Scanning Probe Microscopy (SPM)• Close relative of Atomic Force Microscopy (AFM)• Force sensing probe is magnetic

AFM( left) and MFM (right) image of Glass ceramic Magnetite

Developed in 1987 by Y. Martin and H. K. Wickramsinghe “Magnetic imaging by ‘force microscopy’ with 1000 Å resolution”, Appl. Phys. Lett. 50, 1455, 1987

Bitter Method

Wet Bitter MethodMagnetite (Halgedahl, 1985)

Dried-Bitter MethodTM60 (Moskowitz et al., 1988)

10 μm

Decoration Method: Image of magnetic interactions between small superpara-magnetic particles (ferrofuild) and magnetic stray fields from sample surface

Cullity, 1974

dB/dz

Control The Force

Scanning Force MicroscopyMeasure and manipulate surface and magnetic forces

Cantilever and sharp tipwww.Vecco.com

Can we improve over the Bitter Method?


Magnetic Force Microscopy

MFM produces a 2-D image of the derivatives of the stray magnetic fields (Magnetic Forces) from a sample with lateral resolutions of ~50-100 nm

Surface Forces

Atomic ScaleIonic, Chemisorption Forces

Nanoscale (< 10 nm)Van der Waals, Coulombic Forces

Long range (>10 nm, <~100’s nm)Magnetostatic & Electrostatic Forces

1 nm

10 nm

100 nm

sample

AFM and MFM

S-S

N+N

Contact Mode (AFM)

Sharp tip interacts with surface forces

Maps surface topography

Noncontact Mode (MFM)

Magnetic tip interacts with sample’s stray magnetic field

Maps magnetic forces

MFM=AFM with magnetized tip

Short range forces (< 10nm)

Long range forces (> 10nm)

SPM Components

SPM consist of 5 key components

•Sharp tip probe•x,y,z scanner•Deflection sensor•Feedback control loop•Probe oscillator (piezoelectric bimorph)

cantilever

Tip probe

sample

x,y,zscanner

vibration isolation

Deflection sensor

Feedback control

loop

Computer and Image

SPM controller electronics

Piezoelectricbimorph

x,y,zscanner

sample

Video monitorcantilever

Digital Instruments Nanoscope IV

Cantilever holder

scanner head

A Real MFM


Magnetic Force Microscopy

Advantages• High spatial resolution, better than 50 nm• Operates under ambient conditions• Measure bulk samples• In-field Measurements• Low-Temperature Measurements (but not routine)

Disadvantages• Detects stray-fields, connection to M is indirect• Magnetic tip can influence sample

Deflection Sensor

PhotosenstiveDetector

As the cantilever bends, the position of the laser beam on the detector shifts.

Long beam path (cm’s) amplifies deflections. Can detect cantilever deflections < 0.1 nm

Several Different Methods

Most widely used is Beam Deflection Technique

laser diode

mirror

tip and cantilever

PSD

Video image of cantilever and reflection of laser

Scanners

• Piezoelectirc ceramic transducer (PZT)

PZT changes dimensions when an electric field is applied, e.g., Pb(Zr,Ti)O3

• Application of x-y voltage gives raster scan motion in x,y directions

• Vertical motion (z) tracts surface topography

Typical scan range:x,y: 0-100 μmz: 0-5 μm

PZT configured as a tubular scanner to give 3-axis motion(Rebecca Howland and Lisa Benatar, 2000)

zy

xsample surface

Scanner Configurations

• Scanned Tip– Tip is mounted on scanner, sample is

fixed– Allows larger samples to be scanned

Piezoscanner

• Scanned Sample – Tip is fixed, sample mounted on scanner– Reduced positional noise– Limited to small samples: ~5mm x 5mm– MFM at IRM


Tip is fixed, sample mounted on scannerDigital Instruments (Veeco) Nanoscope IVInstitute for Rock Magnetism, Univ. Of Minnesota

Tip is mounted on scanner, sample is fixedDigital Instruments (Veeco) DimensionMagnetic Microscopy Center, Univ. of Minnesota

Data AcquisitionScanner moves across scan line 1 (trace) and back (retrace).

Steps in perpendicular direction to scan line 2, does trace/retrace, then to the line 3, etc.

Scan procedure is used to minimize hysteresis effects from piezo-scanners

StepsizeFast Scan direction

Slow

sca

n di

rect

ion

1

2

3

4

Step size is determined by the full scan size and the number of data points per line.

Scan sizes run from 10’s nm to over 100 microns with 64 to 512 data points per line.

Acquisition times per image: 2-20 minutes

MFM Tips

h~5-20 μm

l~200-300 μm

•Cantilever and tip usually made from Si or Si3N4

•Tip coated with magnetic thin film (e.g., CoCr)

•Coated tip have end radii ~20-40 nm

•MFM resolution limited by the size of the magnetic volume at tip apex and end radii

SEM images of a commercially purchased AFM tip. The shape of the tip resembles a truncated pyramid (from Foss 1997)

300 nm

10 μm

Typical dimensions

Principles of MFM Operation

Force (F) acting on a flexible cantilever will cause it to be deflected towards or away from the surface of a sample by a distance (ΔZ) according to Hooke’s Law

Where the Fz is the component of the force normal to the cantilever (z-direction) and k is the spring constant of the cantilever. It is assumed that the cantilever is oriented parallel to sample surface.

Typical k values ~ 0.01-0.1 N/m

zF k z= − Δ ΔZ

sampleZ



• For better sensitivity, the cantilever is vibrated near its resonant frequency.

• For small deflections the system can be modeled as a damped driven harmonic oscillator with drive amplitude (Adrive) and damping constant (b).

• Usually called AC or dynamic mode MFM

• In the absence of tip-sample forces the natural resonant frequency (ω0) and Quality factor (Q) of the cantilever are

00

,k kQm b

ωω

= =

Typical values for cantilevers: k ~ 100 kHz and Q=100-1000

R. Prokschwww.AsylumResearch.com


This results in a shift in the resonant frequency, ω0 ω0’. For small oscillation amplitudes and F’<<k (valid for MFM conditions)

When the cantilever experiences a force gradient (∂F/∂z=Fz’) produced by tip-sample interactions, the cantilever behaves as if it has a modified spring constant

eff zk k F ′= −

12

0 0

00 0 0 0 0

1 2

,2

z

z

Fk

Fk

ω ω

ωω ω ω ω ω

′⎡ ⎤′ = −⎢ ⎥⎣ ⎦

′ ′Δ = − ≈ − Δ <<

Δω0

Am

plit

ude

Drive Frequency

Drive Frequency

Phas

e (d

eg)

Δω0

Change in the magnetic force on the tip produces changes in resonance frequency, amplitude, and phase of cantilever oscillations. All measurable properties

Typical amplitude variations of 10-30 nm and frequency shifts of 1-100 Hz

No magnetic forcesWith magnetic forces

Frequency Response of Cantilever

Signal DetectionFrequency shifts can be measured three ways

• Phase detection: measures shifts in the phase of cantilever oscillation

• Amplitude detection: measures shifts in the oscillation amplitude of cantilever

• Frequency modulation: measure shifts in resonance frequency of cantilever

Phase detection and Frequency modulation usually produces superior results to Amplitude detection


Amplitude DetectionSlope detection: Drive the cantilever at a fixed frequency (ωD)

slightly off resonance (ω0) such that ΔA for a shift in resonant frequency (Δω0= ω0- ω’) is maximized.

023 3

A QA Fk

′Δ ≈

Amplitude Detection

Am

plit

ude

Frequency

ΔA

Δω0


ω0

ω’ ωD

Phase DetectionSlope detection: Drive the cantilever at its ‘free’ resonant frequency,

produces a shift in phase lag θ.

0

0

0

0

2F

k

Q Fk

ω

ω

θθ ωω

ω θθω

θ

∂Δ = Δ

∂

∂′Δ = −∂

′Δ ≈

Frequency

Phas

e (d

eg)

ω0

Δθ

Δω0Phase Detection


Image Contrasts

• Attractive Interactions (∂F/∂z>0) Negative phase shiftDark image contrast

• Repulsive Interactions (∂F/∂z<0)Positive phase shiftBright image contrast

S-S

N+N

∂∂F/F/∂∂z>0z>0∂∂F/F/∂∂z<0z<0

magnetite

Effect of Drive Frequency on Amplitude Response

1 3

2

f=70.51 kHz

1

f=70.71 kHz

2

f=70.91 kHz

3

Bit transitions in Hard Drive Media (25x25μm)

Note Contrast Reversal between 1 and 3

Weak response at resonant frequency (2) compared to slightly off resonance at 1 and 2

Height = 50 nm


Magnetic Forces

• Force acting on a point dipole moment in a magnetic field

• Force on dipole if moment is fixed and is attached to the end of a cantilever which oscillates along z-axis

• If mtip is uniform and orientated along z, m=(0,0,mz)

( )tip sampleF m B= ∇ •

ytip tip tipx zz x y z

BB BF m m mz z z

∂∂ ∂= + +

∂ ∂ ∂

2

2,tip tipz zz z z z

B BF m F mz z

∂ ∂′= =∂ ∂

“Real” Magnetic TipsSi3N4

Magnetically coated Si3N4 tip

r’

r

r+r’

dV’2

2

( )( )z tiptip

B r rF m r dVz

′∂ +′ ′ ′=∂∫

In general, the force acting on an MFM tip is actually dependent on the geometry of the tip and its micromagnetic structure as well as the magnetic stray field from the sample.

z

( ( ) ( ))tip sampledF m r B r r dV′ ′ ′= ∇ • +

dV’=volume element of magnetically active part of tip

sample

NB: The detailed magnetic configuration of tips is usually is not known

Magnetic Contrast Formation

2

2

( )( )tiptip

Q B r rm r dVk z

θ′∂ +′ ′Δ ≈

∂∫2

02

2 ( )( )3 3 tip

tip

A Q B r rA m r dVzk

′∂ +′ ′Δ ≈∂∫

Phase detection:

Amplitude detection:

Complications:

•Separation of surface forces from magnetic forces•Tip-sample remagnetization effects•Micromagnetic structure of tip

Magnetic Tips: Resolution and Sensitivity

• Sensitivity proportional to momentlarge moment produced by large extended active

tip volume

• Resolution inversely proportional to active tip volume

Thin tip results in low moment

• Cannot maximize resolution and sensitivity simultaneously


More Tips: Selectable Moment and Coercivity

www.nanosensors.com

Coercivity =30 mTMagnetization= 300 kA/mTip radius < 50 nm

Coercivity =12.5mTMagnetization= 80 kA/mTip radius < 15 nm

High MomentHigh Sensitivity Tip

Low MomentHigh Resolution tip

Scale bar: 350 nm

Scale bar: 350 nm


If the stray fields from the sample are high, or the tip coercivity is small, the sample can remagnetized the tip

S-S

N+N

0tipc sampleH Bμ >

Bsample

High Tip Coercivity (Hctip) prevents surface-induced

remagnetization of tip magnetization

0tip

sample cB Hμ>


If the tip magnetization is high, or the sample coercivity is small, the tip can remagnetized the sample

0samplec tipH Bμ >

Btip

Low moment tip (low Btip) can prevents tip-induced remagnetization of surface magnetization

0sample

tip cB Hμ>

dwProbe-Induced Effects

Tip FieldsMagnetic Lines of Force measured using

electron holography for a MFM Tip with tip radius of ~ 30 nm

Magnetized along the axis of tip (z-direction)

Btip near tip surface: 62 mTBtip at distance of 10 nm: 31 mT

Field at distance ~ 2 tip radii away from tip is approximately dipolar

760 nm x 700 nm

D. Streblechenko et al., Quantitative magnetometry using electron holography: Field profiles near magnetic force microscope tips, IEEE. Trans. Mag., 32, 4124-4129, 1996


Separation of magnetic and topographic interactions

• An image taken with a magnetic tip contains information about both the topography and the magnetic properties of a surface.

• Critical for the interpretation of MFM data is the separation of the response due to magnetic (long-range) interactions from the response due to topographic (short-range) interactions

Solution: “Terrain Correction”

Collect a series of images at two different tip heights

FeedbackConstant force Mode

Deflection of cantilever is used as input to a feedback loop that moves the scanner up/down in z

Feedback loop continually adjusts the z-position at each (x,y) data point to keep cantilever deflection at a selectable (constant) value

With the cantilever deflection held constant, the total force between tip and sample is constant (i.e. constant force)

The image of the surface topography is generated from the motion of the scanner, z(x,y)

sample

x,y,zscanner

Deflection sensor

Feedback loop

SPM controller electronics

www.veeco.com

z

Tapping-Lift ModeSeparating Magnetism from Topography

Measurements are taken during two passes across each scanline

• During first trace/retrace (1-2), TappingMode records z(x,y), surface topography (feedback on)

• During second trace/retrace (4-5), z(x,y) recorded in first pass is repeated with an added offset (3, lift height) so that a constant tip-sample separation is maintained (feedback off). Lift heights ~10-100 nm

• During LiftMode, the spatial variation of the cantilever deflection [ΔA(x,y) or Δθ(x,y,)] is used directly to generate an image of magnetic interactions, while minimizing topographical forces

Digital instruments support notes, No. 229, Rev.B.

Force Calibration Plot

Tip-sample separation

Osc

illat

ion

Am

plit

ude

At “contact point” there is an abrupt change in slope. At this point the cantilever has began to “feel” the surface forces

1. In tapping mode, feedback is set to maintain amplitude just below “knee” of curve

12

2. In lift mode, the z-piezo is offset so cantilever is operating just above the knee


Tapping-Lift ModeSeparating Magnetism from TopographyFirst PassTapping ModeTopography

Second PassLift ModeMagnetic interactions

Hard drive media at 50 nm lift height. The topographic image should be very different from the magnetic image if separation of surface from magnetic forces was successful.

www.veeco.com

Sample PreparationNatural (i.e., rocks) samples for magnetic analysis are usually

prepared as follows:

– Step 1: Polish the surface with diamond pastes starting with coarse grit and working down to finer grits (e.g., 30μ, 15μ, 3μ, 0.25μ grit)

– Step 2: Final polish with colloidal silica to remove residual surface stresses produced by mechanical polishing in step 1

Step 2 is almost always necessary because surface stresses produced during step 1 can give rise to near-surface maze-like magnetic domains that can obscure intrinsic (‘undisturbed’) micromagneticstructures. Important in high-magnetostrictive materials like titanomagnetite.

Some Examples of MFMStudies in Rock magnetism

• Micromagnetic structures in PSD and single crystal magnetite (Bloch walls, Néel caps, Bloch lines)

• Micromagnetic structures in magnetite inclusions in silicates

• Micromagnetic structures in natural titanomagnetites• Micromagnetic structures in magnetite below Verwey

transition (T<120 K)• Imaging magnetic particles in bacteria and other

organisms

Simple Symmetry ConsiderationsField gradient profiles over Bloch (vertical dipole) and Néel (horizontal dipole) Walls

Vertically Magnetized Tip Horizontally Magnetized Tip

symmetric antisymmetric symmetricantisymmetric

Complication

Slight tilt (α) of cantilever relative to sample plane can produce nonzero parallel component of Mtip(x,y) and a ∂2Bx/∂z2 or ∂2By/∂z2 term in the force gradient

MzMy

Mx

α

α < 10°


Domain Walls and Scratches

+ ++ M

WB

WB

d2B/dz2

Antisymmetric contrast for scratch

Approx. Symmetric Contrast for Bloch wall

topography

--

-

DW

scratch

Simple model for scratchHorizontal dipole

Qualitative Interpretation of MFM Images

MFM image of magnetite grain with direction of magnetization nearly parallel to surface of grain as indicated by similar contrast between domains.

High contrast (alternating polarity) domain wallsSubdivided walls with Bloch lines

13x13 μm

Pokhil and Moskowitz, 1997


15x15 μm

2 μm

MFM image of magnetite grain with directions of magnetization oblique to surface of grain as indicated by different contrasts between domains.

Pokhil and Moskowitz, 1997


Fienberg et al., Geology, 2005

Exsolved magnetite Inclusions in Silicates


Internal Domain Wall FeaturesHow Symmetric is Response over Bloch Wall in Magnetite?

• MFM image of a subdivided 180° domain wall in (110) single crystal magnetite. One Bloch line can be seen in this portion of the wall.

• MFM response profiles of two opposite polarity segments. The attractive (black) profile has been inverted and offset in order to compare the symmetries of the profiles.

• The asymmetrical-shaped wall profile is consistent with a Néel cap structure at the surface termination of the interior Bloch wall [after Foss et al., 1998]

BL

Néel cap

Bloch Wall

In-Field Imaging

The switching behavior of a magnetite particle imaged during the descending and ascending branches of a hysteresis cycle between ±500 Oe along the in-plane [110] direction (vertical).

The sequence of images begins with remanent state (a) after application and removal of +500 Oe field.

10x10-μm particle patterned from250 nm thick magnetite film grown on (110) Mg0 (Pan et al., 2002)

H0

Imaging of SD particles in Applied Fields

+1.4 mT +150 mT -150 mT +130 mT

Magnetite particles from Rainbow TroutH0 applied in plane of sampleHigh coercivity tip (500 mT)MFM Images: 75nm x75 nm

Diebel et al., 2000

Moment Flipping: Note that the reversal of the field and dipolar response in (c) are consistent with the particle magnetization flipping

Nearly dipolar responses (b-d) of particle in H0, consistent with SD particle magnetized along the direction of H0

Probe-induced effects

Dark patch in (a) indicates an attractive reaction between tip and sample, consistent with H0from tip magnetizing the particle and causing an attractive interaction.

Probe Induced EffectsEffect of tip field on domain wall (dw)

structure

• MFM profiles (a) and (b) measured above the same 180° dw in magnetite at a lift height of 30 nm.

• Profile (a) measured with Mtip antiparallel(repulsive case) to the dw magnetization. Profile (b) measured with Mtip parallel (attractive case)to the dw.

• In (c) profile (a) was inverted and superimposed on profile (b) The difference between them has been shaded.

• Profile (d) is the difference profile, b-(-a) which shows the additional, attractive MFM response due to the effect of the tip field on the dw structure.

(110) magnetite

Foss et al., 1996

(b)-(-a)


Probe Induced Effects

(b) Results of 2D micromagnetic simulation of a 180° dw in Fe3O4 showing a Néel cap near surface (Xu and Dunlop, 1996).

(c) A cartoon of the 180° dw structure in (b)

(d) Repulsive MFM measurement of dwstructure in which the tip is magnetized antiparallel to the bulk dipole moment. In this case, the tip field enhances the Néel cap.

(e) Attractive dw measurement for which the tip is magnetized parallel to the bulk dipole moment. The tip field reduces the Néel cap in this case.

Foss et al., 1996

Imaging ArtifactDouble Images

Double or multiple images can be produced if the tip is damaged resulting in multiple end points in contact with the sample

Double image of a magnetite inclusion imaged with a damaged tip

Same inclusion imaged with a new tip

Images from J. Feinberg

Imaging ArtifactSurface Contamination

Surface debris can produce image streaking

Magnetite inclusionImage from J. Feinberg

Imaging ArtifactOptical Interference

Interference between incident and reflected light from sample surface during amplitude scanning. Can be reduced/eliminated by moving laser alignment further down the cantilever away from tip.

Same area as above but with phase detection mode. Optical inference is typically not a problem with phase detection

Bit transitions in Hard Drive Media (25x25μm)


Image Artifacts

If an image contains suspicious looking features, which could be imaging artifacts, the following are possible solutions

• Redo the scan to ensure that the image is repeatable.• Rotate the sample and/or scan in a different

direction.• Change the scan size and take an image to ensure that

the features scale properly.• Change the scan speed and take another image

(especially if you see suspicious periodic or quasi-periodic features).

Gallery of MFM images from natural and synthetic magnetites

Starting clockwise from top left: (1) glass ceramic magnetite (Pokhil and Moskowitz, 1997); (2) magnetite inclusion in clinopyroxene (Feinberg et al., 2005); (3) freeze-dried cell of magneto-tactic bacterial stain MV1 containing a chain of magnetosomes(Proksch et al., 1995); (4) vortex-like feature, possibly associated with a dislocation, in hydrothermal magnetite (Muxworthy and Williams, 2006); (5) natural titanomagnetite (Prévot et al., 2001); (6) magnetite inclusions in pyroxene (Frandsen et al., 2004); (7) natural oxidized titanomagnetite (Krása et al., 2005); (8) single crystal (100) TM60; (9) magnetite inclusion in clinopyroxene (from J. Feinberg); (10) single crystal (110) magnetite (Foss et al., 1998); (11) eptixial (110) magnetite grown on (110) MgO (Pan et al., 2001); (12) single crystal (110) magnetite at T≈ 100 K (Moloni et al., 1996); (13) ~40 nm sized magnetite particle from rainbow trout (Oncorhynchus mykiss) in an applied field of 130 mT (Diebel et al., 2000); (14) single crystal (110) magnetite, surface slightly misaligned from (110) plane (from D. Dahlberg); (14) inclusion in clinopyroxene containing magnetite-ulvospinel exsolution texture (Feinberg et al., 2005)

Bibliography: Applications of MFM in Rock Magnetism

Albrecht, M., V. Janke, S. Sievers, U. Siegner, D. Schüler, and U. Heyan (2005). Scanning force microcopy study of biogenic nanoparticles for medical applications, J. Mag. Magnet. Mater., 290-291, 269-271.

Cloete, M., Hart, R. J., Schmid, H. K., Drury, M., Demanet, C. M., & Sankar, K. V. (1999). Characterization of magnetite particles in shocked quartz by means of electron- and magnetic force microscopy; Vredefort, South Africa. Contributions to Mineralogy and Petrology, 137(3), 232-245.

Diebel, C.E., Roger Proksch, Colin R. Green, Peter Neilson and Michael M. Walker (2000). Magnetite defines a vertebrate magnetoreceptor. Nature, 406, 299-302.

Feinberg, J. M., Scott, G. R., Renne, P. R., & Wenk, H. (2005). Exsolved magnetite inclusions in silicates; features determining their remanence behavior. Geology, 33(6), 513-516. doi:10.1130/G21290.1

Foss, S., R. Proksch, E.D. Dahlberg, B. Moskowitz, and B. Walsh (1996). Localized micromagnetic perturbation of domain walls in magnetite using a magnetic force microscope, Appl. Phys. Lett., 69, 3426-3428.

Foss, S., Moskowitz, B. M., Proksch, R., & Dahlberg, E. D. (1998). Domain wall structures in single-crystal magnetite investigated by magnetic force microscopy, Journal of Geophysical Research, 103(B12), 30-30,560.

Frandsen, C., Stipp, S. L. S., McEnroe, S. A., Madsen, M. B., & Knudsen, J. M. (2004). Magnetic domain structures and stray fields of individual elongated magnetite grains revealed by magnetic force microscopy (MFM). Physics of the Earth and Planetary Interiors, 141(2), 121-129. doi:10.1016/j.pepi.2003.12.001

Gruetter, P., Allenspach, R., Williams, W., Hoffmann, V., Heider, F., Goeddenhenrich, T., (1994). Can magnetic-force microscopy determine micromagnetic structures? Geophysical Journal International, 116(2), 502-507.

Haag, M., Heller, F, Lutz, M., and Reusser, E. (1993). Domain observations of the magnetic phases in volcanics with self-reversed magnetization. Geo. Res. Lett., 20, 675-678.

Hartmann, U., (1999). Magnetic Force Microscopy, Ann. Rev. Mater. Sci., 29, 53-87.

Jaeckel, A., Romstedt, J., & Reimold, W. U., (1999). Preliminary results of magnetic force microscopy studies of magnetites in the orgueil meteorite; 62nd annual meeting of the meteoritical society; abstracts. Meteoritics & Planetary Science, 34(4), 58-59.

Krása, D., Shcherbakov, V. P., Kunzmann, T., & Petersen, N. (2005). Self-reversal of remanent magnetization in basalts due to partially oxidized titanomagnetites. Geophysical Journal International, 162(1), 115-136. doi:10.1111/j.1365-246X.2005.02656.x

Martin, Y, and H.K. Wickramasinghe, (1987). Magnetic imaging by “force microscopy” with 1000 Å resolution, Appl. Phys. Lett, 50, 1455-1457.

Moloni, K., Moskowitz, B. M., Dahlberg, E. D., (1996). Domain structures in single crystal magnetite below the Verwey transition as observed with a low-temperature magnetic force microscope, Geophysical Research Letters, 23(20), 2851-2854.

Muxworthy, A. R., and W. Williams (2006), Observations of viscous magnetization in multidomain magnetite, J. Geophys. Res., 111, B01103, doi:10.1029/2005JB003902.

Pokhil, T.G., and B.M. Moskowitz (1996). Magnetic force microscope study of domain wall structures in magnetite, J. Appl. Phys., 79 , 6064-6066.

Pokhil, T. G., & Moskowitz, B. M. (1997). Magnetic domains and domain walls in pseudo-single-domain magnetite studied with magnetic force microscopy. Journal of Geophysical Research, 102(B10), 22-22,694.

Prévot, M., Hoffman, K. A., Goguitchaichvili, A., Doukhan, J., Shcherbakov, V. P., & Bina, M. (2001). The mechanism of self-reversal of thermoremanence in natural hemoilmenite crystals; new experimental data and model, Physics of the Earth and Planetary Interiors, 126(1-2), 75-92.

Proksch, R.B., T.E. Schaffer, B.M. Moskowitz, E.D. Dahlberg, D.A Bazylinski, and R.B Frankel (1995) Magnetic force microscopy of the submicron magnetic assembly in a magnetotactic bacterium, Appl. Phys. Letts., 66, 2582-4

Proksch, R., S. Foss, E. D. Dahlberg, (1994). High resolution magnetic force microscopy of domain wall fine structures, IEEE Trans. Mag., 30, 4467-4469.

Rauschenbach, I., I. Weber, T. Stephan, E.K., Jessberger, and C. Schröder (2004). Magnetic force microscopy of primitive achondrites, (abstract) Lunar and Planetary Science XXXV Meeting.

Rugar, D., J. Mamin, P. Guethner, S.E. Lambert, J.E. Stern, I. McFadyen, and T. Yogi, (1990), Magnetic force microscopy: General principles and application to longitudinal recording media media. J. Appl Phys., 68, 1169-1183.

Sarid, D., (1991). Scanning Force Microscopy, Oxford University Press.

Streblechenko, D. et al.,(1996). Quantitative magnetometry using electron holography: Field profiles near magnetic force microscope tips, IEEE. Trans. Mag., 32, 4124-4129.

Williams, W., Hoffmann, V., Heider, F., Goeddenhenrich, T., & Heiden, C. (1992). Magnetic force microscopy imaging of domain walls in magnetite. Geophysical Journal International, 111(3), 417-423.

Xu, S., Dunlop, D. J., (1996). Micromagnetic modeling of Bloch walls with Néel caps in magnetite; recent progress in rock magnetism. Geophysical Research Letters, 23(20), 2819-2822.

Magnetic Force Microscopy Techniques and Applications · MFM Workshop: Cargese, France, June 3-7...

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