Magnetic Force Microscopy
Techniques and Applications
Bruce Moskowitz
Institute for Rock Magnetism
Department of Geology and Geophysics
University of Minnesota
Workshop presented at
2008 International Conference on Rock Magnetism and its
Earth Science Applications
Institut 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
Magnetic Force Microscopy (MFM)
Topics Covered
•
Brief introduction to SPM
•
•
•
Fundamental principles of MFM
Tips, scanning, and images
Applications
Magnetic Force Microscopy (MFM)
domain
• Noncontact Scanning Probe Microscopy (SPM)
• Close relative of Atomic Force Microscopy (AFM)
• Force sensing probe is magnetic
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
AFM( left) and MFM (right) image of
Glass ceramic Magnetite
Gary Larson, 1984
Can we improve over the Bitter Method?
Bitter Method
Decoration Method: Image of magnetic
interactions between small superparamagnetic particles (ferrofuild) and
magnetic stray fields from sample
surface
Control The Force
Wet Bitter Method
Magnetite (Halgedahl, 1985)
dB/dz
Scanning Force Microscopy
10 μm
Cullity, 1974
Dried-Bitter Method
TM60 (Moskowitz et al., 1988)
MFM Workshop: Cargese, France,
June 3-7
Measure and manipulate surface
and magnetic forces
Cantilever and sharp tip
www.Vecco.com
Magnetic Force Microscopy
AFM and MFM
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
Contact Mode (AFM)
Short range forces (< 10nm)
Sharp tip interacts with
surface forces
Surface Forces
Maps surface topography
100 nm
Long range (>10 nm, <~100’s nm)
Magnetostatic & Electrostatic Forces
10 nm
Nanoscale (< 10 nm)
Van der Waals, Coulombic Forces
1 nm
Long range forces (> 10nm)
Noncontact Mode (MFM)
Magnetic tip interacts with
sample’s stray magnetic field
Atomic Scale
Ionic, Chemisorption Forces
S
S
sample
Video monitor
cantilever
scanner head
cantilever
Tip probe
Piezoelectric
bimorph
sample
sample
Computer and Image
•Sharp tip probe
•x,y,z scanner
•Deflection sensor
•Feedback control loop
•Probe oscillator (piezoelectric bimorph)
MFM=AFM with magnetized tip
Deflection sensor
Feedback
control
loop
SPM consist of 5 key components
Maps magnetic forces
A Real MFM
SPM Components
SPM controller
electronics
N
+
N
x,y,z
scanner
Cantilever
holder
x,y,z
scanner
vibration isolation
MFM Workshop: Cargese, France,
June 3-7
Digital Instruments Nanoscope IV
Deflection Sensor
Magnetic Force Microscopy
mirror
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
Several Different Methods
Photosenstive
Detector
tip and cantilever
Most widely used is Beam
Deflection Technique
Long beam path (cm’s) amplifies deflections.
Can detect cantilever deflections < 0.1 nm
Video image of cantilever
and reflection of laser
Scanner Configurations
• Piezoelectirc ceramic transducer (PZT)
• Scanned Sample
– Tip is fixed, sample mounted on scanner
– Reduced positional noise
– Limited to small samples: ~5mm x 5mm
– MFM at IRM
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
Typical scan range:
x,y: 0-100 μm
z:
0-5 μm
PSD
As the cantilever bends, the position of the
laser beam on the detector shifts.
Scanners
• Vertical motion (z) tracts surface
topography
laser
diode
PZT configured as a tubular
scanner to give 3-axis motion
(Rebecca Howland and Lisa
Benatar, 2000)
z
sample surface
MFM Workshop: Cargese, France,
June 3-7
y
x
• Scanned Tip
– Tip is mounted on scanner, sample is
fixed
– Allows larger samples to be scanned
Piezo
scanner
Scanner moves across scan
line 1 (trace) and back
(retrace).
Tip is mounted on scanner, sample is fixed
Digital Instruments (Veeco) Dimension
Magnetic Microscopy Center, Univ. of Minnesota
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
Slow scan direction Æ
Data Acquisition
4
3
2
1
Step
size
Fast Scan direction Æ
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.
Tip is fixed, sample mounted on scanner
Digital Instruments (Veeco) Nanoscope IV
Institute for Rock Magnetism, Univ. Of Minnesota
Acquisition times per image: 2-20 minutes
MFM Tips
Principles of MFM Operation
•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
10 μm
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
Fz = −k Δz
Typical dimensions
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.
l~200-300 μm
MFM Workshop: Cargese, France,
June 3-7
Z
sample
h~5-20 μm
SEM images of a commercially purchased AFM tip.
The shape of the tip resembles a truncated pyramid
(from Foss 1997)
ΔZ
Typical k values ~ 0.01-0.1 N/m
300 nm
Principles of MFM
Operation
Principles of MFM Operation
• For better sensitivity, the cantilever is
vibrated near its resonant frequency.
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
• For small deflections the system can be
modeled as a damped driven harmonic
oscillator with drive amplitude (Adrive) and
damping constant (b).
keff = k − Fz′
• Usually called AC or dynamic mode MFM
This results in a shift in the resonant frequency, ω0 Æω0’. For small
oscillation amplitudes and F’<<k (valid for MFM conditions)
• In the absence of tip-sample forces the
natural resonant frequency (ω0) and
Quality factor (Q) of the cantilever are
ω0 =
′
ω0′ = ω0 ⎡⎢1 − Fz 2k ⎤⎥
⎣
k
k
, Q=
ω0b
m
Typical amplitude variations of
10-30 nm and frequency shifts
of 1-100 Hz
ω0
2k
Fz′ , Δω0 << ω0
Δω0
Signal Detection
Amplitude
Change in the magnetic force on
the tip produces changes in
resonance frequency, amplitude,
and phase of cantilever
oscillations. All measurable
properties
R. Proksch
www.AsylumResearch.com
Frequency shifts can be measured three ways
• Phase detection: measures shifts in the phase
of cantilever oscillation
Drive Frequency
Phase (deg)
Frequency
Response of
Cantilever
⎦
Δω0 = ω0′ − ω0 ≈ −
Typical values for cantilevers:
k ~ 100 kHz and Q=100-1000
1
2
Δω0
No magnetic forces
With magnetic forces
Drive Frequency
MFM Workshop: Cargese, France,
June 3-7
• 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 Detection
Phase Detection
Slope detection: Drive the cantilever at its ‘free’ resonant frequency,
produces a shift in phase lag θ.
Amplitude Detection
3 3k
Δθ = Δω0
F′
ΔA
Amplitude
ΔA ≈
2 A0Q
Δθ = −
Δθ ≈
ω’
ωD
ω0
No magnetic forces
With magnetic forces
∂θ
∂ω ω0
ω0
2k
F′
Phase Detection
∂θ
∂ω ω0
Phase (deg)
Slope 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.
Δω0
Δω0
Δθ
Q
F′
k
ω0
No magnetic forces
Frequency
With magnetic forces
Frequency
Effect of Drive Frequency on
Amplitude Response
2
Image Contrasts
• Attractive Interactions (∂F/∂z>0)
Negative phase shift
Dark image contrast
magnetite
Weak response at
resonant frequency (2)
compared to slightly off
resonance at 1 and 2
1
3
Note Contrast Reversal
between 1 and 3
Height = 50 nm
• Repulsive Interactions (∂F/∂z<0)
Positive phase shift
Bright image contrast
f=70.71 kHz
f=70.51 kHz
∂F/∂
F/∂z<0
S
S
MFM Workshop: Cargese, France,
June 3-7
f=70.91 kHz
∂F/∂
F/∂z>0
N
+
N
1
Bit transitions in Hard Drive Media (25x25μm)
2
3
Magnetic Forces
“Real” Magnetic Tips
• Force acting on a
point dipole moment
in a magnetic field
F = ∇ ( mtip • Bsample )
• Force on dipole if
moment is fixed and
is attached to the
end of a cantilever
which oscillates
along z-axis
∂By
∂B
∂B
Fz = mxtip x + mtip
+ mztip z
y
∂z
∂z
∂z
• If mtip is uniform
and orientated along
z, m=(0,0,mz)
∂Bz
∂B
Fz = m
, Fz′ = mztip 2z
∂z
∂z
Si3N4
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.
2
tip
z
Magnetically coated Si3N4 tip
dF = ∇(mtip (r ′) • Bsample (r + r ′))dV ′
Fz′ = ∫ mtip (r ′)
tip
∂ 2 B(r + r ′)
dV ′
∂z 2
NB: The detailed magnetic
configuration of tips is usually is
not known
dV’
r’
r+r’
z
r
dV’=volume
element of
magnetically
active part of
tip
sample
Magnetic Tips: Resolution and
Sensitivity
Magnetic Contrast Formation
Phase detection:
Amplitude detection:
Δθ ≈
ΔA ≈
Q
k
∫m
tip
tip
( r ′)
∂ 2 B ( r + r ′)
dV ′
∂z 2
2 A0Q
∂ B(r + r ′)
mtip (r ′)
dV ′
∂z 2
3 3k tip∫
•
large moment produced by large extended active
tip volume
2
•
Complications:
•Separation of surface forces from magnetic forces
•Tip-sample remagnetization effects
•Micromagnetic structure of tip
MFM Workshop: Cargese, France,
June 3-7
Sensitivity proportional to moment
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
Scale bar: 350 nm
High Moment
High Sensitivity Tip
Coercivity =30 mT
Magnetization= 300 kA/m
Tip radius < 50 nm
If the stray fields from the sample are high, or the tip
coercivity is small, the sample can remagnetized the tip
Bsample > μ0 H ctip
Bsample
Scale bar: 350 nm
Low Moment
High Resolution tip
More Tips: Selectable Moment and
Coercivity
Coercivity =12.5mT
Magnetization= 80 kA/m
Tip radius < 15 nm
S
S
N
+
N
High Tip Coercivity (Hctip) prevents surface-induced
remagnetization of tip magnetization
μ0 H ctip > Bsample
www.nanosensors.com
More Tips: Selectable Moment and
Coercivity
If the tip magnetization is high, or the sample coercivity is
small, the tip can remagnetized the sample
Btip > μ0 H csample
Btip
Probe-Induced Effects
dw
Low moment tip (low Btip) can prevents tip-induced
remagnetization of surface magnetization
μ0 H csample > Btip
MFM Workshop: Cargese, France,
June 3-7
Tip Fields
Magnetic Lines of Force measured using
electron holography for a MFM Tip
with tip radius of ~ 30 nm
Magnetized along the axis of tip (zdirection)
Btip near tip surface:
Btip at distance of 10 nm:
62 mT
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
Feedback
SPM controller
electronics
Constant force Mode
Deflection of cantilever is used as
input to a feedback loop that
moves the scanner up/down in z
Deflectio
n sensor
Feedback
loop
z
Feedback loop continually adjusts the
z-position at each (x,y) data point
to keep cantilever deflection at a
selectable (constant) value
sample
x,y,z
scanner
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)
www.veeco.com
Tapping-Lift Mode
Separating Magnetism from Topography
Force Calibration Plot
• 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 tipsample 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
At “contact point”
there is an abrupt
change in slope. At
this point the
cantilever has began
to “feel” the surface
forces
Oscillation
Amplitude
Measurements are taken during two passes across each scanline
1
2
Tip-sample separation
1. In tapping mode, feedback is set to maintain amplitude just below
“knee” of curve
Digital instruments support notes, No. 229, Rev.B.
MFM Workshop: Cargese, France,
June 3-7
2. In lift mode, the z-piezo is offset so cantilever is operating just
above the knee
Tapping-Lift Mode
Separating Magnetism from Topography
First Pass
Tapping Mode
Topography
Sample Preparation
Natural (i.e., rocks) samples for magnetic analysis are usually
prepared as follows:
Second Pass
Lift Mode
Magnetic interactions
– 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
www.veeco.com
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.
Some Examples of MFM
Studies 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
MFM Workshop: Cargese, France,
June 3-7
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’) micromagnetic
structures. Important in high-magnetostrictive materials like
titanomagnetite.
Simple Symmetry Considerations
Field gradient profiles over Bloch (vertical dipole) and
Néel (horizontal dipole) Walls
Vertically Magnetized Tip
symmetric
antisymmetric
Horizontally Magnetized Tip
antisymmetric
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
symmetric
α < 10°
α
Mz
My
Mx
Domain Walls and Scratches
topography
Simple model for scratch
Horizontal dipole
+
-
-
d2B/dz2
+
scratch
-
+
Qualitative Interpretation of MFM Images
M
Antisymmetric contrast for
scratch
13x13 μm
W
Approx. Symmetric Contrast
for Bloch wall
B
DW
B
W
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 walls
Subdivided walls with Bloch lines
Pokhil and Moskowitz, 1997
Qualitative Interpretation of MFM
Images
Exsolved magnetite Inclusions in Silicates
MFM image of magnetite
grain with directions of
magnetization oblique to
surface of grain as indicated
by different contrasts
between domains.
2 μm
15x15 μm
Pokhil and Moskowitz, 1997
MFM Workshop: Cargese, France,
June 3-7
Fienberg et al., Geology, 2005
Internal Domain Wall Features
How 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.
In-Field Imaging
The switching behavior of a
magnetite particle imaged during
the descending and ascending
H0
branches of a hysteresis cycle
between ±500 Oe along the inplane [110] direction (vertical).
BL
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 sequence of images begins
with remanent state (a) after
application and removal of +500
Oe field.
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]
10x10-μm particle patterned from
250 nm thick magnetite film grown on
(110) Mg0 (Pan et al., 2002)
Néel cap
Bloch Wall
Probe Induced Effects
Imaging of SD particles in Applied Fields
Effect of tip field on domain wall (dw)
structure
Probe-induced effects
Dark patch in (a) indicates an
attractive reaction between tip
and sample, consistent with H0
from tip magnetizing the particle
and causing an attractive
interaction.
+1.4 mT
Nearly dipolar responses (b-d) of
particle in H0, consistent with SD
particle magnetized along the
direction of H0
Moment Flipping: Note that the reversal of
the field and dipolar response in (c) are
consistent with the particle magnetization
flipping
+150 mT
-150 mT
Magnetite particles from Rainbow Trout
H0 applied in plane of sample
High coercivity tip (500 mT)
MFM Images: 75nm x75 nm
Diebel et al., 2000
MFM Workshop: Cargese, France,
June 3-7
•
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.
+130 mT
(b)-(-a)
(110) magnetite
Foss et al., 1996
Imaging Artifact
Double Images
Probe Induced Effects
Double or multiple images can be produced if the tip is damaged
resulting in multiple end points in contact with the sample
(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 dw
structure 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 Artifact
Surface Contamination
Double image of a magnetite
inclusion imaged with a damaged
tip
Same inclusion imaged with a new tip
Imaging Artifact
Optical 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.
Surface debris can produce
image streaking
Same area as above but with phase
detection mode. Optical inference is
typically not a problem with phase
detection
Magnetite inclusion
Image from J. Feinberg
MFM Workshop: Cargese, France,
June 3-7
Bit transitions in Hard Drive Media (25x25μm)
Images from J. Feinberg
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 quasiperiodic features).
MFM Workshop: Cargese, France,
June 3-7
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., 290291, 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 singlecrystal 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.
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