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What the NSA is patenting
I just spent a pleasant hour or so searching a patent database for all
patents assigned to the NSA. There's some interesting stuff:
"Self-locking, tamper-evident package"
Method of retrieving documents that concern the same topic"
Fifty-Four patents total. (Used to be they just kept stuff secret; now
they patent some of it.) Attached is the most interesting thing I found: a
patent on techniques for reading data off overwritten magnetic media.
Bruce
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United States Patent Patent Number: 5264794
Date of Patent: 23 Nov 1993
Method of measuring magnetic fields on magnetically recorded media using
a scanning tunneling microscope and magnetic probe
Inventor(s): Burke, Edward R., Silver Spring, MD, United States
Mayergoyz, Isaak D., Rockville, MD, United States
Adly, Amr A., Hyattsville, MD, United States
Gomez, Romel D., Beltsville, MD, United States
Assignee: The United States of America as represented by the Director,
National Security Agency, Washington, DC, United
States (U.S. government)
Appl. No.: 92-947693
Filed: 21 Sep 1992
Int. Cl. ............. G01R033-00; G01R033-12
Issue U.S. Cl. ....... 324/260.000; 324/212.000
Current U.S. Cl. ..... 324/260.000; 324/212.000
Field of Search ...... 324/212; 324/244; 324/260; 324/262
Reference Cited
PATENT DOCUMENTS
Patent
Number Date Class Inventor
---------- --------- -------------- ------------
US 4232265 Apr 1980 324/260.000 Smirnov
US 4567439 Jan 1986 324/304.000 McGregor
US 4625166 Nov 1986 324/223.000 Steingroever et al.
US 4710715 Dec 1987 324/307.000 Mee et al.
US 4791368 Dec 1988 324/301.000 Tsuzuki
OTHER PUBLICATIONS
Magnetic Tip Sees Fine Detail, Lost Data, E. Pennisi, Feb. 29, 1992,
Science News, p. 135.
Magnetic Field Imaging by Using Magnetic Force Scanning Tunneling
Microscopy, Gomez, Burke, Adly, Mayergoyz, Feb. 17, 1992 pp. 906-908
Appl. Phy. Lett.
Tunneling-Stabilized Magnetic Force Microscopy of Bit Tracks . . . ,
Rice, Moreland, IEEE Trans. on Magnetics vol. 27 No. 3 May 1998, pp.
3452-3454.
Magnetic Force Scanning Tunneling Microscope Imaging of Overwritten
Data, Gomez, Adly, Mayergoyz, Burke, IEEE Journal of Magnetics, Sep.
1992.
Analysis of Tunneling Magnetic Force Microscopy Using a Flexible
Triangular Probe, Burke, Gomez, Adly, Mayergoyz, IEEE Journal of
Magnetics, Sep. 1992.
Magnetic Force Microscopy: General Principles and Application to . . . ,
Rugar, Mamin, et al. Journal of Appl. Phys., Aug. 1, 1990 pp. 1169-1183.
Analysis of In-Plane Bit Structure by Magentic Force Microscopy, Wadas,
Grutter, Guntherodt, J. Appl Phys. Apr. 1, 1990 pp. 3462-3467.
Theoretical Approach to Magnetic Force Microscopy, Wadas, Grutter,
American Physical Society, Jun. 1, 1989, 12,013-17.
Theory of Magnetic Imaging by Force Microscopy, Saenz, Garcia,
Slonczewski, Appl. Phys. Letters, Oct. 10, 1988 pp. 1449-1451.
Description of Magnetic Imaging in Atomic Force Microscopy, Wadas,
Journal of Magnetism and Magnetic Materials, Aug. 1989 pp. 263-268.
Art Unit - 267
Primary Examiner - Snow, Walter E.
Attorney, Agent or Firm - Morelli, Robert D.; Maser, Thomas O.
---------------------
8 Claim(s), 4 Drawing Figure(s), 4 Drawing Page(s)
ABSTRACT
The present invention discloses a method of measuring magnetic fields on
magnetically recorded media. The method entails replacing the metal tip
typically used with a scanning tunneling microscope with a flexible
thin-film nickel of iron magnetic probe. The present invention describes
a mathematical equation that relates probe position to magnetic field
strength. In order to establish a tunneling current between the magnetic
probe and the magnetically recorded media, any protective layer on the
magnetically recorded media is removed. The magnetic probe and the
magnetically recorded media may be coated with at least three-hundred
angstroms of gold in order to reduce spurious probe deflections due to
oxide growths on either the magnetic probe or the magnetically recorded
media. The scanning tunneling microscope is designed to maintain a
constant tunneling current between the probe and the item being scanned.
The present invention uses the scanning tunneling microscope to scan the
recording tracks of magnetically recorded media. Any change in the
magnetic field of the magnetically recorded media will cause a change in
the tunneling current. The microscope will change the position of the
probe in order to maintain a constant tunneling current. These changes
in position are recorded as an image. A mathematical equation that
relates probe position to magnetic field strength is then used to
extract the magnetic fields of the magnetically recorded media from the
recorded image of probe positions.
BACKGROUND OF THE INVENTION
1. Field of Invention
This invention relates to a method of measuring the magnetic fields of a
recorded surface and more particularly to a method of measuring the
magnetic fields of magnetically recorded information using a scanning
tunneling microscope.
2. Description of Related Art
One of the most active areas in magnetic recording technology is the
study of processes occurring at the microscopic level. In recent years,
several techniques based on scanning tunneling microscopy have been
developed to study magnetization patterns in recording media with
sub-micron resolution. These include magnetic force microscopy (MFM),
and tunneling stabilized (TS) or magnetic force scanning tunneling
microscopy (MFSTM).
In "Tunneling-stabilized Magnetic Force Microscopy of Bit Tracks on a
Hard Disk," a published article by P. Rice and J. Moreland in IEEE
Trans. Magn., vol. Mag-27, 1991, pp. 3452-3454 it was shown that
magnetic data on a hard disk can be imaged with a tunneling microscope
by using a flexible triangular probe cut from a thin film of magnetic
material.
In U.S. Pat. No. 4,791,368, entitled "Automatic Magnetic Field Measuring
Apparatus Using NMR Principles," a method of more accurately measuring
magnetic fields is described which entails surrounding the item being
measured with a coil, initially measuring the magnetic field, estimating
the magnetic resonance frequency of the item being measured, applying a
high-frequency voltage of the estimated magnetic resonance frequency,
iteratively refining the estimate of the magnetic resonance frequency
until the variation in coil inductance is a maximum, and finally, from
the resulting magnetic resonance frequency, calculating the magnetic
field of the item being measured.
In U.S. Pat. No. 4,710,715, entitled "Method Of Mapping Magnetic Field
Strength And Tipping Pulse Accuracy Of An NMR Imager," a method of
checking the homogeneity of a magnetic field by producing contour lines
of equal field strength is disclosed that utilizes a different
preparation phase for NMR imaging. The new preparation phase consists of
tipping the spins of the volume elements with a 90 degree wait 90 degree
RF pulse sequence.
In U.S. Pat. No. 4,625,166, entitled "Method For Measuring Magnetic
Potentials Using Hall Probes," a method of measuring the hysteresis
curve of a magnetic material is disclosed. The steps of the method
include subjecting the material to a magnetic field, summing the
voltages from a plurality of Hall probes that are spaced in an arc,
obtaining the magnetic flux density in the material, and deriving a
hysteresis curve of the material from the magnetic flux density and the
magnetic field intensity.
In U.S. Pat. No. 4,567,439, entitled "Apparatus For Measuring The
Magnitude Of A Magnetic Field," a method of measuring the magnitude of a
magnetic field is disclosed. The steps of the method include magnetizing
the item, inducing an oscillating magnetic field, permitting free
precession, inducing signals during free precession, and producing an
output that is proportional to the frequency deviation of the induced
signals.
In U.S. Pat. No. 4,232,265, entitled "Device For Measuring Intensity Of
Magnetic Or Electromagnetic Fields Using Strain Gauges Mounted On
Ferromagnetic Plates," a device is disclosed that measures magnetic
fields by monitoring the electrical signal produced by strain gauges
which are connected to overlapping ferromagnetic plates. The magnetic
field to be measured causes the gap between the plates to change which
in turn causes the electrical output signal from the strain gauges to
change. The magnitude of the electrical signal indicates the magnitude
of the magnetic field.
SUMMARY OF THE INVENTION
It is an object of this invention to provide a method of measuring
magnetic fields.
It is another object of this invention to provide a method of measuring
magnetic fields of magnetically recorded information.
It is another object of this invention to provide a method of measuring
magnetic fields of magnetically recorded information using a scanning
tunneling microscope.
It is another object of this invention to provide a method of measuring
magnetic fields of magnetically recorded information using a scanning
tunneling microscope that incorporates a thin-film magnetic probe that
is used to relate probe position to magnetic field strength.
These objects are achieved by using a magnetic force scanning tunneling
microscope to measure magnetic fields. This microscope, which is
typically used for recording surface topology of an item, is modified by
replacing the fine metallic tip with a flexible magnetic probe.
In the typical operation of a scanning tunneling microscope, the fine
metallic tip, which is held at a bias potential, is placed in close
proximity to the sample surface so that a tunneling current is
established between the tip and the sample surface. As the tip scans
across the surface, changes in surface topology cause the tunneling
current to change. In order to maintain a constant tunneling current,
the microscope changes the position of the tip. These changes in tip
position are recorded in a two dimensional image that reflects the
surface topology of the item scanned.
The present invention shows that by replacing the tip with a magnetic
probe and by scanning recorded media along the recording tracks, which
have no significant topological variations, the scanning tunneling
microscope can be used to record the magnetic fields of the recorded
media.
Just as surface variations caused changes in the tunneling current,
changes in magnetic field cause changes in the tunneling current. The
microscope will change the position of the probe, as it did with the
metallic tip, in order to maintain a constant tunneling current. These
position changes are recorded and, with the use of a mathematical
equation that relates probe position to magnetic field strength, are
used to measure the magnetic fields of the recorded media.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a typical image created by a scanning
tunneling microscope;
FIG. 2 is a perspective view of the magnetic probe superimposed upon a
graph that indicates the critical dimensions, coordinates, and angles;
FIG. 3 is a chart showing the relationship between magnetic probe
amplitude and the angle theta; and
FIG. 4 is a chart that compares theoretically expected results of probe
amplitude versus the angle phi against experimentally obtained data of
probe amplitude versus the angle phi.
DESCRIPTION OF PREFERRED EMBODIMENTS
There is a growing interest in measuring magnetic fields created by
magnetization patterns recorded on magnetic media. Since these fields
vary over microscopic distances, various microscopic techniques have
been developed. The present invention describes a method for measuring
magnetic fields on magnetically recorded media by using a modified
scanning tunneling microscope. These magnetic fields are measured by
determining the relationship between the microscope probe movement and
magnetic field strength.
The scanning tunneling microscope operates by scanning the surface of an
object with a metal tip. The tip is biased with a dc voltage and placed
close enough to the surface of the object to establish a tunneling
current. Changes in the surface topology of the object cause a change in
the tunneling current. A feedback system in the microscope adjusts the
vertical position of the tip in order to maintain a constant tunneling
current. As the tip is scanned across the object, the changes in tip
position are recorded. These recordings reflect the surface topology of
the item scanned. An example of such an image is indicated in FIG. 1.
The present invention discloses a method for using a modified magnetic
force scanning tunneling microscope to measure magnetic fields. The
metal tip of the microscope is replaced with a thin-film magnetic probe
20 of FIG. 2. Instead of scanning the surface topology of an item, the
modified microscope is used to scan individual recording tracks of a
magnetically recorded media which do not have any significant
topological variations.
Just as was done with the metal tip, the probe 20 is placed in close
proximity with the recorded media in order to establish a tunneling
current. The probe 20 is then scanned along the recording tracks of the
magnetically recorded media. Changes in magnetic field cause a change in
the tunneling current. The microscope then changes the position of the
probe 20 in order to maintain a constant tunneling current. These
position changes are recorded and, with the use of a mathematical
equation that relates probe position to magnetic field strength, used to
measure the magnetic fields of the recorded media.
The energy of interaction between the probe 20 and the magnetic field
emanating from the sample surface was evaluated using the geometry as
shown in FIG. 2. It was assumed that the field interacts only with the
last magnetic domain (i.e., a region that is magnetized in one direction
only) at the tip of the probe 20 and that this domain is magnetized
uniformly along its length. The magnetization pattern is typically a
recorded signal with repetition in the x-direction and infinite extent
in the y-direction.
Measurements were taken with a scanning tunneling microscope operating
in a constant current mode with a maximum scan range in excess of 100
micrometers in each lateral dimension. The tunneling current is
typically 0.11 nanoamperes, at a dc bias of 2.7 volts. The scan rate is
about 1.5 lines per second. Any protective coatings on the recorded
media must be removed. Adverse effects due to surface oxides on the
probe 20 or recorded media are reduced by coating the recorded media and
the tip of the probe 20 with approximately 300 angstroms of gold. Such a
coating is typically deposited by conventional sputtering techniques.
The tunneling current changes as the probe 20 interacts with the surface
and its magnetic fields. Feedback compensates for this change and the
vertical displacement of the probe 20, .DELTA.z, is recorded as a
function of its horizontal position. Therefore, a two dimensional image,
similar to the image shown in FIG. 1, is formed that maps variations in
z as a function of lateral position, i.e., .DELTA.z(x,y). Such an image
reflects both the topological and magnetic features of the magnetically
recorded media. With the appropriate choice of probe 20 properties, it
is possible to extract the magnetic fields from this image.
The magnetic contribution to the displacement, .DELTA.z, is determined
by the forces acting on the probe 20. Several theoretical calculations
that relate recorded images using such a probe 20 with the forces on the
probe 20 have appeared in "Analysis of in-plane bit structure by
magnetic force microscopy", a published article by A. Wadas, P. Grutter,
and H. Guntherodt in J. Appl. Phys., vol. 67, 1990, p. 3462 and "Theory
of magnetic imaging by force microscopy," a published article by J.
Saenz, N. Garcia, and J. Slonczewski in Appl. Phys. Lett. 53, 1988, p.
1449. However, these calculations have not directly addressed the issue
of the dependence of image contrast and resolution on the orientation of
the probe 20 as the present invention does.
By assuming that the probe 20 is uniformly magnetized along the
direction of its length, the vertical displacement can be modeled by
considering the interaction of the surface magnetic fields with a
magnetic charge distribution at the tip of the probe 20. Flexible
magnetic probes 20 made of nickel (Ni) can be used. The probes 20 used
in the present invention were fabricated by evaporating approximately
500 nanometers of Ni onto pre-patterned substrates. These films retain
the shape of the substrate pattern when peeled away from the pattern. A
typical probe would have a thickness (t) of less than or equal to one
micrometer, a length (l) of two millimeters, and a width (w) of one
micrometer. The angle delta is typically 15 degrees. The angle theta can
vary over a range of zero degrees to pi/2 degrees. The angle phi can
vary over a range of -pi/2 to pi/2. It has been observed that these
probes 20 produce consistent images of magnetization patterns.
FIG. 1 also shows the parameters for the equations used in the present
invention. It was assumed that the recorded signal is a repetitive
pattern of wavelength lambda (.lambda.) in the x direction, with
infinite extent in the y direction.
In "Theoretical approach to magnetic force microscopy," a published
article by A. Wadas and P. Grutter in Phys. Rev. B, vol. 39, no. 16,
June 1989, pp. 12013-12017 it was shown that the energy (E) of
interaction between the field from the pattern and the last domain on
the probe tip can be expressed as
E=-.intg.H.multidot.M dV,
where H is the magnetic field from the pattern, M is the magnetization
of the domain, and V is the volume of the domain. The magnetic field can
be expressed as the gradient of a scalar potential capital phi (.PHI.),
and, if the magnetization is uniform (.gradient..multidot.M=0 is
sufficient), then the above equation for E can be rewritten as
E=.intg..gradient..multidot.(.PHI.M) dV.
This new equation for E can then be converted to a surface integral
using Gauss's theorem to obtain
E=.intg..PHI.M.multidot.dA.
This latest equation simplifies the calculation of E and the
identification of the source of the different terms. The scalar
potential will then be of the form ##EQU1## where k=2.pi.n/.lambda. and
the coefficients .PHI.n match the series solution to the particular
field pattern. Specific values of .PHI.n for various field patterns can
be found in "Theoretical approach to magnetic force microscopy," a
published article by A. Wadas and P. Grutter in Phys. Rev. B, vol. 39,
no. 16, pp 12013-12017, June 1989 and in "Analysis of in-plane bit
structure by magnetic force microscopy," a published article by A.
Wadas, P. Grutter, ad H. Gutherolt in J. Appl. Phys. 67 (7), pp.
3462-3467, 1990.
In the present invention, it was assumed that 1) the domain is
magnetized along the probe axis by shape anisotropy, 2) the domain is
much longer than .lambda. so that the limit of integration in the z
direction can be extended to infinity, and 3) the thickness of the
probe, t, is much less than the wavelength .lambda..
In "Magnetic force microscopy: General principles and application to
longitudinal recording media," a published article by D. Rugar, H.
Mamim, P. Guethner, S. Lambert, J. Stern, I. McFadyen, and T. Yogi in J.
Appl. Phys. 68 (3), 1990, pp. 1169-1183, it was shown that the last
domain on the probe was 20 micrometers in length. A domain length of
this size is typically much longer than the wavelength of patterns on
modern recording surfaces.
In calculating the energy of interaction (E), the last two equations are
used to obtain ##EQU2## The integrals were preformed so that the point
(x,z) is the coordinate of the probe tip. The first term in the
calculation of the energy of interaction is due to a magnetic charge,
Mtw, at the tip of the probe. The magnetic potential is weighted by a
sampling factor caused by the variation in the field across the width,
w, of the probe tip. The next two terms can be thought of as the
contributions from the magnetic charges on the sides of the probe,
separated from the tip by the distances x.+-..
The quantity that is measured by the tunneling microscope is the
displacement, .DELTA.z, of the probe tip. The displacement is caused by
both the surface topology and magnetic field of the recorded media. If
the probe tip is properly designed, the magnetic interaction will
predominate and the effects due to surface topology will b minimized.
If the probe is constrained to rotate in the theta (.theta.) direction,
the displacement will be given by lsin.theta..DELTA..theta., where l is
the length of the probe's 20 moment-arm. A force, F.sub.N, normal to the
probe 20 will cause a rotation in the theta (.theta.) direction such
that lF.sub.N =-K.DELTA..theta. where K is the tip torque constant. The
displacement .DELTA.z is then given by ##EQU3##
The force acting on the tip is the gradient of the energy,
F=-.gradient.E, so that .DELTA.z further becomes ##EQU4##
Using the last equation and the equation for the energy (E) of
interaction, .DELTA.z becomes ##EQU5##
These last three equations give a complete description of the
interaction between the probe and the recorded pattern. In general, the
equations are quite complicated and their usefulness is not readily
apparent. In the case where the probe lines up with the pattern (i.e.,
phi=0), so that the probe scans along the recorded information, the
equation for .DELTA.z reduces to a simple form, ##EQU6##
The first two terms give the interaction between the magnetic field and
the magnetic charge at the tip. The third term gives the effect of the
charges on the sides of the probe. The third term was written in the
integral form so that it could be expressed in terms of the magnetic
field Hz. This last equation can be used to obtain relative values of
the magnetic field components Hx and Hz. To obtain absolute values, the
probe would have to be calibrated in a known field to obtain the factor
(1**2)Mtw/K.
An alternative way to obtain the fields from the last equation is by
obtaining three images at three different values of the angle theta
(.theta.). The fields Hx and Hz can then be obtained at every point from
a linear combination of the three images. As an example, if the images
were taken at theta equal to 30, 45, and 60 degrees then Hx and Hz would
be given by the following two equations:
H.sub.x =-18.01z(30.degree.)-13.55z(60.degree.)+29.35z(45.degree.),
H.sub.z =-23.48z(30.degree.)-10.40z(60.degree.)+29.35z(45.degree.)
where ##EQU7##
If phi=0 is chosen as the angle of rotation of the probe, the angle
theta must be determined to give the best image sensitivity. For
##EQU8## the relative amplitude of the harmonics, for phi=0, will vary
with theta as ##EQU9## The amplitude will have a maximum near theta=pi/2
for both large and small values of a. Raising the elevation of the probe
to this value would cause interactions with all the domains in the probe
so a smaller value would have to be chosen. The smallest value of theta
for which the amplitude is a maximum occurs when a=1, cos(theta)=1/3,
and theta=70.5 degrees. This is still a relatively large elevation, but
as can be seen from FIG. 3, the maximum occurs over a broad range.
Adequate sensitivity can be achieved when theta is as small as 45
degrees.
Numerous experiments were performed to verify the equations given above
for .DELTA.z, C**2, and beta. Agreement between experimental data and
theory, as shown in FIG. 4, is quite good. The theoretical curve was
obtained using delta (.delta.)=15 degrees, theta=12 degrees and w=1
micrometer. Error is introduced into the experimental data if, during
rotation of the sample, a different recorded track is followed.
The method of the present invention shows how the constituent magnetic
fields from recorded magnetic patterns can be obtained using a magnetic
force scanning tunneling microscope. The sensitivity of the microscope
will vary with the orientation of the probe. Changes and modifications
in the specifically described embodiments can be carried out without
departing from the scope of the invention which is intended to be
limited only by the scope of the appended claims.
1. A method of measuring magnetic fields on magnetically recorded media
comprising the steps of: (a) replacing the fine metallic tip of a
scanning tunneling microscope with a flexible thin-film magnetic probe
in order to relate probe position to magnetic field strength; (b)
removing any protective layer from said magnetically recorded media so
that said protective layer does not impede the establishment of a
tunneling current between said magnetic probe and said magnetically
recorded media; (c) aligning said magnetic probe with a recorded track
of said magnetically recorded media at an angle of zero degrees; (d)
positioning the tip of said magnetic probe to said magnetically recorded
media at an angle in the range of zero degrees to pi/2 degrees in order
to establish said tunneling current; (e) scanning said recorded track of
said magnetically recorded media with said magnetic probe; (f) recording
changes in position of said magnetic probe during said scanning of step
(e) due to changes in the magnetic field of said magnetically recorded
media; and (g) computing the magnetic fields associated with said
recordings of step (f) by using a mathematical equation that relates the
position of said magnetic probe to the strength of the magnetic field.
2. The method of claim 1 further comprising the step of plating said
magnetic probe and said magnetically recorded media with at least
three-hundred angstroms of gold in order to reduce spurious probe
deflection due to surface oxides on either said magnetic probe or said
magnetically recorded media.
3. The method of claim 1 wherein said step of replacing the fine
metallic tip of a scanning tunneling microscope with a flexible
thin-film magnetic probe is accomplished by replacing the fine metallic
tip of said scanning tunneling microscope with a thin-film nickel probe.
4. The method of claim 1 wherein said step of replacing the fine
metallic tip of a scanning tunneling microscope with a flexible
thin-film magnetic probe is accomplished by replacing the fine metallic
tip of said scanning tunneling microscope with a thin-film iron probe.
5. A method of measuring magnetic fields on magnetically recorded media
comprising the steps of: (a) replacing the fine metallic tip of a
scanning tunneling microscope with a flexible thin-film magnetic probe
in order to relate probe position to magnetic field strength; (b)
removing any protective layer from said magnetically recorded media so
that said protective layer does not impede the establishment of a
tunneling current between said magnetic probe and said magnetically
recorded media; (c) aligning said magnetic probe with a recorded track
of said magnetically recorded media at an angle of zero degrees; (d)
positioning the tip of said magnetic probe to said magnetically recorded
media at an angle in the range of zero degrees to pi/2 degrees in order
to establish said tunneling current; (e) scanning said recorded track of
said magnetically recorded media with said magnetic probe a first time;
(f) recording changes in position of said magnetic probe during said
scanning of step (e) due to changes in the magnetic field of said
magnetically recorded media; (g) positioning the tip of said magnetic
probe to said magnetically recorded media at an angle in the range of
zero degrees to pi/2 degrees but at an angle that is different then the
angle used in step (d) in order to establish said tunneling current; (h)
scanning said recorded track of said magnetically recorded media with
said magnetic probe a second time; (i) recording changes in position of
said magnetic probe during said scanning of step (h) due to changes in
the magnetic field of said magnetically recorded media; (j) positioning
the tip of said magnetic probe to said magnetically recorded media at an
angle in the range of zero degrees to pi/2 degrees but at an angle that
is different than the angles used in step (d) and step (g) in order to
establish said tunneling current; (k) scanning said recorded track of
said magnetically recorded media with said magnetic probe a third time;
(l) recording changes in position of said magnetic probe during said
scanning of step (k) due to changes in the magnetic field of said
magnetically recorded media; (m) combining the resulting three
recordings of step (f), step (i), and step (l) linearly in order to
obtain a single record of the position changes of said magnetic probe
due to changes in the magnetic field of said magnetically recorded
media; and (n) computing the magnetic fields associated with said
combination of step (m) by using a mathematical equation that relates
the position of said magnetic probe to the strength of the magnetic
field.
6. The method of claim 5 further comprising the step of plating said
magnetic probe and said magnetically recorded media with at least
three-hundred angstroms of gold in order to reduce spurious probe
deflection due to surface oxides on either said magnetic probe or said
magnetically recorded media.
7. The method of claim 5 wherein said step of replacing the fine
metallic tip of a scanning tunneling microscope with a flexible
thin-film magnetic probe is accomplished by replacing the fine metallic
tip of said scanning tunneling microscope with a thin-film nickel probe.
8. The method of claim 5 wherein said step of replacing the fine
metallic tip of a scanning tunneling microscope with a flexible
thin-film magnetic probe is accomplished by replacing the fine metallic
tip of said scanning tunneling microscope with a thin-film iron probe.
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* Bruce Schneier 2,000,000,000,000,000,000,000,000,002,000,
* Counterpane Systems 000,000,000,000,000,000,002,000,000,002,293
* [email protected] The last prime number...alphabetically!
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* 101 E Minnehaha Pkwy trillion, two thousand, two hundred and
* Minneapolis, MN 55419 ninety three.
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