Magnetic structures of a sample are imaged by measuring Lorentz force-induced deflection of the tip of a scanning tunneling microscope. While scanning the sample, an a.c. voltage signal at a first predetermined frequency equal to the resonance frequency of the tip is applied to the tip for generating a current between the tip and the surface of the sample for causing the tip to undergo vibratory motion relative to the sample. The tip motion, indicative of the presence of a magnetic field, is optically detected. In an alternative embodiment for providing improved resolution the tip is made to undergo motion at a second predetermined frequency in a direction parallel to the longitudinal axis of the tip and normal to the surface of the sample. The tip motion is optically detected at the sum or difference frequency of the first and second predetermined frequencies for providing improved lateral resolution of the magnetic field measurements using a scanning tunneling microscope. In the alternative embodiment the sum or difference frequency, which ever is detected, is made equal to the resonance frequency of the tip. The magnetic field measurement and tip position are provided to a computer which, in turn, provides an output signal to a device for providing a graphical representation of the magnetic field at different positions on the surface of the sample.

BACKGROUND OF THE INVENTION 
The present invention concerns Lorentz force microscopy and in particular 
concerns imaging magnetic structures in a sample with high resolution by 
measuring Lorentz force-induced deflection of the tip in a scanning 
tunneling microscope (STM). 
Several approaches exist for imaging magnetic field distributions on a 
microscopic scale. For moderate resolutions optical techniques based upon 
the Kerr effect are adequate and provide spatial resolution of 
approximately 0.5 micron which is limited by the optical wavelength. 
Another approach is to use the Bitter pattern technique which requires the 
spreading of a magnetic particle suspension over the surface to be imaged 
and subsequently obtaining an image using light. In order to achieve 
higher spatial resolution, it is necessary to resort to the use of 
electron beam imaging techniques such as spin polarized imaging and 
Lorentz microscopy. 
Presently, leading techniques for high-resolution imaging of magnetic 
structures include the use of magnetic force microscopy (MFM) as is 
described in the article by Y. Martin and H.K. Wickramasinghe entitled 
"Magnetic Imaging by "Force Microscopy" with 1000 .ANG. Resolution", Appl. 
Phys. Lett Vol. 50, No. 20, May 18, 1987, pp. 1455-1457, in which the 
lateral resolution is limited by the tip size, typically 1000 angstroms. 
Another technique is the use of scanning electron microscopy with 
polarization analysis (SEMPA) as is described in the article by R.T. 
Celotta and D.T. Pierce entitled "Polarized Electron Probes of Magnetic 
Surfaces", Science, Vol. 234, Oct. 17, 1986, pp. 333-340, which in 
principle is limited in resolution to the far-field electron beam spot 
size. The SEMPA technique also suffers from the difficulties associated 
with surface preparation and in the reliability of the 
polarization-sensitive detector. To date, the SEMPA technique has been 
demonstrated with a resolution of 1000 angstroms, but the potential exists 
of achieving 100 angstroms resolution. 
The present invention provides for accurate measurement of the force 
between a tip and a sample as a function of the spacing between the tip 
and sample surface. A tip is vibrated in close proximity to &he surface 
and an optical heterodyned interferometer is employed to accurately 
measure the vibration of the tip. The technique provides a sensitive and 
flexible arrangement for measuring the force. As a result, it is possible 
to image the magnetic field by noncontact profiling on a scale of a few 
angstroms. 
Specifically, the measuring technique of the present invention is 
theoretically capable of attaining resolution which is limited only by the 
near-field beam size, i.e. better than 5 angstroms lateral resolution, as 
demonstrated using high-resolution images of a scanning tunneling 
microscope. 
In accordance with the teachings of the present invention, a scanning 
tunneling microscope is operated using a long, thin tip. In such a 
configuration the tip is stiff in a direction normal to the plane of the 
sample surface but is flexible in a direction parallel to the plane of the 
sample surface. In the presence of a magnetic field in a plane parallel to 
the sample surface, and with a tunneling current passing between the tip 
and the sample, there will be a static deflection of the tip. When 
applying a first alternating current bias voltage at a first frequency 
between the tip and sample, the oscillatory current causes the tip to 
undergo vibratory motion at the first frequency in a direction parallel to 
the sample surface. The oscillatory motion is detected by means of an 
optical heterodyned interferometer by measuring the laser phase 
variations. 
The motion of the tip may be detected in two orthogonal planes, which as 
will be described hereinafter determine the magnitude and direction of the 
component of the magnetic field parallel to the sample surface. The 
detection is accomplished, for example, either by using two, independent 
interferometers or by using a simple interferometer and measuring both the 
amplitude and phase of the detected optical signal. By scanning the tip 
across the sample surface, an image of the vector magnetic field 
throughout the sample is thus obtainable. 
Scanning tunneling microscopes are well known and are described, for 
example, in U.S. Pat. No. 4,343,993 entitled "Scanning Tunneling 
Microscope", issued to G. Binnig et al and assigned to the same assignee 
as the present invention, which patent is incorporated herein by 
reference. 
SUMMARY OF THE INVENTION 
A principal object of the present invention is therefore, the provision of 
an apparatus for and a method of imaging magnetic structures in a sample 
with high resolution by measuring the Lorentz force-induced deflection of 
the tip in a scanning tunneling microscope. 
Another object of the invention is the provision of an apparatus for and a 
method of imaging magnetic structures in a sample in which the resolution 
is in the order of approximately several angstroms. 
A further object of the invention is the provision of an apparatus for and 
a method of simultaneously measuring the topography and lateral field 
strength of a sample. 
Further and still other objects of the invention will become more clearly 
apparent when the following description is read in conjunction with the 
accompanying drawing.

DETAILED DESCRIPTION 
Referring now to the figures and to FIG. 1 in particular there is shown 
schematically the essential components of a conventional scanning 
tunneling microscope. A sample 10 to be imaged acts as an electrode above 
which and in close proximity thereto a tip 12 is disposed. The sample and 
tip are capable of undergoing motion relative to each other in each of the 
three coordinate axes designated x, y and z. The sample and/or the tip are 
also provided with three piezoelectric drives 14, 16, 18. Piezoelectric 
drives 14 and 16 operate in the lateral directions x and y respectively. 
The drives may act either on the tip 12, the sample 10 or a combination of 
both to cause relative motion between the tip and sample along the x and y 
axes. Vertical piezoelectric drive 18 adjusts the spacing between the tip 
12 and surface of sample 10 in the z-axis direction, in the vertical 
direction as shown. A measuring device 20 is coupled to sample 10 and tip 
12 as well as to piezoelectric drives 14, 16 and 18. Controller 22 is 
coupled both to measuring device 20 and z-axis piezoelectric drive 18 for 
controlling the separation distance between the sample 10 and tip 12. 
Measuring device 20 is connected to analyzer 24 which in turn is connected 
to an output device such as a plotter 26 or a viewing screen 28. The 
electrodes are drawn schematically in exaggerated size. The actual 
mechanical dimensions of the electrodes, sample and tip, as well as their 
possible range of adjustment are extraordinarily small because of the 
delicate nature of the tunneling effect. The controller 22 must be able to 
operate very precisely and the measuring device 20 must be extremely 
sensitive. 
The present invention provides a measurement resolution of better than 5 
angstroms in a lateral direction. As shown in FIG. 2, a scanning tunneling 
microscope is operated using a long thin tip 40 supported by support 42. 
The tip 40 is rigid in a direction along the longitudinal axis of the tip, 
i.e. in a direction substantially normal to the surface 44 of a metallic 
sample 46, and is flexible in a direction substantially parallel to the 
sample surface 44. The tip, preferably fabricated from tungsten, is 
dimensioned approximately 200 microns in length with a diameter tapering 
from 10 microns at the base to a final point approximately 20 nanometers 
in diameter. 
When a magnetic field is manifest in the plane of the sample and a current 
from source 48 is passed between the tip 40 and sample 46, there will be a 
static deflection in the direction r=I.times.B. When applying an a.c. bias 
voltage at a frequency .omega..sub.1 from a voltage generator 50 between 
the tip 40 and sample 46, the operating current causes the tip 40 to 
undergo vibratory motion in a direction substantially parallel to the 
plane of the sample surface 44. The motion of the tip 40 is detected and 
measured using an optical heterodyned interferometer 51 comprising laser 
probe 52 and lens 54. 
Optical heterodyned interferometers are known. A preferred interferometer 
which has been used successfully in applications with a scanning force 
microscope is described in detail in the article "Atomic Force 
Microscope-Force Mapping and Profiling on a sub 100-.ANG. Scale" by Y. 
Martin, C.C. Williams and H.K. Wickramasinghe, J. Appl. Phys., Vol. 61, 
No. 10, May 15, 1987, pages 4723-4729, which article is incorporated 
herein by reference. The tip 40 and holder 42 are coupled to x, y and z 
piezoelectric drives shown schematically as elements 56, 58, and 60 
respectively. The position of the tip relative to a point on the 
stationary sample 46 in the x, y and z directions respectively is provided 
along conductors 62, 64, and 66 to a computer 68. While the tip is scanned 
over the sample in the x-axis and y-axis direction, the position 
calculated by computer 68 from the piezoelectric drive signals received 
from each of the element 56, 58 and 60 along conductors 62, 64 and 66 
respectively and the magnetic field strength B provided from the 
interferometer 51 along conductor 70 to the computer 68 are combined to 
generate at an output device 72 a representation of the magnetic field 
along the surface of the sample 46 as the tip is scanned over the surface. 
The output device 72 may be a screen presentation, plotter, recorder or 
any other device capable of providing a graphical or tabular 
representation of the magnetic field as a function of position along the 
surface 44 of the sample 46. 
In operation, the tip is located at a distance in the order of one 
nanometer from the surface of the sample. The amplitude of the vibratory 
motion is in the range between 0.1 to 10 nanometers. The computer 68 is 
preferably an IBM PC/AT or a computer of equal or better capability for 
data acquisition. 
While the above description discloses motion of the tip relative to a 
stationary sample, it will be apparent to those skilled in the art that 
relative motion between a stationary tip and moving sample or between a 
moving tip and moving sample, as described in conjunction with the 
description of the STM shown in FIG. 1, will perform equally as well. 
The magnitude of the magnetic field effect is calculable by the computer 68 
as follows. In a material with a magnetic field B located just outside of 
the sample which decreases over a characteristic length scale l exhibiting 
a tunnel current I, and where the spring constant of the tip 40 is k, the 
static deflection of the tip is in the order of IBl/k. For the case of an 
alternating current current having a frequency .omega..sub.1 of the bias 
voltage selected to be approximately equal to the mechanical resonance 
frequency of the tip, the amplitude a of the tip motion is Q multiplied by 
the static deflection or a=QIBl/k. In the case of high spatial frequency 
components of the magnetic field, the length l over which the magnetic 
field B decays is approximately equal to the spatial wavelength of B. 
Therefore, in order to resolve 100 angstrom fluctuations of the tip in the 
field B, l is set to 100 angstroms. For a typical Q of 100, B=1W/m.sup.2, 
k=10.sup.-2 N/m, an alternating current of 1.mu.A and l=100 angstroms, the 
tip will oscillate at a peak-to-peak amplitude of 1 angstrom. The 
intrinsic limit of resolution of the microscope for magnetic field imaging 
will be similar to that of a scanning tunneling microscope, possibly being 
limited by increased tunneling area and gap distance due to field emission 
from the tip. Both of these effects are known to be several orders of 
magnitude below the resolution available with currently known techniques. 
These effects are described, for instance, in the article entitled "The 
Topografiner: An Instrument for Measuring Surface Microtopography" by R. 
Young, J. Ward and F. Scire, Rev. Sci. Instr., Vol. 43, No. 7, July 1972, 
pages 999-1011. 
The signal-to-noise ratio of the measurement is determined by the noise 
limit of the optical interferometer and by thermally excited oscillation 
of the tip. Tests have shown that the optical interferometer described in 
the Martin et al article supra is able to measure tip displacements as low 
as approximately 5.times.10.sup.-5 .ANG./.sqroot.Hz for 100.mu.W of laser 
power and therefore does not represent a severe limitation. For a spring 
constant of 10.sup.-2 N/m, the root-mean-square fluctuation in tip 
position is approximately 12.ANG. at room temperature. The amplitude in a 
bandwidth .beta. is given by the expression N=(4R.sub.B 
TQ.beta./k.omega..sub.1).sup.1/2. When attempting to achieve 100 angstroms 
resolution (i.e., a=1) with the parameters set forth hereinabove, the 
bandwidth .beta. and the resonant frequency .omega..sub.1 of the tip 40 
are related as follows: .omega..sub.1 /.beta.=1.6.times.10.sup.4 in order 
to achieve a signal-to-noise ratio of 1. Typically, .omega..sub.1 is 
approximately 50 kHz, so that .beta. is approximately 4 Hz. The practical 
limit to measurement resolution will then be due to drift in the scanning 
tunneling microscope, which sets a lower bound on .beta. of approximately 
0.1 Hz to 1 Hz, or roughly 15.ANG. resolution. 
Further immunity from environmental noise sources is achievable by 
vibrating the tip at a second frequency .omega..sub.2 in a direction along 
the z-axis, substantially normal to the plane of the surface 44 of the 
sample 46. The tip is made to undergo vibratory motion by applying a 
suitable a.c. voltage signal to the z-axis piezoelectric drive. The 
frequency .omega..sub.2 is not at the resonant frequency of the tip and 
.omega..sub.2 so that the sum or difference frequency, which ever is 
detected, is at the resonance frequency of the tip. A typical value for 
.omega..sub.2 is between 10 kHz and 100 kHz. Detection of the tip motion 
by the optical heterodyned interferometer at a difference or sum frequency 
of the two applied motions (.omega..sub.1 .+-..omega..sub.2) results in 
the interaction of only the tip 40 and sample 46 being detected and 
measured. In addition to rejecting low resolution components of the force 
interaction with the tip, the described heterodyned scheme eliminates 
spurious signals resulting from Joule heating-induced modulation of the 
sample height. Either a single interferometer, as shown, capable of 
measuring laser phase variations or two interferometers, each measuring 
motion along one of the axes of motion, measure the tip motion. 
While the above refers to motion of the tip, it will be apparent to those 
skilled in the art that the relative motion between the tip and sample is 
important. Therefore, motion of the tip, sample or both the tip and sample 
may be used in practicing the present invention. 
The tip motion and x, y and z axes position are provided to the computer as 
described above. The computer, in turn, calculates the magnetic field 
strength at each associated tip position relative to the sample surface, 
using the above described equation relating tip vibration amplitude and 
field strength and provides an output signal responsive to the calculated 
values. 
The above described invention offers unique advantages over the prior 
methods. First, the apparatus operates independently as a conventional 
scanning tunneling microscope. Thus, the topography and lateral magnetic 
field strength are measured simultaneously. Since the static deflection of 
the tip (for topographical measurement) is quite small compared to the 
length scales of interest, the topography and magnetic field image is 
readily separated. Therefore, an independent measure of magnetic field 
strength, apart from the topographic measurement, is conveniently 
achieved. Second, the resolution is much better than that achieved using 
either magnetic force microscopy or scanning electron microscopy with 
polarization analysis since the better high resolution obtainable with the 
scanning tunneling microscope determines resolution of the magnetic field 
measurement. Tip shape affects resolution in the same manner as in a 
conventional scanning tunneling microscope, particularly when measuring 
rough surfaces. Also, secondary election emission will not play a large 
role in the resolution limit. Finally, by detecting the tip oscillation in 
two orthogonal directions, the direction of magnetization in the sample 
can be determined. 
While there has been described and illustrated a method and preferred 
embodiment of an apparatus for measuring the magnetic field strength of a 
sample, it will be apparent to those skilled in the art that modifications 
and variations thereof are possible without deviating from the broad 
spirit of the invention which shall be limited solely by the scope of the 
claims appended hereto.