Magnetic resonance method and apparatus for detecting an atomic structure of a sample along a surface thereof

A method and an apparatus are disclosed for detecting an atomic structure of a sample along a surface thereof. The method comprises arranging the sample in a constant magnetic field (B.sub.0) of predetermined field strength and high homogeneity and irradiating a high-frequency magnetic field (B.sub.1) of a predetermined frequency on the sample, wherein the fields (B.sub.0) and (B.sub.1) are oriented perpendicularly to each other. The method further comprises providing a force-sensitive sensor having a paramagnetic tip comprising a paramagnetic material. The sensor is placed in close vicinity to the sample such that the paramagnetic tip is in atomic interaction with the sample surface which means that the distance between the tip and the surface is in the order of between 1 and 10 .ANG.. The predetermined field strength and the predetermined frequency are set such that electron paramagnetic resonance (EPR) is excited within the tip paramagnetic material. The paramagnetic tip is then displaced parallel to the sample surface for mapping predetermined points on the sample surface. During displacing the tip the force exerted on the tip by a local inhomogeneous magnetic field (B.sub.loc) caused by atomic magnetic moments (m.sub.e,k) of the sample is measured.

BACKGROUND OF THE INVENTION 
The invention relates to a method and an apparatus for detecting an atomic 
structure by means of magnetic resonance of a sample along a surface 
thereof. Such apparatus could be identified as a Scanning Electron 
Paramagnetic Resonance Microscope (SEPRM). However, the invention is not 
only adapted for studying surface structures, moreover, it is an atomic 
scale analytical tool. 
In particular, the invention relates to a magnetic resonance method for 
detecting an atomic structure of a sample along a surface thereof. More 
specifically, the invention relates to a method by which a force is 
measured acting on a mechanical force-sensitive sensor having a tip, the 
tip being brought into atomic interaction with the sample surface with the 
sample and the tip being displaced relatively to each other in directions 
parallel to the sample surface and a deflection of the force-sensitive 
sensor being detected at predetermined points of the sample surface. 
The invention, further, relates to a magnetic resonance apparatus for 
detecting an atomic structure of a sample along a surface thereof, in 
particular for carrying out the afore-specified method. Still more 
specifically, the invention relates to such an apparatus having a probe 
head and a force-sensitive sensor being provided with a tip. Further, 
means are provided for contacting the sample surface with the tip and for 
displacing the sample relative to the tip in directions parallel to the 
sample surface. Further, means are provided for detecting a deflection of 
the force-sensitive sensor. 
DISCUSSION OF RELATED ART 
In the prior art, various types of so-called scanning probe microscopes 
have been disclosed. The first scanning probe microscope was the Scanning 
Tunneling Microscope (STM) (cf. G. Binnig et al. "Surface Studies by 
Scanning Tunneling Microscopy", Phys. Rev. Lett. 49, 57, (1982) and 
"7.times.7 Reconstruction on Si (111) Resolved in Real Space", Phys Rev 
Lett 50, 120, (1983). Later on, Atomic Force Microscopes (AFM) were 
disclosed (cf. G. Binnig et al. "Atomic Force Microscopy", Phys. Rev. 
Lett. 56, 930, (1986)), which were more general and proliferated into many 
sub-branches using different detection modes for different problems, 
called: "Magnetic Force Microscopy" (MFM), Friction Force (lateral force) 
Microscopy, recently even Magnetic Resonance Force Microscopy (MRFM). 
The underlying common element of these Scanning Probe Microscopes is the 
use of a local sensor in combination with piezoelectric displacers 
providing sub-.ANG.ngstrom precision displacements in three dimensions, 
and a feed-back loop to maintain a constant interaction between the sensor 
and the sample (regulating the z-direction) while the sample is displaced 
in the x-y plane relative to the sensor. The resulting topographic image 
is usually the z-position as a function of x and y at constant force or 
the corresponding force at constant z-position. 
Scanning Tunneling Microscopes (STM) use conducting tips as sensors and the 
distance is regulated keeping a constant tunneling current (typically of 
the order of 1 nA) between the tip and the sample. The tip does not touch 
the sample, in general. When used as spatially resolved tunneling 
spectroscopy (non-atomic resolution), STM provides bulk information about 
the material since the tunneling current is proportional with the 
conduction electron density. 
The main success of STM consists in that it is relatively easy to achieve 
atomic resolution with it. This is precisely because of the short-range 
interaction detected since the tunneling current falls off exponentially 
in atomic (.ANG.ngstrom) scale, allowing to differentiate with resolution 
better than atomic distances. The handicap of STM is that it needs a 
current, though very small, so that the sample studied may not be an 
insulator. A practical inconvenience of STM is that one has to deal with 
vacuum tunneling and the surface cleanness is extremely critical because 
it influences the stability of the tunneling current. Therefore, nearly 
all STM experiments require an expensive multi-chamber UHV installation. 
The extraordinary sensitivity of the STM allows to observe modulation of 
tunneling current attributed to the Larmor precession of a single electron 
spin on oxidized Si surface (Y. Manassen et al., "Direct Observation of 
the Precession of Individual Paramagnetic Spins on Oxidized Silicon 
Surfaces", Phys. Rev. Lett. 62, 2531 (1989)). This observation, however, 
has not been exploited in practice, as the nature of the interaction of 
the localized spin with the tunneling current, leading to the observed 
modulation is completely unknown, and it might be specific to the given 
material and experiment. The quantitative analysis was also hindered by 
the unknown nature of the mechanism. Only an external static field has 
been applied in this experiment. 
Spin-polarized tunneling has also been reported, using a ferromagnetic tip 
(CrO.sub.2) to study antiferromagnetic atomic terraces (Cr) (R. Wiesender 
et al., "Observation of Vacuum Tunneling of Spin-Polarized Electrons with 
the Scanning Tunneling Microscope", Phys Rev Lett 65, 247, (1990)). The 
mechanism, how magnetism influences the tunneling current, however, stays 
unidentified. 
Atomic Force Microscopes (AFM) may be used on a more general scale. The 
phenomenon underlying this technology is based on interactions of varying 
nature and the strength, depending on the sample studied. These 
interactions comprise hard core repulsion and Van der Waals interactions 
for covalent materials. Electrostatic interactions for ionic crystals are 
studied with ionic tips and magnetic interactions are studied if the tip 
is ferromagnetic, etc. In general, these forces are not enough short range 
to insure atomic resolution. Each case and each material need special 
efforts and techniques to achieve highest resolution. Typically, these 
forces change only an order of magnitude in the entire range of useful 
distances (2-10 .ANG.), while the tunneling current changes three orders 
of magnitude with a single atomic step (2-5 .ANG.). AFM became popular in 
spite of these difficulties, because of the more general use and because 
UHV environment is avoidable (most of the experiments are made in ambient 
conditions or moderate vacuum) and atomic resolution has been achieved on 
hard materials such as graphite and on ionic salts (due to the strong 
contrast of the alternate charged atoms). 
Atomic force-microscopes (AFM) essentially consist of a mechanical 
force-sensitive sensor being designed as an elongate elastic arm attached 
to a base at one end thereof and being designated in the art as 
"cantilever". The cantilever is provided with an extremely pointed tip. 
By means of the tip it is possible to sense attracting and repelling 
forces, respectively, in a distance of a few .ANG.ngstroms from a surface 
of a sample. Such static atomic forces may, for example, be the attracting 
Van-der-Waals force, electromagnetic forces, or the repelling force being 
generated, when two atoms contact each other like two hard spheres. 
Furthermore, static magnetic forces existing in the vicinity of the 
surface of ferromagnetic samples may be detected with such a 
force-sensitive sensor. The force-sensitive sensors mentioned before have 
a sensitivity for forces down to 10.sup.-18 N. 
A deflection of the force-sensitive sensor being caused by atomic forces 
and amounting only to .ANG.ngstroms may best be detected by optical means. 
For that purpose a beam of laser light is directed to and reflected from 
the force-sensitive sensor, the reflected beam impinging on a detector. 
The deflection of the force-sensitive sensor thus, results in a deflection 
of the laser beam which may easily be measured. 
By displacing the tip along the surface (x, y) of the sample in various 
distances, for example between 1 and 10 .ANG., or in the .mu.m range an 
electronic data processing of the z-height at constant force yields a 
topographic three-dimensional picture of the surface structure. The 
sampling operation of an AFM may be illustrated with the example of the 
tip of a classical record player needle following the grooves of a record. 
By means of an AFM surface structures may be made visible within a range 
from micrometers down to the atomic scale, i.e. even single atoms near the 
surface may be detected. In a computer generated diagram of z at constant 
force as a function of x and y, generated during the scanning or mapping 
of a surface the atoms appear as bright semi-spheres in front of a dark 
background and may be seen three-dimensionally. However, it would also be 
possible to generate a force diagram at constant height z. 
Furthermore, although an AFM allows to detect single atoms, it does not 
allow to distinguish between different kinds of atoms. However, in 
poly-atomic samples one would be interested in gathering information about 
the question which is the kind of detected atoms and what the relative 
position is between the various atoms with respect to each other. 
Another scanning probe microscope is the magnetic force microscope (MFM). 
Due to the nature of the magnetic interactions, force can be created only 
between a field gradient and a magnetic dipole. The same holds true for 
two dipoles, as the field gradient can always be viewed as having been 
generated by another dipole. Ferromagnetic tips are used with MFM as 
magnetic dipoles, and the field gradients originated from the domain 
structure or walls of different magnetic medias are studied. A resolution 
of the order of 100 nm may be achieved. An atomic resolution is not even 
aimed for with MFM. 
The gradient of the magnetic field is detected as a force acting on the 
macroscopic magnetic dipole moment of the tip. The tip is usually lifted 
several hundred .ANG. from the surface, to avoid the influence of other 
forces. 
As both the field gradient studied and the dipole of the tip are static, 
the cantilever is mechanically vibrated to increase the sensitivity of the 
detection. The force derivative is detected, or, with other words, the 
advantages of an AC (synchronous) detection are used in combination with 
the high quality factor of the mechanical resonance of the cantilever. 
Further, it is known to use nuclear magnetic resonance (NMR) or electron 
spin resonance (ESR) (also identified as paramagnetic resonance (EPR)), 
respectively, for identifying atoms and electrons, respectively by 
quantitatively measuring their magnetic moments, in particular their 
g-factors. With NMR or EPR, respectively, a sample is investigated with 
respect to its magnetic properties within magnetic fields being oriented 
perpendicularly to each other. By doing so one does not only detect the 
sample surface, instead NMR or EPR, respectively, are also excited in 
deeper sample layers. However, conventional NMR or EPR, respectively, does 
not allow high resolution localization of detected magnetic moments in the 
atomic scale. 
Generally, the various techniques of magnetic resonance comprise placing 
the spin in a static, high magnetic field while applying a perpendicular 
alternating magnetic field with frequencies in the vicinity of the Larmor 
frequency determined by the static field. This allows to control the spin 
orientation via techniques generally known as slow adiabatic passage, 
transient nutation spin inversion by .pi. (180.degree.) pulses, etc. 
The suggested magnetic resonance force microscopes (MRFM) comprise a sample 
attached to a cantilever and placed in a static field gradient exerting an 
oscillating force on the cantilever as a result of the free Larmor 
precession of the magnetic moments of the individual nuclear and electron 
spins (J. A. Sidles et al., "Folded Stern Gerlach experiment as a means of 
detecting magnetic resonance in individual nuclei", Phys Rev Lett. 68 
1124-1127, (1992) and "Noninductive detection of single-proton magnetic 
resonance", Appl. Phys. Lett. 58, 2854-2856, (1991)). 
As the field is different in the different points of the space, these 
Larmor precessions are of different frequencies as a function of the spin 
location. Thus, it was suggested to use this method to image individual 
spins and atoms as it is usual in magnetic resonance imaging. Further 
experiments (Rugar et al., "Mechanical detection of magnetic resonance", 
Nature 360, 563-566, (1992), and "First images from a magnetic resonance 
force microscope", Appl. Phys. Lett. 63, 2496-2498, (1993)) used the 
following configuration: 
The sample is attached to a high quality factor cantilever. A small 
ferromagnetic particle is placed in the vicinity and provides the field 
gradient. An external constant field and an RF coil create a 
perpendicularly oscillating field. The resonance frequency is much higher 
as compared to the cantilever mechanical resonance frequency (natural 
frequency). Therefore, these experiments have used the means of magnetic 
resonance to oscillate the magnetic moment of the sample at a desired 
frequency, tuned to the mechanical resonance frequency of the cantilever. 
The oscillating moment, being in the static field gradient of the 
ferromagnetic particle, results in an oscillating force, driving the 
cantilever to oscillate. The amplitude of the cantilever oscillation is 
detected. 
Rugar also used a sample consisting of DPPH (diphenyl-picryl-hydracyl) and 
being attached to a mechanical force-sensitive sensor. An inhomogeneous 
magnetic field is generated in the area of the sample by means of a 
conically shaped permanent magnet. Due to the gradient of the 
inhomogeneous magnetic field a magnetic force acts on the sample, causing 
a deflection of the force-sensitive sensor. Concurrently, EPR is excited 
within the DPPH sample by simultaneously irradiating a high-frequency 
magnetic field. Due to the inhomogeneity of the magnetic field generated 
by the permanent magnet, the EPR resonance condition is only met along a 
certain surface within the sample. Insofar, this method corresponds to 
classical MR-tomography obtaining a localization of magnetic resonance 
(MR) by imposing gradient fields. 
In the prior art method the force-sensitive sensor is, further, excited to 
oscillate at its natural frequency by modulating the inhomogeneous 
magnetic field with a modulating magnetic field of low amplitude. The 
resonant deflection of the force-sensitive sensor is detected by optical 
means. The values of the so-detected magnetic force along the sample 
surface are fed into a memory for various distances between the sample and 
the permanent magnet for generating localized spin density pictures by 
means of electronic data processing. 
By doing so a resolution in the order of between 1 and 20 .mu.m is 
obtained. This unsatisfying resolution depends on the weak field gradient 
of the inhomogeneous magnetic field generated by the permanent magnet. For 
achieving a resolution in the order of .ANG.ngstroms a field gradient in 
the order of about 100 Gauss/.ANG. is required. In the Rugar experiment, 
however, the field gradient was only about 5 Gauss/.mu.m. A strong 
magnetic field gradient in the atomic range, as described before, may be 
obtained with a ferromagnetic source of magnetic field only when the field 
source itself has atomic dimensions. For example, a ferromagnetic sphere 
having a diameter of about 300 .ANG. would have to be manufactured for 
obtaining a field gradient of about 100 Gauss/.ANG. in a distance of 50 
.ANG. from the sphere. 
It is, therefore, an object underlying the invention to provide a method 
and an apparatus as mentioned at the outset which, on the one hand side, 
has the advantages of AFM, namely allowing high resolution topographical 
atomic determination of structures on sample surfaces but, on the other 
hand side, allowing to determine the identity of atoms, in particular of 
their atomic magnetic moments and the distribution of atomic magnetic 
moments within the sample by using magnetic resonance effects for 
particularly detecting single spins in the sample surface. 
SUMMARY OF THE INVENTION 
According to a first aspect of the invention, there is suggested a method 
for detecting an atomic structure of a sample along a surface thereof, the 
method comprising the steps of: 
arranging said sample in a constant magnetic field B.sub.0 of predetermined 
field strength and high homogeneity, said constant magnetic field B.sub.0 
having a first direction; 
irradiating a first high-frequency magnetic field B.sub.1 of a first 
predetermined frequency on said sample, said first high-frequency magnetic 
field B.sub.1 having a second direction perpendicular to said first 
direction; 
preferably irradiating a second high-frequency magnetic field B.sub.2 of a 
second predetermined frequency on said sample, said second high-frequency 
magnetic field B.sub.2 having a second direction perpendicular to said 
first direction, and setting said second pre-determined frequency such 
that magnetic resonance is excited within said sample surface; 
providing a force-sensitive sensor having a paragraph magnetic tip 
comprising a paramagnetic spin at a terminal end of said paramagnetic tip, 
said spin being accessible for electron paramagnetic resonance (EPR) 
excitation; 
placing said sensor in close vicinity to said sample such that said sensor 
tip is in atomic interaction with said sample surface; 
setting said predetermined field strength and said predetermined frequency 
such that EPR is excited within said paramagnetic tip; 
displacing said paramagnetic tip parallel to said sample surface for 
mapping predetermined points on said sample surface; and 
during said step of displacing measuring the force exerted on said 
paramagnetic tip by a local in-homogeneous magnetic field B.sub.loc caused 
by atomic magnetic moments m.sub.e,k of said sample. 
Further, according to a second aspect of the invention, there is disclosed 
an apparatus for detecting an atomic structure of a sample along a surface 
thereof, the apparatus comprising: 
means for arranging said sample in a constant magnetic field B.sub.0 of 
predetermined field strength and high homogeneity, said constant magnetic 
field B.sub.0 having a first direction; 
means for irradiating a first high-frequency magnetic field B.sub.1 of a 
first predetermined frequency on said sample, said first high-frequency 
magnetic field B.sub.1 having a second direction perpendicular to said 
first direction; 
preferably means for irradiating a second high-frequency magnetic field 
B.sub.2 of a second predetermined frequency on said sample, said second 
high-frequency magnetic field B.sub.2 having a second direction 
perpendicular to said first direction, and setting said second 
predetermined frequency such that magnetic resonance is excited within 
said sample surface; 
means for providing a force-sensitive sensor having a paramagnetic tip 
comprising a paramagnetic spin at a terminal end of said paramagnetic tip, 
said spin being accessible for electron paramagnetic resonance (EPR) 
excitation; 
means for placing said sensor in close vicinity to said sample such that 
said sensor tip is in atomic interaction with said sample surface; 
means for setting said predetermined field strength and said predetermined 
frequency such that EPR is excited within said paramagnetic tip; 
means for displacing said paramagnetic tip parallel to said sample surface 
for mapping predetermined points on said sample surface; and 
means for measuring the force exerted on said paramagnetic tip by a local 
inhomogeneous magnetic field B.sub.loc caused by atomic magnetic moments 
m.sub.e,k of said sample during said step of displacing. 
The object underlying the invention is thus entirely achieved. 
The fundamentally new idea of the present invention is to use the EPR of a 
spin located at the tip to measure atomic scale magnetic field gradients. 
The aim is to provide atomic scale analytical information beside the usual 
topographic information obtained by AFM. 
The present invention places a special tip, having an electron spin on its 
far end, inside of a millimeter wave EPR resonant structure and, 
preferably, a broad band NMR probe. The aim is to detect any other spin in 
the sample in the .ANG. scale vicinity of the tip spin through the 
mechanical force arising from their interaction. 
This force is expected to be orders of magnitude smaller than the other 
forces of atomic origin acting on the tip. Subjecting these spins to 
various EPR and NMR excitations allows to control their relative 
orientation, i.e. a modulation of the minority force component at will. A 
large variety of synchronous detection schemes can be envisaged to 
separate and measure this minority force. This allows to identify (in the 
analytical, chemical sense) and precisely locate (in the structural sense) 
the unknown sample spin. 
For the first time the advantages offered by an AFM, for example the 
excellent local resolution is combined with the advantages inherent to 
conventional NMR and EPR, respectively, namely their ability to identify 
atoms by means of their magnetic properties. The method and apparatus 
according to the present invention, therefore, provide localized data on 
the distribution of atoms within the sample surface as well as 
non-localized data of magnetic moments associated to atoms and, further, 
localized microscopic magnetic fields in the vicinity of the respective 
atoms may be detected with a resolution of the atomic scale. 
The invention, therefore, distinguishes over the approach suggested by 
Rugar under several aspects. First, the sample is not attached to a 
force-sensitive sensor but, in contrast, the force-sensitive sensor itself 
is provided with a paramagnetic tip. Therefore, the force-sensitive sensor 
may be used for many subsequent and many different experiments. 
Furthermore, the inhomogeneous magnetic field is not externally generated 
by means of a permanent magnet, instead, the microscopic inhomogeneous 
magnetic field of every single atomic magnetic moment is used as a source 
of magnetic field gradients. The microscopic inhomogeneous magnetic 
fields, further, provide for the field gradients of several 100 
Gauss/.ANG. required for the high local resolution so that even single 
spins may be detected in the sample. Furthermore, the inhomogeneous 
magnetic field caused by the atomic moments may be varied by additional 
exciting NMR and EPR within the sample. 
As explained before, the present invention uses forces originated from the 
interaction of the dipole moments of two spins; one situated at the far 
end of the tip, the other being on the surface of the sample under 
investigation. In this arrangement, the cantilever properties do not 
depend on the parameters of the sample under investigation (like the 
resonant frequency of the cantilever influenced by the mass of the 
sample). This can be viewed only as the interchange of sample and 
ferromagnetic particle in the MRFM approach of Sidles and Rugar cited 
above. 
These two dipoles are placed to .ANG. scale distance from each other 
producing the maximum gradient or maximum force on each other. As a tip 
spin or sensor spin an electron spin is chosen as being the one providing 
the largest accessible field gradient in the nature at the closest 
accessible distance as compared to any ferromagnetic particle, the largest 
gradient of which at the pole or on the surface is smaller. This means 
that from the field gradient originated from a single spin the strongest 
force will be exercised on the paramagnetic tip as defined in the present 
invention, resulting in the highest sensitivity possible. 
A fundamental difference to the approach suggested by Rugar is that in the 
present invention none of the magnetic dipoles (field gradients) are 
static. Their relative orientation is fixed only by the high applied 
static magnetic field and the orientation of both can be manipulated 
independently by magnetic resonance means. 
Magnetic resonance means, preferably EPR, are used first to modulate the 
orientation of spin located on the sensor tip. This results in an 
alternating force on the cantilever if the field gradient experienced by 
the tip spin is not zero, independently of the origin of the field 
gradient, thereby realizing the most sensitive local field gradient 
measurement possible on atomic scale. 
Preferably, magnetic resonance means are used the second time to identify 
the source of the field gradient experienced by the cantilever tip. This 
is done by finding the resonance frequency in the NMR or in the EPR 
frequency range, and modulating the orientation of that specific sample 
spin. It is in this step that the magnetic moment in the sample is 
chemically identified. 
Another advantage resides in the fact that EPR is excited within the tip. 
Due to the fact that the magnetic moments within the tip are detectors for 
magnetic forces acting from the inhomogeneous magnetic fields of the 
single atomic moments of the sample, the resonance properties of both, the 
tip spin and the sample spin, may be entirely used and their orientation 
with respect to each other may be controlled and modulated. 
According to a preferred embodiment of the invention, the claimed method 
comprises further steps of 
irradiating a second high-frequency magnetic field B.sub.2 of a second 
predetermined frequency on said sample, said second high-frequency 
magnetic field B.sub.2 having a second direction perpendicular to said 
first direction, and setting said second predetermined frequency such that 
magnetic resonance is excited within said sample surface. 
Preferably, in case of this preferred embodiment, the step of exciting 
magnetic resonance comprises exciting either nuclear magnetic resonance 
(NMR) or electron paramagnetic resonance (EPR) . 
These embodiments of the invention have the advantage that not only a 
topographig image of the surface under investigation may be generated; 
instead, a chemical identification of surface material is possible. 
In a preferred embodiment of the invention, the static or constant magnetic 
field is set to be stronger than the inhomogeneous magnetic field created 
by the sample and the tip spins. 
According to a further preferred embodiment of the inventive method the 
constant magnetic field is selected above 2 Tesla, preferably in the range 
between 2 and 4 Tesla. 
These measures have the advantages that the magnetic moments within the tip 
and within the sample will preferably be oriented along the constant 
magnetic field. 
According to another embodiment of the method the constant magnetic field 
is set to extend perpendicularly to the sample surface. 
Considering that this is the orientation of maximum force between the 
sample and the tip, this orientation may be easily controlled. 
It is further preferred when the paramagnetic material of the tip is 
selected different from the material constituting the sample. 
As the materials distinguish with respect to their NMR and EPR properties, 
such that their magnetic resonance lines may be distinguished within the 
frequency spectrum, the NMR or EPR, respectively, may be selectively 
excited within the sample and within the tip, independently from each 
other. 
The method according to the invention is carried out with an extremely high 
local resolution when the tip is designed with a terminal end having an 
isolated paramagnetic moment. 
Due to the fact that a single paremagnetic moment at the terminal end of 
the paramagnetic tip does not or only weakly interact with other magnetic 
moments within the tip and, further, considering that such an isolated 
paramagnetic moment may be placed into very close vicinity to the sample 
surface, the force-sensitive detector is a point-shaped detector with 
respect to the detection of magnetic forces with the "point" having a 
dimension in the atomic scale and the magnetic moment having thus the 
smallest possible dimension. 
It is preferred to detect the force at a distance of the tip from the 
sample surface in the order of between 1 and 10 .ANG.. 
With such a distance the local inhomogeneous magnetic fields of the single 
magnetic moments of the sample have a sufficient strength and the gradient 
of the inhomogeneous magnetic fields are sufficiently strong at such a 
distance for yielding a measurable force and a sufficient local 
resolution. 
A particularly sensitive measurement may be made if a force-generated 
deflection of the force-sensitive sensor is detected by optical means. 
In a preferred embodiment of the invention a laser beam is used being 
reflected from the force-sensitive sensor and impinging subsequently on a 
four-quadrant diode. The deflection of the force-sensitive sensor may be 
measured as a difference signal between an upper segment and a lower 
segment of the four-quadrant diode. 
Optical measuring methods are preferred due to their extremely high 
precision. Due to the fact that a laser beam is reflected from the 
force-sensitive sensor and is then detected on a four-quadrant diode, the 
extremely small deflection on the force-sensitive sensor from its initial 
position, being of the order of 1 .ANG. is optically amplified by means of 
a corresponding long optical path of the light beam. 
As an alternative, the deflection caused by forces acting on the 
force-sensitive sensor may be detected by measuring a variation of 
electrical resistance within the force-sensitive sensor itself (F. J. 
Giessibl, Science 267, 68, (1995)). 
According to a group of embodiments the constant magnetic field is adapted 
to be amplitude modulated with a modulation frequency in the range of 
between 10 and 100 kHz. 
Applying a suitable frequency B.sub.1, the magnetic moment on the tip is 
periodically inverted with the modulation frequency. Thereby, an 
oscillating force is generated exciting the mechanical force-sensitive 
sensor to oscillate. The oscillating force may result in an amplification 
of the force-sensitive sensor deflection and, hence, in an amplification 
of the measuring sensitivity. 
According to an alternate group of embodiments the high frequency magnetic 
field is frequency modulated with a modulation frequency in the range of 
between 10 and 100 kHz. 
According to a preferred variation of the last-mentioned embodiment the EPR 
resonance conditions are controlled by a modulating magnetic field being 
superimposed to the homogeneous constant magnetic field. 
This measure has the advantage that the EPR resonance condition may be 
precisely controlled and set. 
It is particularly preferred to select the modulation frequency to be equal 
to the natural or resonance frequency of the force-sensitive sensor. 
If the force-sensitive sensor is excited to oscillate at its resonance or 
natural frequency, a particular high sensitivity of the measured signal is 
obtained. 
Furthermore, it is preferred to synchronously detect a measured signal with 
a modulation frequency of the amplitude modulated constant magnetic field 
by using a lock-in amplifier. 
When doing so, the sensitivity may be increased and the modulation 
frequency may be exactly tuned to the resonance frequency of the 
force-sensitive sensor. 
According to another embodiment a measuring signal having the modulation 
frequency of the frequency modulated high-frequency magnetic field is 
synchronously detected in a first lock-in amplifier, a reference signal 
having the low-frequency modulation frequency of the constant magnetic 
field being synchronously detected in a second lock-in amplifier with an 
output signal of the first lock-in amplifier, the second lock-in amplifier 
having an output signal being processed as an error signal for fine 
adjusting the constant magnetic field and, thereby, EPR resonance 
conditions. 
These measures result in another advantage because the measuring effect is 
amplified by tuning the modulation frequency to the resonance frequency of 
the force-sensitive sensor. Further, a fine tuning of the constant 
magnetic field takes place allowing to guarantee EPR conditions at any 
time. 
According to another group of embodiments the force-sensitive sensor is 
mechanically excited to oscillate at its natural frequency, the 
high-frequency magnetic field being irradiated as a sequence of 
.pi.-pulses synchronous with the sensor oscillations, a variation of the 
sensor natural frequency being detected along the sample surface. 
When doing so, one takes advantage of the fact that the natural frequency 
of the force-sensitive sensor is linearly depending on the gradient of the 
inhomogeneous force caused by the magnetic field within which the tip is 
arranged. 
Preferably, for distinguishing between nuclear moments and paramagnetic 
moments within the sample, additional further high-frequency magnetic 
fields are irradiated on the sample parallel to the high-frequency field 
for exciting nuclear magnetic resonance (NMR) and/or further paramagnetic 
resonance (EPR). 
By doing so it is possible to investigate whether a detected magnetic 
moment of the sample is a nuclear or an electronic magnetic moment. 
In particular, the magnetic moments of the sample may be quantitatively 
investigated. 
According to another preferred embodiment of the invention the tip of the 
force-sensitive sensor is brought into interaction with the sample surface 
such that the sum of static atomic non-magnetic forces acting on the tip 
equals zero. 
When doing so it is prevented on the one hand side that such atomic 
non-magnetic forces disrupt the detection of the magnetic force, and, on 
the other hand side the distance values at which the non-magnetic forces 
disappear allow to generate a topographic picture of the surface 
corresponding to those used with conventional AFMs. 
Preferably, the distance between the tip of the force-sensitive sensor and 
the sample surface at which the sum of the static atomic non-magnetic 
moments equals zero is set and controlled by means of a DC signal from the 
four-quadrant diode.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 shows an extremely simplified block diagram of a scanning electron 
paramagnetic resonance microscope (SEPRM) being designated by reference 
numeral 1. 
SEPRM 1 comprises a systems control 2 cooperating via a common bus with a 
primary EPR excitation 3a and a secondary EPR excitation 3b. Further, a 
field modulation generator 4 is provided. A secondary NMR excitation 5 may 
also be provided. A displacement control and force detector are identified 
with reference numeral 6. 
Modulation coils 7 are fed by field modulation generator 4. NMR coils 8, in 
turn, are fed by secondary NMR excitation 5. 
SEPRM 1 uses a probe head 10 that will be described in more detail with 
respect to FIG. 2 hereinafter. 
In FIG. 2, reference numeral as a whole indicates a probe head. Probe head 
10 comprises a Fabry-Perot resonator 11 consisting of a spherical upper 
mirror 12 and a plane lower circular mirror 14. Spherical mirror 12, for 
example, has a radius of curvature of about 35 mm and a diameter of about 
30 mm, whereas lower mirror 14 has a diameter of about 10 mm. 
A sample 16 is arranged approximately in the center of lower mirror 14. 
Resonator 11 is surrounded by a cylindrical housing 18 (for example made 
from aluminum). Housing 18 extends upwardly until upper mirror 12, 
however, is in no mechanical contact with either upper mirror 12 or lower 
mirror 14. Upper mirror 12 is arranged separately from fixed housing 18 to 
allow free adjustment of the distance between upper mirror 12 and lower 
mirror 14 and, hence, the resonance frequency of resonator 11. 
Lower mirror 14 is attached to a piezo-electrical scanner 20 allowing a 
displacement of lower mirror 14 and, hence, of sample 16 as well in the 
plane of lower mirror 14 (x-y-plane) as well as in a direction (z) 
perpendicular thereto (x-y-z-coordinate system 21). Piezo-electrical 
scanner 20 is attached to a bottom of housing 18, such that it may be 
displaced by means of a mechanical course adjustment 22 in z- and in 
x-y-directions on a larger scale of about 1 mm. 
The required electrical supply lines are not shown in FIG. 2. 
A cantilever 24, i.e. an elongate free arm is attached as a mechanical 
force-sensitive sensor adjacent sample 16 on a piezo-electrical modulator 
27. Modulator 27, in turn, is attached above lower mirror 14 on an annular 
plate 28 of housing 18 extending around lower mirror 14. Cantilever 24 is 
provided with a pointed tip having a paramagnetic material on its free 
end. The free end of cantilever 24 together with tip 26 may be deflected 
in the z-direction under the action of a force. 
The properties of cantilever 24 together with tip 26 will be explained in 
more detail below. 
Cantilever 24 is oriented such that tip 26 above sample 16 is pointed to 
the surface of sample 16. The sample surface is brought into contact with 
tip 26 by means of course adjustment 22 and by actuating piezo-electrical 
scanner 20 in the z-direction. The term "bringing into contact" shall be 
understood such that the distance between tip 26 and the surface of sample 
16 is set to be so small that both elements are in the range of 
short-range atomic interaction between the atoms of tip 26 and the atoms 
of sample 16. Such interactions occur in a distance ranging between about 
1 and 10 .ANG.ngstrom. 
Housing 18 is provided with an opening at the position where cantilever 24 
is attached to allow a simple exchange of sample 16 and/or cantilever 24. 
Housing 18 is provided with a laser diode 30 at the vertical position of 
upper mirror 12. Laser diode 30 is directed such that a beam 31 of laser 
light emitted therefrom is focussed on the free end of cantilever 24. A 
four-quadrant diode 32 acting as a position sensitive detector and having 
four segments is attached to housing 18 at a position opposite laser diode 
30. Further, four-quadrant diode 32 may be displaced along the x-and the 
y-direction by means of a micrometer adjustment 33. 
Instead of laser diode 30 and four-quadrant diode 32 other optical means 
may be used as an alternative, for example an optical interferometer. 
Further, it is possible to detect deflections of cantilever 24 by 
detecting the variation of electrical resistance of cantilever 24 itself. 
Sample 16 and tip 26 of cantilever 24 are surrounded by a superconducting 
coil (not shown), generating a constant homogeneous magnetic field B.sub.0 
at the position of tip 26 and being directed in the z-direction as shown 
by arrows in FIG. 2. 
A modulation coil (also not shown) superimposes constant magnetic field 
B.sub.0 with a modulating magnetic field B.sub.MOD being parallel to 
magnetic field B.sub.0 and having a frequency in the range of between 10 
and 100 kHz with an amplitude of about 10.sup.-3 Tesla. The strength of 
constant magnetic field B.sub.0 is selected to be preferably in the range 
of between 2 and 4 Tesla. The magnetic field strength must be set 
sufficiently high as will be explained further below. 
Resonator 11 is provided with a microwave frequency magnetic field B.sub.1 
via a waveguide 36. Microwave magnetic field B.sub.1 is fed into resonator 
11 by means of an iris opening 38. Iris opening 38 may be varied by means 
of a matching screw 40 or the like for matching resonator 11. Microwave 
magnetic field B.sub.1 is directed parallel to the plane of lower mirror 
14 and perpendicular to the homogeneous static or constant magnetic field 
B.sub.0 for exciting magnetic resonance, in particular electron 
paramagnetic resonance (EPR) within tip 26 and/or sample 16. 
When the constant magnetic field B.sub.0 is set to be 3,5 Tesla, the 
microwave frequency magnetic field B.sub.1 must have a frequency of about 
94 GHz for exciting EPR of spins having a gyromagnetic ratio g of about 2. 
If the distance between upper mirror 12 and lower mirror 14 is 35 mm, a 
standing wave of about 10 wavelengths is generated within resonator 11 at 
a frequency of 94 GHz of microwave magnetic field B.sub.1. Microwave 
magnetic field B.sub.1 is exactly focussed on sample 16 and tip 26, 
respectively. By doing so disrupting effects from housing 18 are 
minimized. 
Further, another coil to may be provided within housing 18 for generating 
an additional high-frequency magnetic field B.sub.2 in the MHz-range 
within resonator 11 parallel to microwave frequency magnetic field 
B.sub.1, for additionally exciting a nuclear magnetic resonance (NMR) 
within sample 16. For doing so a frequency of high-frequency magnetic 
field B.sub.2 in the order of 140 MHz is required for exciting NMR of 
protons in the homogeneous constant magnetic field B.sub.0 of 3,5 Tesla 
field strength. 
FIG. 3 shows in enlarged scale an essential element of the method and 
apparatus according to the present invention, namely the cantilever 24 
being provided with tip 26. 
Cantilever 24 consists of a base plate 50. Base plate 50 rigidly connects 
cantilever 24 with housing 18 via piezo-electrical modulator 27. Base 
plate 50 integrally extends as a free arm 52 of length 1 (typically 0.1 to 
1 mm) and thickness d (preferably less than 20 82 m, typically 1 .mu.m or 
even less). The terminal end of arm 52 may be deflected under the action 
of a positive or negative, respectively, force being directed in the 
z-direction, however, arm 52 is twisted under forces acting on the tip 26 
in directions perpendicular to the z-direction. 
The force sensibility of cantilever 24 is determined by its length 1 and 
the spring constant of arm 52. If cantilever 24 is used as a 
force-sensitive sensor for an oscillating force, the relevant parameters 
are its resonance frequency and its damping time from which its quality 
factor may be derived. 
Modern technology cantilevers are manufactured from silicon single crystals 
and have resonance frequencies in the order of between 10 and 100 kHz with 
quality factors of above 10.000. They are able to detect forces down to 
10.sup.-18 N. 
Arm 52 is provided at its free end with preferably pyramid-shaped pointed 
tip 26. Tip 26 has a paramagnetic material end. 
The paramagnetic material at the terminal end of tip 26 may be selected 
from a wide variety of materials. The only condition that the present 
invention requires is that at the very end of tip 26 (as close as possible 
to its material end) an unpaired spin has to be found, weakly coupled to 
the rest of tip 26, and accessible for EPR excitations. This does not 
necessarily mean that the material of tip 26 as a whole has to be 
paramagnetic. 
Si tips to the best of present knowledge have a dangling bond on their 
terminal end (cf. the Manassen article, cited above and showing the 
existence of a dangling bond on an oxidized Si surface). 
Further possibilities to manufacture a paramagnetic tip would include: 
materials which are ferromagnetic or antiferromagnetic as a bulk material 
for tip 26. The tip as a whole will display a broad ferromagnetic or 
antiferromagnetic resonance, however, the atoms at the terminal end of the 
tip would display EPR at fields practically shifted outside of the broad, 
bulk resonance; 
a few paramagnetic atoms like Eu, Gd, etc. can be placed at the terminal 
end of a prefabricated tip by electron beam deposition. 
The free terminal end of tip 26 has a dimension in the .ANG.ngstrom scale, 
i.e. the dimension of a single atom. Such tips may be manufactured with 
modern technologies and are in use in the field of AFM (atomic force 
microscopy). Principally, any material with covalent bonding character may 
be used as the required paramagnetic material. As such, semiconductors or 
isolators may be used, such as silicon nitride (Si.sub.3 N.sub.4). With 
the described method tip 26 is preferably selected as a material having 
different microscopic magnetic properties as compared with the material of 
sample 16, for what concerns the excitation of EPR. 
In contrast to the AFM technology the present invention takes advantage of 
the fact that the outermost terminal end of tip 26 has a so-called 
"dangling bond" or defect, i.e. a free bonding electron. The existance of 
such a defect may be assumed for a pointed tip of the order of 1 
.ANG.ngstrom. Such an electron which does not take part in a bonding has 
an unpaired spin and, together with its orbital angular momentum has a 
single paramagnetic moment which does not interact with other moments in 
the tip. 
For avoiding a compensation of the free bonding by adsorbed radicals (e.g. 
oxygen) resonator 11 is subjected to a low-pressure atmosphere of an inert 
gas, for example helium. 
FIG. 4 illustrates the physical principles on which the invention is based. 
Tip 26 is directed to the surface 60 of sample 16. Tip 26 and sample 16 
are located within the static homogeneous magnetic field B.sub.0 being 
generated within resonator 11 by the superconducting coil. The z-axis of 
coordinate system 21 is directed parallel to B.sub.0, as mentioned before. 
Atoms 62 are schematically shown in tip 26. Only atom 63 being located at 
the outermost terminal end of tip 26 has a free electronic paramagnetic 
moment m.sub.p. Of course, also a nuclear magnetic moment caused by a 
nuclear spin could be taken into account and the following considerations 
would be the same mutatis mutandis. 
It should be mentioned here that the term "moment" should be understood to 
be the expectation value of such a moment within the meaning of quantum 
mechanics. 
Within sample 16 an uppermost layer of atoms 64 and, representative for 
all, an atomic magnetic moment m.sub.e,k is shown which could be an 
electronic moment or a nuclear moment or the sum of both. 
Within the strong homogeneous static magnetic field B.sub.0 of e.g. 3,5 
Tesla strength, the magnetic moments m.sub.p and m.sub.e,k are oriented 
parallel to magnetic field B.sub.0. For electrons m.sub.e 
=9,27.times.10.sup.-24 Am.sup.2 and for protons m.sub.k 
=1,41.times.10.sup.-26 Am.sup.2. Each of the magnetic moments m.sub.e,k in 
its surrounding and in the vicinity of surface 60 of sample 16 generates a 
local, inhomogeneous magnetic dipole field B.sub.loc, the field lines of 
which are shown in FIG. 3 in dashed lines for representative moment 
m.sub.e,k. 
At the location of paramagnetic moment m.sub.p of tip 26 the component of 
the field intensity of magnetic dipole field B.sub.loc in the direction of 
static magnetic field B.sub.0 is given by equation 
##EQU1## 
Within equation (1) .mu..sub.0 is the vaccum permeability. .theta. is the 
angle between the z-axis and the interconnecting line between point-shaped 
magnetic moment m.sub.e,k and the paramagnetic moment m.sub.p. r is the 
distance between magnetic moments m.sub.p and m.sub.e,k. 
Paramagnetic moment m.sub.p views the strongest magnetic dipole field when 
moments m.sub.p and m.sub.e,k are located directly above each other 
(.theta.=0). If sample 16 is displaced within the x-y-plane below tip 26, 
paramagnetic moment m.sub.p according to the distribution of the magnetic 
moments m.sub.e,k within sample 16 in the neighborhood of surface 60 is 
located alternately within areas of increasing and decreasing strength, 
respectively, of magnetic dipole field B.sub.loc. 
Due to the inhomogeneity of magnetic dipole field B.sub.loc a force acts on 
paramagnetic moment m.sub.p and, hence, on tip 26 of cantilever 24 
according to the equation 
EQU F=(m.sub.p .multidot.v)B (2) 
wherein, in particular, the force directed in z-direction 
##EQU2## 
is of interest because it deflects cantilever 24. 
Table 1 shows the force F.sub.z on paramagnetic moment m.sub.p according to 
equation (3) for various distances between magnetic moments m.sub.e of an 
electron or m.sub.k of a proton, respectively, as are present within 
surface 60, and paramagnetic moment m.sub.p of tip 26 for an angle 
.theta.=0 as well as the field strength of magnetic dipole field B.sub.loc 
according to equation (1) as well as the strength of gradient B'.sub.loc 
=.delta.B.sub.loc .delta..sub.z of field strength B.sub.loc. 
From the values shown in Table 1 it can be particularly seen that due to 
the strong descrease of inhomogeneous dipole field B.sub.loc as a function 
of the distance between paramagnetic moment m.sub.p or tip 26 and the 
magnetic moments m.sub.e,k only the paramagnetic moment m.sub.p being 
closest to the outermost terminal end of tip 26 is sensitive for the 
magnetic force. 
The same applies for neighbored moments m.sub.e,k of sample 16 having a 
distance of the order of a few .ANG.ngstrom from each other so that 
superposition effects through neighbored moments m.sub.e,k are negligible. 
TABLE 1 
__________________________________________________________________________ 
m.sub.e m.sub.k 
Distance r 
B.sub.loc 
B'.sub.loc 
F.sub.z 
B.sub.loc 
B'.sub.loc 
F.sub.z 
[.ANG.] 
[Gauss] 
[Gauss/.ANG.] 
[N] [Gauss] 
[Gauss/.ANG.] 
[N] 
__________________________________________________________________________ 
1 18557 
5,6 .multidot. 10.sup.4 
5,2 .multidot. 10.sup.-13 
28,2 
84,7 8 .multidot. 10.sup.-15 
3 687,3 
687,3 6,4 .multidot. 10.sup.-15 
1,04 
1,04 9,7 .multidot. 10.sup.-18 
10 18,6 
5,6 5,2 .multidot. 10.sup.-17 
0,028 
0,008 8 .multidot. 10.sup.-20 
__________________________________________________________________________ 
Force F.sub.z acting on tip 26 of cantilever 24 may be detected as a 
deflection of arm 52 from its initial position. 
Therefore, according to the method of the present invention force F.sub.z 
is derived from the gradient of local inhomogeneous magnetic dipole field 
B.sub.loc of magnetic moments m.sub.e,k within the vicinity of surface 60 
of sample 16. Due to the fact that with such a detection method the 
resolution that may be obtained is inversely proportional to the gradient 
of local inhomogeneous magnetic dipole field B.sub.loc, magnetic 
structures within sample 16 may be resolved within the .ANG.ngstrom-range 
due to the extremely high gradients (cf. Table 1) when the claimed 
detection method is used. 
The strength of homogeneous static magnetic field B.sub.0 has to be 
selected such that it is higher as compared to the strength of 
inhomogeneous magnetic dipole field B.sub.loc in the vicinity of surface 
60 of sample 16 for ensuring that magnetic moments m.sub.p and m.sub.e,k 
are properly oriented. With a field strength of e.g. B.sub.0 =3,5 Tesla 
this is certainly the case. 
Up to now only the generation of a static force was discussed as acting on 
tip 26 and resulting in a deflection of arm 52 of cantilever 24 to one 
side only. However, preferably an oscillating force instead of a static 
force is measured with cantilever 24, thereby yielding an amplification of 
the measurement effect, provided that the frequency of the oscillating 
force is the same as the resonant frequency or natural frequency of 
cantilever 24. 
EPR is excited in tip 26 by irradiating microwave magnetic field B.sub.1 
orthogonally to homogeneous static magnetic field B.sub.0. When a static 
magnetic field B.sub.0 of 3,5 Tesla strength is used, the resonance 
condition for EPR in the paramagnetic material of tip 26 is fulfilled at a 
frequency of microwave magnetic field B.sub.1 of about 94 GHz. The exact 
position of the resonance line within the EPR spectrum depends on the 
superimposed inhomogeneous dipole field B.sub.loc caused by the magnetic 
moments m.sub.e,k of sample 16 at the location of tip 26. 
If EPR is excited periodically, an oscillating force, in particular with 
the resonance frequency of cantilever 24 may be generated, as will be 
described in connection with the following embodiments of the invention, 
by inverting the paramagnetic moment m.sub.p at tip 26 through a 
modulation of the EPR with the resonance frequency of cantilever 24. In 
particular, it shall be discussed how the oscillating force may be 
detected. 
Force detection modes suitable for carrying out the present invention would 
comprise DC and AC detection modes, however, for sensitivity reasons, AC 
detection modes are contemplated better. 
The AC detection operates by creating means to modulate the force and 
detects the derivative of the force with the aid of a lock-in amplifier 
(J. A. Sidles et al., "Signal-to-noise ratios in electrical and mechanical 
detection of magnetic resonance", Phys. Rev. Lett. 70, 3506-3509, (1993)). 
Using an AFM, one observes static forces, therefore, to implement this type 
of detection, one has to add an active means to modulate the sample-tip 
distance. This is the function of the piezoelectric modulator placed below 
the probe (cf. reference numeral 28 in FIG. 2). Moving periodically the 
tip in a range within the forces acting on it are changing, the resonance 
frequency of the cantilever will change proportionally with the space 
derivative of the force acting on the tip. Two types of AC detection modes 
may be used, namely amplitude modulated (AM) and frequency modulated (FM) 
detection. 
In the AM mode the cantilever is driven to oscillate at a constant 
frequency by applying constant amplitude oscillating voltage on the 
piezoelectric modulator. The amplitude variation of the oscillating 
cantilever is monitored with a lock-in amplifier under the influence of 
the forces. The largest amplitude oscillation is created by setting the 
drive voltage frequency to be equal to the mechanical resonance frequency 
of the cantilever. As the force derivative appears as a resonant frequency 
change, the highest sensitivity achieved (the largest amplitude variation) 
when the driving frequency is set off resonance by an amount of the half 
width of the mechanical resonance. 
In the FM mode the high quality factor cantilever is literally used as the 
frequency-determining element of an oscillator, just as the quartz piece 
is used in a common quartz oscillator. The electronics driving the 
piezoelectric modulator monitors the oscillator component of the 
photodiode signals, and maintains it to be constant in amplitude. The 
frequency variation of the signal of the cantilever is then measured, 
which is directly related to the force gradient experienced by the tip. 
Within the scope of the present invention, the suggested example 
configurations use the combinations of these detection modes. The magnetic 
force component being the component of interest, is a minority component. 
The magnetic resonance means are disposed of to modulate it, calling for 
the use of ac detection. The examples shown in FIGS. 5 and 6 use an AM 
mode AC detection, but this is not the signal which controls the 
tip-sample distance. The DC part of the signal is used to set and control 
the working point or working distance of the tip. The magnetic force is 
modulated by periodically alternating the direction of the tip-spin. 
Therefore, there is no need to drive the cantilever oscillation with the 
piezoelectric modulator, since it will be driven by the magnetic force. It 
is the amplitude of the cantilever oscillation which is detected 
synchronously with the force modulation. Tuning the force modulation (EPR 
excitation) frequency to the mechanical resonance frequency of the 
cantilever results in a sensitive narrow band receiver, i.e. a sensitivity 
increase by the Q factor of the mechanical resonance. All other forces 
present, usually investigated by AFM, are static forces while the present 
invention provides means to make the magnetic force time dependent. 
Further, before turning to the block diagrams of FIGS. 5 to 8, various spin 
manipulation means should be discussed, as are suitable for carrying out 
the present invention. 
The classics of the magnetic resonance literature offer many possibilities 
to achieve a periodical modulation (inversion) of the spin orientation in 
an external static field of high enough magnetic field strength. They can 
be grouped in three categories, speaking in terms of the underlying 
physical phenomena. 
1. The adiabatic inversion corresponds to an adiabatic demagnetization in 
the rotating frame. Applying a continuous wave excitation and passing 
slowly through the resonance will invert the expectation value of m.sub.z, 
if the variation is slow compared to the Larmor frequency in the rotating 
frame. This can be realized in two equivalent ways: 
applying a constant frequency CW millimeter-wave (B.sub.1) or RF for the 
sample spin (B.sub.2), while sweeping the static field B.sub.0 through 
resonance; 
keeping the static field constant and sweeping the frequency of the CW 
millimeter-wave (or RF for the sample-spin) through resonance. 
A periodic repetition of any of the above two procedures, i.e. a large 
amplitude modulation of B.sub.0 an FM modulation of B.sub.1 and/or B.sub.2 
will result in a periodic inversion of the spin. 
2. Transient nutation means staying close to resonance and applying a long 
pulse resulting in nutation of the spin, i.e. an oscillation of m.sub.z 
with the period of about the Larmor frequency in the rotating frame. The 
difficulty of this technique is that the frequency of the oscillation will 
vary as the resonance condition will vary while the tip is moving. The 
advantage of this technique is that the variation of the frequency can be 
used to measure the field at the position of the tip-spin. 
3. Finally, a third spin manipulation means would comprise pulsing at a 
periodical rate. If the value of B.sub.1 allows, quick inversions can be 
produced by .pi. (180.degree.) pulses without precisely tracking the 
resonance condition. To avoid the accumulation of rotation angle errors, 
in practice one will need to use more complicated pulse sequences (a phase 
alternation of the pulses, at least) than a simple repetition of identical 
.pi. pulses. 
The afore-mentioned three spin manipulation possibilities can be applied 
both as a primary excitation on the tip-spin and as a secondary excitation 
on the sample-spin in combination with any of the different force 
detection modes, raising the possible number of operation modes under the 
present invention for the apparatus difficult to count. 
The operation mode examples given on the block diagrams deal only with the 
primary excitations and use the two possibilities offered by adiabatic 
inversion (FIG. 5 for the field modulation, FIG. 6 the FM modulation) and 
the simplest variant of the pulsing method (FIG. 7). 
These physically different means represent different advantages and they 
will be useful under different conditions and will perform differently in 
terms of required measuring time and information provided. For selecting 
one of the three spin manipulation means, the following should be borne in 
mind: 
The adiabatic inversion method is the most straight forward, and the 
easiest example to show, how one can combine the modulated excitation and 
the detected signal through a lock-in amplifier to achieve the selective 
detection of the magnetic force. It is also the simplest configuration 
(FIG. 5) to search for a signal, i.e. for resonance field. The FM case is 
included as a separate example to show a possibility of field tracking. 
Both examples use AM mode force detection, but nothing prevents the use of 
this excitation modes in connection with any other force detection mode. 
This is the most natural choice for secondary excitations, i.e. 
frequencies swept continuous RF excitation, as well. 
The transient nutation method has no reference signal coherent with the 
excitation frequency. It requires a real time, high resolution 
digitization of the cantilever signal, and a subsequent Fourier analysis 
to single out the oscillating component. The measured amplitude is 
proportional to the force. The measured frequency contains information 
about the variation of the off-resonance field. If signal-to-noise allows, 
this technique has the advantage to measure simultaneously and 
continuously the force and the field variation at the same time without 
adjustment of B.sub.0. This is an AM-like force detection mode, that is 
the nutation frequency has to match the cantilever resonance frequency and 
band width. 
The pulsing method is used in connection with the FM force detection as 
shown in FIG. 7. It is the easiest to realize externally triggered, but it 
is equally suited to AM force detection. If the spectral coverage of 
pulses are sufficient, it will allow for force measurement without 
worrying about field adjustment. 
FIG. 5 shows a block diagram of a first embodiment of an apparatus 
according to the invention enabling to carry out the method according to 
the invention. 
First, sample 16 is brought into contact, i.e. into atomic interaction with 
tip 26 of cantilever 24 by means of piezo-electrical scanner 20. 
A power supply 70 is provided for feeding a superconducting coil (not 
shown) generating the strong homogeneous magnetic field B.sub.0 along the 
z-direction in the area of resonator 11. A source of microwave frequency 
72 generates the microwave frequency magnetic field B.sub.1 being fed to 
resonator 11 via waveguide 36 in continuous wave operation. Within 
resonator 11 magnetic fields B.sub.0 and B.sub.1 are oriented orthogonally 
to each other. The microwave frequency magnetic field B.sub.1 is 
irradiated with a fixed frequency and the homogeneous static magnetic 
field B.sub.0 is set such that EPR is excited only within the paramagnetic 
material of tip 26. In contrast, no EPR is excited within sample 16 at 
this time because the paramagnetic material of tip 26 has a different 
gyromagnetic ratio as compared to that of the sample material. 
A low-frequency generator 74 generates a modulation field B.sub.MOD of weak 
amplitude and parallel to magnetic field B.sub.0 within resonator 11 via a 
modulation coil (not shown). The modulation frequency lies in the range of 
between 10 and 100 kHz and is selected to be equal to the resonance 
frequency of cantilever 24. The modulation of homogeneous static magnetic 
field B.sub.0 around the EPR resonance line causes a periodical inversion 
of paramagnetic moment m.sub.p within tip 26 of cantilever 24 at the 
modulation frequency. Hence, an oscillating force f.sub.z of same 
frequency acts on tip 26 being proportional to the gradient of 
inhomogeneous magnetic dipole field B.sub.loc caused by sample 16. As a 
result cantilever 24 is excited to oscillate in z-direction with a 
frequency being equal to the frequency of modulating field B.sub.MOD. 
Light beam 31 emitted by laser diode 30 is reflected by the free end of 
cantilever 24 and then impinges on four-quadrant diode 32 for being 
detected therein. Four-quadrant diode 32 is oriented such that the 
currents within its four segments are equal when cantilever 24 is in its 
neutral position. 
As soon as cantilever 24 is deflected, e.g. downwardly in the z-direction, 
the current within the lower segment increases and within the upper 
segment decreases. A differential amplifier 76 is switched behind 
four-quadrant diode 32 for generating a differential signal of the upper 
and the lower segment of four-quadrant diode 32. The output signal of 
differential amplifier 26 has an alternating current (AC) component caused 
by the above-described oscillation of cantilever 24 and has a direct 
current (DC) component caused by the deflection of cantilever 24 due to 
static atomic non-magnetic forces acting on tip 26 of cantilever 24 if tip 
26 is at a distant of a few .ANG.ngstroms from the surface 60 of sample 
16. Such non-magnetic forces are e.g. the attracting van-der-Waals force 
or the repelling force of the electron envelope. 
The AC portion and the DC portion of the output of differential amplifier 
26 are separated in a AC/DC decoupler 78. The DC portion of the output 
signal of AC/DC decoupler 78 is fed to a control unit 80 for 
piezo-electrical scanner 20, initiating a computer-controlled adjustment 
of the distance between tip 26 and sample 16, wherein for every point 
(x,y) of sample surface 60 the distance is set such that the sum of the 
static atomic non-magnetic forces on tip 26 is constant. The obtained 
values for distance z as a function of x and y are stored and are the 
basis for the generation of a topographical atomic structure picture of 
surface 60 of sample 16 as may be obtained with an atomic force 
microscope. 
The AC portion of the output signal of AC/DC decoupler 78 is synchronously 
detected in a lock-in amplifier 82 with a reference signal from 
low-frequency generator 74. By doing so a fine tuning of the modulation 
frequency on the resonance frequency of cantilever 24 may be obtained. The 
measured signal is digitized in an analog/digital converter 84. 
By means of piezo-electrical scanner 20 sample 16 is displaced below tip 26 
of cantilever 24 in directions parallel to surface 60 of sample 16 wherein 
in predetermined points, preferably in all of the points x, y of surface 
60 of sample 16 the amplitude of oscillation of cantilever 24 is detected 
being a measure for the intensity of the gradient of the inhomogeneous 
magnetic dipole field B.sub.loc along the surface 60 of sample 16 and, 
hence, a measure for the atomic magnetic structure of surface 60 of sample 
16. 
The digitized measured signal is fed to a computer 90 providing the entire 
control of the apparatus and the processing of the measured values. 
FIG. 6 shows a block diagram of a second embodiment being slightly modified 
as compared to the first embodiment of FIG. 5. Within the source of 
microwave energy 72 the microwave signal and, hence, the microwave 
frequency magnetic field B.sub.1 is frequency modulated with a 
FM-frequency and is then fed to resonator 11. The quality factor of 
resonator 11 allows a frequency modulation of e.g. up to 50 MHz. By 
frequency modulating the microwave frequency magnetic field B.sub.1 an 
oscillating force is generated. 
The measured signal, i.e. the AC component of AC/DC decoupler 78 is 
initially fed to a first lock-in amplifier 82 of the present embodiment 
and is synchronously detected with the FM signal of the source of 
microwave frequency 72 as a reference signal and is then evaluated via 
analog/digital converter 84. 
A low-frequency magnetic field B.sub.MOD generated by low-frequency 
generator 74 and amplitude modulating the homogeneous static magnetic 
field B.sub.0 is used in this embodiment for tuning magnetic field B.sub.0 
in order for precisely controlling EPR. The amplitude modulation frequency 
is much smaller as compared to the resonance frequency of cantilever 24 
and is typically in the order of 100 Hz. For doing so an output signal of 
first lock-in amplifier 82 is synchronously detected in a second lock-in 
amplifier 94 with a reference signal from low-frequency generator 74. The 
output signal of second lock-in amplifier 94 is used as an error signal 
for adjusting static magnetic field B.sub.0. 
FIG. 7 shows a third embodiment in which the magnetic force is detected in 
a different manner as compared to that described before. 
Cantilever 24 is excited by piezo-electric modulator 27 to oscillate at 
resonance with constant amplitude. The inversion of paramagnetic moment 
m.sub.p of tip 26 is effected by irradiating the microwave frequency 
magnetic field B.sub.1 as a sequence of .pi.-pulses (180.degree.-pulses) 
which are generated by the source of microwave energy 72 in a gated mode 
of operation. The .pi.-pulses are set with their repetition rate to be 
synchronous to the resonance frequency or natural frequency of tip 26 by 
means of a trigger/delay generator 96. For example a .pi.-pulse may be 
irradiated into resonator 11 at every zero transition of the oscillating 
output signal of differential amplifier 76. 
Care should be taken that the homogeneous static magnetic field B.sub.0 is 
kept exactly on the EPR resonance line which is not that easy because tip 
26 due to its oscillation views a modulated inhomogeneous magnetic field 
B.sub.loc from the dipoles within surface 60 in a z-direction. 
When sample 16 is displaced below tip 26 in x- and y-directions, i.e. when 
tip 26 travels through the gradient of inhomogeneous magnetic field 
B.sub.loc caused by the magnetic moments m.sub.e,k of sample 16, then a 
steady variation of the resonance frequency of cantilever 24 may be 
detected. For, the resonance frequency of cantilever 24 is proportional to 
the gradient of the force due to the inhomogeneous magnetic field 
B.sub.loc in the vicinity of surface 60 of sample 16. This effect is 
explained in more detail in an article of Sidler et al. (Phys. Rev. Lett. 
70, p. 3506 (1993)). 
The variation of the resonance frequency of cantilever 24 is detected by a 
frequency counter 100. 
A feedback control 98 feeds the measured signal back to piezo-electric 
modulator 27 to keep the oscillation amplitude constant. 
Up to now it was discussed how the inhomogeneous magnetic field B.sub.loc 
caused by magnetic moments m.sub.e,k within sample 16 in the vicinity of 
surface 60 may be detected. It has not been taken into account, insofar, 
whether the moments were pure electron or nuclear magnetic moment or the 
sum of both. 
Independently of which of the embodiments of the method according to the 
present invention, described before, in addition to the microwave 
frequency magnetic field B.sub.1 an additional high-frequency magnetic 
field B.sub.2 may be irradiated into resonator 11 by means of coil to 
(FIG. 2) for additionally exciting an NMR within sample 16. In such a 
so-called electron-nuclear-double-resonance set-up (ENDOR) the frequency 
of additional high-frequency magnetic field B.sub.2 is sweeped through the 
NMR line, the NMR being detected as a decrease of the magnetic force on 
tip 26 of cantilever 24. In such a way the magnetic moments m.sub.e,k may 
be measured quantitatively. 
The same applies, mutatis mutandis, when an electron magnetic moment shall 
be detected. For that purpose an electron-electron-double-resonance set-up 
(ELDOR) is used and, instead of an additional ratio-frequency magnetic 
field a second microwave frequency magnetic field is irradiated in 
addition to the standard microwave frequency magnetic field B.sub.1 as 
B.sub.2. 
According to the method and the apparatus of the present invention one can, 
therefore, generate a conventional topographic picture of the surface 60 
of sample 16 by using the apparatus like a conventional atomic force 
microscope. 
However, by taking advantage of the magnetic resonance within tip 26 of 
cantilever 24 the gradient of the inhomogeneous magnetic field B.sub.loc, 
caused by the various electron and nuclear moments, may be measured via 
the action of a force. 
Furthermore, it is possible to combine the detection of magnetic forces 
with conventional ENDOR and ELDOR concepts, respectively, for identifying 
the atoms with respect to their magnetic moments and their relative 
position with respect to each other. 
FIG. 8, finally, shows another block diagram to illustrate the use of 
transient nutation. 
In contrast to the above-described block diagrams, a trigger output of 
source 72 of microwave energy is used to trigger a fast digitizer 102 
receiving its input signals from AC/DC decoupler 78.