Magnetic resonance force microscopy : interaction forces and channels of energy dissipation

Today, smaller and smaller electron and nuclear magnetic resonance structures
are extensively studied both from an applied and from a fundamental point of view.
The powerful tool of magnetic resonance imaging (MRI) has demonstrated that
it is possible to visualize subsurface three dimensional structures with micrometer
resolution [1] containing 1012 nuclear spins; nuclear magnetic resonance (NMR) spectroscopy
has the capacity to determine the three dimensional structure of biological
macromolecules [2]. Owing to the larger gyromagnetic ratio of electrons as compared
to paramagnetic nuclei, electron spin resonance (ESR) has pushed detection
sensitivity to 107 spins [3]. Finally, a single electron spin [4] has been detected by
magnetic resonance force microscopy (MRFM), employing a device which combines
two sensing technologies, namely magnetic resonance imaging (MRI) and atomic
force microscopy (AFM). The ultimate goal of MRFM is to map the interior of a
material sample, such as a complicated semiconductor structure or a bio-molecule,
at atomic scale resolution.
The idea of introducing MRFM to improve the detection sensitivity down to a
single spin and thus to resolve atoms of proteins [5],[6] was originally proposed in
1992. Ten years later, Rugar and co-workers reported the detection of a single electron
spin resonance in a silica substrate with paramagnetic defects, using a magnetic
resonance force microscope [4] with a lateral resolution of 25 nm in one dimension.
To achieve this single spin detection, the magnetic resonance force microscopy uses
a soft cantilever with a tiny hard magnetic tip material. The inhomogeneity field
Binhom generated from the magnetic tip is superimposed with the homogenous magnetic
field B0 which polarizes the sample. For a radio frequency field the resonance
condition is fulfilled in the region where !1 =
(B0 + Bgrad) and where
is the
gyromagnetic ratio of electron or proton. Consequently, the next foreseeable step is
to detect a single nuclear spin. In fact, the correspondence between ESR and NMR
is very close, and much of the basic theory of ESR is directly applicable to NMR.
ESR requires an unpaired electron whereas NMR requires an unpaired nuclear spin
for detection. Furthermore, an external static magnetic field is necessary in both
ESR and NMR detection. The major difference between the two techniques is due
to the gyromagnetic ratio of the proton and electron. ESR entails the higher electron
gyromagnetic ratio, as compared to the nuclear gyromagnetic ratio involved in
NMR and the sensitivity of EPR is correspondingly higher (approximately a factor
of 1000).
The force generated by a single spin is in the attonewton range. Thus, non
commercial, soft single crystalline silicon cantilevers with a high quality factor and
minimized spring constants have to be used for detecting a single spin. Measurements are performed at liquid helium temperature where thermal noise is reduced
by a factor of 10. The UHV condition makes for a very stable environment reducing
the oxidation of the sample and of the cantilever. In our low temperature force
microscope force sensitivities on the order of 10−18 N/pHz at 10 K are obtained
without any external static field [7]. A force sensitivity in the order of 9x10−18
N/pHz should be reached at 4 K in a static magnetic field of 100 mT.
In this work we design, build and assemble the entire UHV machine working
at a pressure of <10−10 mbar and at helium boiling temperature starting from the
existing microscope and the Janis cryostat. This work took about one year producing
hundreds of schemes and designs. The entire cryogenic machine plan is detailed in
the appendix. For detailed subsystem schemes please refer to the scheme library in
the appendices.
The extreme high sensitivity of 10−18 N/pHz that the magnetic force resonance
microscope should reach, requires the study of interaction phenomena. The small
spring constant for high force sensitivity makes it necessary to have the cantilever
perpendicular to the sample surface. Otherwise, the cantilever will stick electrostatically
to the sample surface. This vertical configuration introduces new design
parameters involving the cantilever’s approach to the sample. In fact the cantilever
is subject not only on the lateral force gradient but also to a vertical force. The vertical
attractive force as a uniform force will cause an increase in the frequency similar
to the uniform gravitational force that causes a pendulum to have a frequency that
is proportional to gravity.
The tip-sample interaction dissipation is then measured by the Q factor change
as a function of the distance. The dissipation is caused mainly by the electrostatic
charge fluctuation. The fluctuation of charge stored on a capacitance C induces the
noise denoted as ”KTC”. The noise of the fluctuation charge is on the order of
observed charge fluctuations of single-electron transistors. This shows a probably
common origin of the charge fluctuation.
A severe loss in force sensitivity and a frequency shift are observed while exposing
the cantilever with a magnetic tip to a homogenous magnetic field. The micrometer
sized magnetic particles generate a magnetic field of 500 Gauss and magnetic
field gradients (dB/dz>> 1x105 T/m). To minimize the damping losses of the
cantilevers with ferromagnetic particles various magnetic materials (e.g. Sm2Co17,
SmCo5, Nd2Fe14B, and Pr2Fe14B) with different grain materials and domain sizes
are investigated. The lowest magnetic dissipation is observed with SmCo5 tips having
a higher anisotropy constant. A correlation between frequency of oscillation and
magnetic field hysteresis is then measured. A detection sensitivity in the order of
10−18N/pHz is reached at 100 mT. This sensitivity should be enough for measuring
less than 100 electron spins.
Finally, a home-built spectrometer is compared with a home-built magnetic resonance
force microscope with the sample mounted on the cantilever. At room temperature
and at 50 mT the magnetic resonance force microscope has a sensitivity
improvement of a factor of more than 100000. This suggests the huge potential of
this instrument for biological and chemical sample analysis.
This work is part of ultimate limits of measurement of module IX of the National
Center of Competence in Research in Nanoscience (NCCR). The NCCR is the national Swiss research projects in nano technologies with the leading house in Basel.
The main goal of this submodule is to ultimately perform single spin experiments
at low temperature and in ultra high vacuum (UHV). Achieving this goal requires
mechanical force sensors to be improved and all relevant forces to be understood.
The channels of energy dissipation should be determined in order to improve the
detection sensitivity.