Quantitative measurement of the magnetic moment of individual magnetic nanoparticles by magnetic force microscopy.
ABSTRACT The quantitative measurement of the magnetization of individual magnetic nanoparticles (MNPs) using magnetic force microscopy (MFM) is described. Quantitative measurement is realized by calibration of the MFM signal using an MNP reference sample with traceably determined magnetization. A resolution of the magnetic moment of the order of 10(-18) A m(2) under ambient conditions is demonstrated, which is presently limited by the tip's magnetic moment and the noise level of the instrument. The calibration scheme can be applied to practically any magnetic force microscope and tip, thus allowing a wide range of future applications, for example in nanomagnetism and biotechnology.
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ABSTRACT: The use of magnetic force microscopy (MFM) to detect probe-sample interactions from superparamagnetic nanoparticles in vitro in ambient atmospheric conditions is reported here. By using both magnetic and nonmagnetic probes in dynamic lift-mode imaging and by controlling the direction and magnitude of the external magnetic field applied to the samples, it is possible to detect and identify the presence of superparamagnetic nanoparticles. The experimental results shown here are in agreement with the estimated sensitivity of the MFM technique. The potential and challenges for localizing nanoscale magnetic domains in biological samples is discussed.Small 03/2008; 4(2):270-8. · 7.82 Impact Factor
Quantitative measurement of the magnetic moment of an
individual magnetic nanoparticle by magnetic force microscopy.
K.-F. Braun1, S. Sievers1, D. Eberbeck2, S. Gustafsson3, E. Olsson3, H. W. Schumacher1, U.
1Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
2Physikalisch-Technische Bundesanstalt, Abbestraße 2-12, 10587 Berlin, Germany
3Department of Applied Physics, Chalmers University of Technology, 41296 Gothenburg,
We demonstrate the quantitative measurement of the magnetization of individual magnetic
nanoparticles (MNP) using a magnetic force microscope (MFM). The quantitative
measurement is realized by calibration of the MFM signal using an MNP reference sample
with traceably determined magnetization. A resolution of the magnetic moment of the order
of 10-18 Am2 under ambient conditions is demonstrated which is presently limited by the tip's
magnetic moment and the noise level of the instrument. The calibration scheme can be
applied to practically any MFM and tip thus allowing a wide range of future applications e.g.
in nanomagnetism and biotechnology.
Magnetic nanoparticles (MNP) show potential use for a wide range of applications for
example in biomedicine 1 and for data storage 2. For research purposes as well as for quality
control, a precise characterization of the magnetic properties of the MNPs is essential.
However, standard characterization techniques like SQUID magnetometry only allow for the
measurement of integral properties of ensembles of MNPs. A direct characterization of
individual particles is only possible by microscopy techniques.
Due to its high spatial resolution, magnetic force microscopy (MFM) is a powerful tool for
imaging magnetic nanostructures. MFM is a stray field sensitive technique with a resolution
down to 10 nm. However, a quantitative interpretation of the measured stray field data is not
straight forward. The standard approach for the quantitative characterization of small
structures is the point probe approximation 3-5. However, since the point probe approach
disregards the non-local character of the MFM tip magnetization, the approximation is
inadequate for patterns with dimensions comparable to the tip dimensions.
In this paper it is shown that a calibration of MFM tips can be obtained for the quantitative
measurement of the magnetic moment of spherical nanoparticles. No assumption regarding
the tip geometry is required since the stray field of a homogeneously magnetized sphere
equals the stray field of a point dipole positioned in the centre of the MNP. This calibration
scheme is based on an MNP reference sample, which provides traceability to the SI units for
the measurement of magnetic moments of individual MNPs as small as 10-18 Am2.
In magnetic force microscopy, the tip scans over the sample at a given lift height h and the
frequency shift ∆f of the oscillating MFM cantilever is recorded. The frequency shift ∆f can
be calculated from the force F that is acting on the magnetic tip in the stray field H of the
sample as ∆f=Q/k·d/dz Fz =Q/k·d2/dz2 Etip-sample. Here, k and Q are the spring constant and the
quality factor of the oscillating cantilever, respectively, FZ is the component of F
perpendicular to the sample surface, and Etip-sample is the interaction energy between the
magnetic stray field of the MNP and the tip. In general, the magnetic coating of an MFM tip
has a finite spatial extent. Hence, Etip-sample can be expressed in terms of a convolution of the
tip magnetization Mtip and the sample stray field H, which reads for a tip whose apex is at the
position r =(x,y,z):
tip sample tip
Now, we focus on single domain MNPs, which can be modeled as magnetic nanospheres with
saturation magnetization Ms and volume V=1/6 πd3, with d being the diameter of the MNP.
For this geometry the stray field H is equal to the stray field of a magnetic dipole which is
positioned in the center of the sphere 6. The absolute value m of the dipole moment m is then
given by m=Ms·V=Ms/6πd3 and the stray field of an MNP that is located at r'=0 is given by:
If the magnetic anisotropy of a nanoparticle is sufficiently small, the stray field emerging
from the magnetic tip is sufficient to fully align the nanoparticle magnetization7 as sketched in
Fig. 1 a). Since for the most common MFM tips the stray field underneath the tip is oriented
perpendicular to the x-y scanning plane, also the magnetization of the nanoparticle is aligned
perpendicular when the MFM tip is located at a lift height h above the centre position of the
nanoparticle, i.e. at r=(0,0,z)=(0,0,h). At this specific position, the particle magnetization m is
given by m=m·z, with z the unit vector in z-direction. Hence, the frequency shift ∆f over the
centre of the MNP can be calculated as
)( )) , 0 , 0 ((
The integral term becomes a constant that only depends on the magnetic properties of the
magnetic probe. For a given tip height h it therefore represents a tip dependent proportionality
constant 1/c(h) connecting the magnetic moment m of the spherical nanoparticle and the
measured MFM frequency shift by ∆f=m/c(h)=πMsd3/6c(h). As a consequence, for spherical
MNPs a calibration of the magnetic tip can be achieved by measuring the MFM signal of a set
of nanoparticles with known magnetic moment.
In the following, the realization and characterization of such an MNP based reference sample
for MFM calibration is described. A suitable MNP reference sample has to fulfill the
following requirements: (i) the MNPs do not agglomerate and (ii) the magnetization of the
MNPs is well known. We selected commercial magnetite nanoparticles with 20 nm nominal
diameter, in the following referred to as SHP 20 (a). A sample of well separated MNPs was
prepared by pouring the particles in solution onto a silicon substrate which is exposed to a
vertical magnetic field (≈ 500 mT). Thereby the particles are magnetically aligned and repel
each other which prevents particle agglomeration during the drying process. The MNP’s size
distribution was first determined by transmission electron microscopy (TEM) (Fig. 1b). The
resulting mean particle diameter is dTEM=(18.7±3) nm. To traceably determine the saturation
magnetization MS of the reference MNPs we first measured the total magnetic moment of a
small sample volume of the MNP suspension by SQUID magnetometry. Then, the iron
content of the same sample volume was determined by titration using prussian blue staining.
From the total magnetic moment and the magnetite volume derived by titration the saturation
magnetization was determined to be MS=(250±10) kA/m at 293 K. The measured value of MS
allows for a calculation of the magnetic moment of the SHP20 MNPs for a given particle
diameter using the relation m=MS·V=Ms/6πd3. Note that in these considerations possible
effects resulting from a non-magnetic shell are not accounted for.
A SHP20 reference sample, prepared as described above, was then employed to calibrate the
signal of commercial MFM cantilevers (b). Atomic force microscopy (AFM) and MFM was
performed using an SIS instrument working in a self excitation mode. The tip scans the
sample at a constant lift height h with respect to the sample surface. For the calibration in a
first step an AFM topography image was recorded as shown in Fig. 2a. The height and thus
the diameter of the particles was determined by fitting a two dimensional Gaussian function to
each scanned particle (see Fig. 2c, red solid line). The theoretical AFM topography curve of a
spherical nanoparticle (Fig. 2c, black dashed line) can be described by a convolution of two
semicircles describing the spherical particle of diameter d and the tip with a certain tip
curvature radius. In contrast a Gaussian fit (red solid line) overestimates the amplitude by a
factor of about 1.08. This factor is practically constant over the range of particles used here.
Therefore, for ease of computation, we used the two dimensional Gaussian fit and corrected
the resulting amplitudes by this factor to determine the particle diameter d. For the AFM
image shown in 2(a) the resulting mean particle diameter is dAFM=(17.1±2.7) nm, in good
agreement with the TEM analysis.
In a second step, the corresponding MFM images were taken at a constant lift height of h=60
nm (Fig. 2b). In the MFM image the MNP appear as a depression consistent with the concept
of a particle that is magnetized by the magnetic stray field of the tip 7. As described above the
calibration has to be carried out when the tip is positioned directly over the MNP. Only here,
the moment of the MNP is aligned perpendicular by the tip field and the frequency shift ∆f of