12 Magnetic Force Microscopy and Magnetic …
291
MFM is the quantitative determination of magnetic parameters of isolated NPs by
analyzing MFM images, which however has been only rarely reported.
In particular, the magnetic moment m N P of a single NP can be evaluated from θ
or f measured in correspondence of the center of the NP as a function of the lift
height z. To this purpose, a suitable model to describe the tip-sample interaction
must be assumed. The NP is generally described as a sphere uniformly magnetized,
possibly with a core-shell structure a magnetic dipole with moment m N P , different
models have been assumed to describe the tip. For instance, Angeloni et al. [28]
obtained m N P of Fe 3 O 4 NPs with diameter in the range 18–32 nm describing the tip
as a single dipole with moment m tip which was previously calibrated. Passeri et al.
[50] analyzed the moment of the magnetic core 11 nm sized magnetoferritin explicitly
considering the magnetic coating of the tip and describing the latter as a uniformly
magnetized hemispherical shell. A more comprehensive model has been introduced
by Schreiber et al. [16] who developed a model including the hemispherical apex and
the side surface of the cone-shaped tip and used it to evaluated m N P of iron oxide
NPs in the range 5–35 nm. Other authors proposed different models, e.g., Haberle et
al. [51] who described the probe as the magnetized surface of a cone using pseudopole model validating the model 18 nm sized Co NPs on a Si substrate covered by
23 nm thick silicon oxide layer. Also, Ra¸ sa et al. proposed a uniformly magnetized
ideally conical surface or a truncated conical one [52]. In an interesting work, Sievers
et al. [53] proposed an experimental procedure to phenomenologically calibrate the
magnetic moment of the tip without any assumption about its actual shape by using
a magnetic NPs traceable reference material, and used this approach to evaluate the
magnetic moment of magnetic NPs with diameter of about 17 nm. In addition to the
description of the tip, when the NP magnetization M N P must be evaluated, the actual
shape of the NPs must be described with a suitable model, the simplest one being a
uniformly magnetized perfect sphere [28].
In addition to the need for sufficiently comprehensive models, the quantification/deletion of tip-sample electrostatic artifacts is fundamental for the accurate
determination of magnetic parameters of the investigated NPs. Really, when magnetic
NPs deposited on flat substrates are analyzed, which is the common experimental
configuration in the analysis of NPs using MFM, nonmagnetic artifacts in standard
MFM images may be comparable to pure magnetic signals and their presence may
lead to results difficult to rationalize [18]. Therefore, methods capable to decouple
nonmagnetic artifacts should be preferred to standard MFM. For instance, Angeloni
et al. [28] used CM-MFM for the determination of the magnetic moment of Fe 3 O 4
NPs with diameter in the range 18–32 nm. Moreover, Li et al. [25] recently demonstrated the high sensitivity and accuracy of FM-MFM by measuring the magnetic
moment of individual Fe 3 O 4 NPs with diameter of about 14 nm.
Magnetic moment is undoubtedly the magnetic parameter of NPs more often
investigated using MFM and related techniques, also due to the fact that the experimental configuration is relatively simple as the measurement is generally performed
applying either no external static magnetic field or a single value of external magnetic
field to maintain the magnetization of the NPs. Nevertheless, by varying the intensity
and the direction of the external applied static magnetic field, complete magnetization
291
MFM is the quantitative determination of magnetic parameters of isolated NPs by
analyzing MFM images, which however has been only rarely reported.
In particular, the magnetic moment m N P of a single NP can be evaluated from θ
or f measured in correspondence of the center of the NP as a function of the lift
height z. To this purpose, a suitable model to describe the tip-sample interaction
must be assumed. The NP is generally described as a sphere uniformly magnetized,
possibly with a core-shell structure a magnetic dipole with moment m N P , different
models have been assumed to describe the tip. For instance, Angeloni et al. [28]
obtained m N P of Fe 3 O 4 NPs with diameter in the range 18–32 nm describing the tip
as a single dipole with moment m tip which was previously calibrated. Passeri et al.
[50] analyzed the moment of the magnetic core 11 nm sized magnetoferritin explicitly
considering the magnetic coating of the tip and describing the latter as a uniformly
magnetized hemispherical shell. A more comprehensive model has been introduced
by Schreiber et al. [16] who developed a model including the hemispherical apex and
the side surface of the cone-shaped tip and used it to evaluated m N P of iron oxide
NPs in the range 5–35 nm. Other authors proposed different models, e.g., Haberle et
al. [51] who described the probe as the magnetized surface of a cone using pseudopole model validating the model 18 nm sized Co NPs on a Si substrate covered by
23 nm thick silicon oxide layer. Also, Ra¸ sa et al. proposed a uniformly magnetized
ideally conical surface or a truncated conical one [52]. In an interesting work, Sievers
et al. [53] proposed an experimental procedure to phenomenologically calibrate the
magnetic moment of the tip without any assumption about its actual shape by using
a magnetic NPs traceable reference material, and used this approach to evaluate the
magnetic moment of magnetic NPs with diameter of about 17 nm. In addition to the
description of the tip, when the NP magnetization M N P must be evaluated, the actual
shape of the NPs must be described with a suitable model, the simplest one being a
uniformly magnetized perfect sphere [28].
In addition to the need for sufficiently comprehensive models, the quantification/deletion of tip-sample electrostatic artifacts is fundamental for the accurate
determination of magnetic parameters of the investigated NPs. Really, when magnetic
NPs deposited on flat substrates are analyzed, which is the common experimental
configuration in the analysis of NPs using MFM, nonmagnetic artifacts in standard
MFM images may be comparable to pure magnetic signals and their presence may
lead to results difficult to rationalize [18]. Therefore, methods capable to decouple
nonmagnetic artifacts should be preferred to standard MFM. For instance, Angeloni
et al. [28] used CM-MFM for the determination of the magnetic moment of Fe 3 O 4
NPs with diameter in the range 18–32 nm. Moreover, Li et al. [25] recently demonstrated the high sensitivity and accuracy of FM-MFM by measuring the magnetic
moment of individual Fe 3 O 4 NPs with diameter of about 14 nm.
Magnetic moment is undoubtedly the magnetic parameter of NPs more often
investigated using MFM and related techniques, also due to the fact that the experimental configuration is relatively simple as the measurement is generally performed
applying either no external static magnetic field or a single value of external magnetic
field to maintain the magnetization of the NPs. Nevertheless, by varying the intensity
and the direction of the external applied static magnetic field, complete magnetization