12 Magnetic Force Microscopy and Magnetic …
289
if a soft magnetic tip is used and the vertical component of the ac magnetic field ∂ H
ac
z
is spatially homogeneous, the amplitude of the cantilever oscillation at f c ± f m is
proportional to the gradient along z of the vertical component of the dc magnetic
field, i.e., to ∂ H
dc
z /∂z [24]. Therefore, depending on the magnetic properties of the
tip, FM-MFM can be used to detect static or dynamic magnetic fields. Notably, FMMFM has been demonstrated to minimize the presence of artifacts in the magnetic
images due to topographical crosstalk [25].
In the previously described methods, the cantilever is set into oscillation along
the vertical z axis. This, combined with the orientation of the magnetization of the
tip which is generally along the z axis, makes the techniques sensitive to the vertical
component of the magnetic stray field generated by the sample. Really, MFM tips can
be magnetized along one in-plane direction and in this case the vertical oscillation
of the cantilever is affected by the in-plane direction of the sample magnetic field
[12, 26]. A more effective method to probe horizontal magnetic fields is represented
by torsional resonance MFM (TR-MFM). In TR-MFM the first torsional resonance
is excited in order to set the cantilever into oscillation at the first torsional resonance
f 0,T R along the scan direction, i.e., the y axis [27]. In presence of a magnetic field
with a component along the y axis, a shift of the torsional resonance frequency
f 0,T R is observed which is given by
f 0,T R = −
1
2k T R
f 0,T R
∂ F y
∂ y
,
(12.4)
where k T R is the torsional spring constant of the cantilever, F y is the component of
the tip-sample interaction force along the y axis and ∂ F y /∂ y is its gradient along the
y axis. Notably, TR-MFM is free from topographical artifacts which originate from
the tip-sample electrostatic force along z [27].
12.3 Magnetic Force Microscopy and Magnetic
Nanoparticles
12.3.1 Quantitative Nanomagnetic Characterization
The constantly growing interest for the use of magnetic NPs in many different scientific and technological fields has increased the demand for NPs with optimized
performances. This, in turns, requires the availability of methods capable to characterize magnetic properties of NPs at the nanometer scale and to relate them to
‘tunable’ physical parameters, e.g., size or shape, in order to tailor them for specific
applications. Really, several methods for the characterization of magnetic properties of ensembles of NPs are available, e.g., vibrating sample magnetometry (VSM)
[29], superconducting quantum interference devices (SQUID) [30], or alternating
gradient field magnetometry (AGFM) [31]. These methods are well-established and
289
if a soft magnetic tip is used and the vertical component of the ac magnetic field ∂ H
ac
z
is spatially homogeneous, the amplitude of the cantilever oscillation at f c ± f m is
proportional to the gradient along z of the vertical component of the dc magnetic
field, i.e., to ∂ H
dc
z /∂z [24]. Therefore, depending on the magnetic properties of the
tip, FM-MFM can be used to detect static or dynamic magnetic fields. Notably, FMMFM has been demonstrated to minimize the presence of artifacts in the magnetic
images due to topographical crosstalk [25].
In the previously described methods, the cantilever is set into oscillation along
the vertical z axis. This, combined with the orientation of the magnetization of the
tip which is generally along the z axis, makes the techniques sensitive to the vertical
component of the magnetic stray field generated by the sample. Really, MFM tips can
be magnetized along one in-plane direction and in this case the vertical oscillation
of the cantilever is affected by the in-plane direction of the sample magnetic field
[12, 26]. A more effective method to probe horizontal magnetic fields is represented
by torsional resonance MFM (TR-MFM). In TR-MFM the first torsional resonance
is excited in order to set the cantilever into oscillation at the first torsional resonance
f 0,T R along the scan direction, i.e., the y axis [27]. In presence of a magnetic field
with a component along the y axis, a shift of the torsional resonance frequency
f 0,T R is observed which is given by
f 0,T R = −
1
2k T R
f 0,T R
∂ F y
∂ y
,
(12.4)
where k T R is the torsional spring constant of the cantilever, F y is the component of
the tip-sample interaction force along the y axis and ∂ F y /∂ y is its gradient along the
y axis. Notably, TR-MFM is free from topographical artifacts which originate from
the tip-sample electrostatic force along z [27].
12.3 Magnetic Force Microscopy and Magnetic
Nanoparticles
12.3.1 Quantitative Nanomagnetic Characterization
The constantly growing interest for the use of magnetic NPs in many different scientific and technological fields has increased the demand for NPs with optimized
performances. This, in turns, requires the availability of methods capable to characterize magnetic properties of NPs at the nanometer scale and to relate them to
‘tunable’ physical parameters, e.g., size or shape, in order to tailor them for specific
applications. Really, several methods for the characterization of magnetic properties of ensembles of NPs are available, e.g., vibrating sample magnetometry (VSM)
[29], superconducting quantum interference devices (SQUID) [30], or alternating
gradient field magnetometry (AGFM) [31]. These methods are well-established and