Magnetic force microscopy is a magnetic characterization method of samples usually with a maximum of a few ten nanometers surface roughness. It works by measuring an atomic force microscopy (AFM) image of the surface topography of a sample, followed by lifting the probe to avoid short-range van der Waals interactions between the tip and sample and instead measuring the long-range magnetic interactions. In addition to this simplest form of magnetic force microscopy (MFM), there are more sophisticated ones, including frequency-modulated Kelvin probe force MFM, dynamic magneto-electric force microscopy, phase-locked loop methods, and even measurements in different environments, e.g., in liquids, that have been shown.
1. MFM on Magnetic Nanowire Arrays
Nanowire arrays can be produced, e.g., by e-beam lithography of a photo-resist template, followed by filling the produced channels with a magnetic material by electrodeposition. Such samples can be used for magnetic recording with high density 
or magnetic energy storage 
. Nanowire arrays produced in this manner usually have similar heights of all nanowires throughout the array, rendering MFM investigations slightly easier than on systems with larger height deviations along the surface.
Several MFM investigations can, thus, be found in the literature, which are performed on magnetic nanowire arrays. In the following text, measurements were performed under ambient conditions or environmental conditions were not mentioned in the papers. Whether they were performed in an external magnetic field or at remanence is mentioned where it is specified in the literature.
Qin et al., e.g., used a porous anodic aluminum oxide (PAO) template to prepare Fe0.3
nanowires of diameters around 50 nm in an array 
. They used MFM images with an undefined lift height of the very smooth surface, polished to a roughness below ±10 nm, to show that each nanowire end is single-domain in the demagnetized state and can, thus, be used to represent a single bit. While the common PAO template resulted in arbitrary positioning of the nanowires, the same group also used a highly ordered anodic alumina oxide (AAO) membrane with similar diameters to grow Co nanowires and used MFM on the polished composite surface to investigate the magnetic states of the single nanowires at saturation and at remanence 
. Similarly, Ni nanowires in a hexagonal arrangement were investigated by MFM in order to study the role of magnetostatic interaction in the array, here investigating the sample at different remanent states after in situ application of magnetic fields up to 500 Oe 
. This fact was also taken into account by Yuan et al. who calculated the reversal field distribution with and without the correction of magnetostatic fields according to a set of MFM images, taken at different external magnetic fields, in comparison with isothermal remanent magnetization and DC demagnetized magnetization curves 
Even for highly polished surfaces, MFM may become difficult due to insufficient lateral resolution. Asenjo et al. discussed the possibility of evaluating remanent magnetization of a nanowire array from MFM images, taken after in situ application of a magnetic field 
. They prepared Ni polycrystalline wires with diameters around 35 nm and length 1000 nm by electrodeposition into the nanopores of an alumina membrane template. For MFM investigations, they used a standard MFM tip with 50 nm Co coating, i.e., broader than the wire diameter. By simulations, they showed the influence of the MFM tip diameter, which has to be taken into account in case of quantitative MFM measurements performed with thicker tips.
The aforementioned spin-ice structures belong to the often examined 2D structures consisting of in-plane oriented nanowires or, more often, nano-lines typically attained from lithographic processes. These structures are often investigated by MFM since the spatially resolved magnetization is of high interest 
. However, they are in most cases two-dimensional and, thus, not within the scope of this paper, which aims at discussing possibilities for investigating three-dimensional nanofibrous structures.
For single magnetic nanowires or nanofibers, placed on a sample holder and, thus, investigated along their entire length (instead of from top, as in the previously mentioned nanowires arrays), it must be firstly mentioned that due to the MFM being sensitive to field gradients, the interpretation of MFM images is sometimes not straightforward. Berganza et al., e.g., explained MFM images of multisegmented nanowires from CoNi and Ni by a periodic multivortex structure with opposite vortex chiralities or a single vortex configuration, as depicted in Figure 1 
. The group used an amplitude modulation mode with phase-locked loop enabled and home-made Co MFM probes as well as MagneticMulti75-G (Budget Sensors) with CoCr coating 
. The same setup was reported by Bran et al. who reported an oscillation amplitude of the cantilever of 10–15 nm and a typical lift height of 40 nm for investigations of metastable transverse and vortex domains in cylindrical nanowires, measured at remanence or under in situ applied magnetic fields 
) Topography, (b
) geometry sketch, and (c
) MFM images of different nanowires. In (c
), the segment in the red square shows a uniform magnetization, while in (d
) a multidomain structure is displayed. Figures (e
) schematically show the expected magnetization configurations corresponding to (c
) MFM images, respectively. Reprinted from 
and originally published under a CC-BY license.
A more complicated image series taken by Askey et al. working with Ni nanowires produced by two-photon lithography 
. During magnetization reversal from remanence, they found complex spin structures including vortex and antivortex pairs and generally a spiraling domain along the external magnetic field direction. They reported using a lift height of 80 nm and a low moment (5 × 10−14
emu) tip, measuring in an applied field between 0 mT and 10 mT.
Another important effect that has to be taken into account in the interpretation of MFM measurements is the stray field of the tip 
. Nasirpouri et al. investigated tri-segmented nickel nanowires with alternating thicker and thinner sections of different lengths by MFM with a commercial CoCr standard tip and found strong contrast due to accumulated magnetic charges at the ends of the nanowires, as typical for axial magnetization, as well as at the points where the nanowire diameter was modulated 
. They used micromagnetic simulations to prove that magnetization reversal began with domain wall nucleation in a thick segment and propagation towards this diameter modulation point and that the interpretation of their MFM images was not misled by possible stray fields of the tip.
Core-León et al. investigated in detail the effect of tip shape and orientation of the magnetic field when magnetizing the tip on the residual magnetization and, thus, the stray fields around the tip and revealed a doubled MFM phase contrast for special V-shaped samples 
. Moreover, they showed that the strong shape anisotropy in their custom-made tips was suitable for measuring MFM at large fields up to 80 mT without the danger of switching the magnetization of the tip. Finally, both in-plane and out-of-plane magnetization could be measured with their tips, as depicted in Figure 2 
Numerically simulated magnetization and stray fields of suggested MFM probe. (a
) Stray field created by the V-shaped magnetic nanostructure when magnetization is either in head-to-head state (top row) or curl state (bottom row). Corresponding images for (b
) magnetization, (c
) magnetic charge distribution, and (d
) the direction of the stray field during MFM measurements. Reprinted from 
and originally published under a CC-BY-NC license.
Generally, thin magnetic nanowires often show magnetization orientation along the nanowire axis so that only a magnetic contrast is visible in MFM at the end, as measured in remanence after applying an external magnetic field pulse during which the tip was lifted away from the field by 12 µm 
. This magnetization, however, can be measured by a laterally magnetized MFM tip 
, as also suggested in 
. On the other hand, there are other diverse reports of more interesting magnetic structures, either in the form of domain walls during magnetization reversal, measured at different magnetic fields 
, or as multi-domain structure at remanence 
During the last years, the focus of MFM investigations of single magnetic nanowires shifted to nanowires with modulated diameters, as already mentioned before 
. Bochmann et al. reported domain walls in multi-segment nickel-cobalt nanowires along the segment borders as well as close to them without providing further information about experimental conditions 
. In a previous investigation, the group prepared NiCo/Cu nanowires of diameter 40 nm and could nicely demonstrate small single-domain bits separated by the nonmagnetic Cu segments by MFM at remanence, as depicted in Figure 3 
. Here, MESP tips (Bruker, Billerica, USA) with cobalt chromium coating were used.
MFM images of an isolated Ni60
/Cu wire of diameter 40 nm (top
); scheme of how the pattern observed in MFM originates from the alternation of magnetized and non-magnetic segments (bottom
). Reprinted from 
and originally published under a CC-BY license.
3. MFM on Magnetic Nanofiber Mats
One study working on electrospun magnetic nanofibers was published by Choopani et al. who prepared Y3
core-shell nanofibers by coaxial electrospinning 
. The paper, however, shows only MFM images of a single nanofiber taken out of the complete nanofiber mat and taken under conditions that are not further defined.
Another example of freestanding nanofibers is shown by Chearkasov et al., who grew layered Ni/Cu nanowires in a highly three-dimensional structure 
. However, only a single nanofiber was investigated here again at remanence and in an external magnetic field of 16 mT, placed flat on a substrate. Arias et al. used a very low scanning area of 200 nm width so that they could even measure MFM completely on top of a single ZnFe2
electrospun nanofiber 
Single nanofibers 
and crossing points of two nanofibers 
were investigated by Prashanthi et al. in the MFM lift-mode with phase detection, and they used sol-gel based electrospinning to prepare BiFeO3
nanofibers. Here, no further information about tip or lift height was provided.
Baranowska-Korczyc et al. managed taking MFM images of an ensemble of electrospun Fe doped ZnO nanofibers on an even surface 
, as depicted in Figure 4
. While it can be assumed that most of the contrast between the fibers in Figure 8
b and the substrate result from morphological contrast, there are also structures visible on top of the nanofibers that are stronger in the MFM images than in the AFM image (Figure 4
a) and can, thus, be attributed to magnetic contrast. The authors used an OTESPA 160 μm tip and a lift height of 150 nm, i.e., larger than the diameter of the thickest fibers.
) AFM and (b
) MFM images of Fe doped ZnO nanofibers. The scanned areas of both images are 30 μm × 30 μm. Reprinted from 
and originally published under a CC-BY-NC license.
However, most other papers showing MFM images on electrospun nanofibers deal with single nanofibers taken out of the mat and not with the full nanofiber mat 
. Lift heights were, e.g., reported in the range of 50–100 nm 
, while hard-magnetic tips (coercivity 300 Oe) 
or silicon nitride tip 
were used to detect signals from the single fibers mounted e.g., by setting them in a polymer glue 
. In an aforementioned paper of our group demonstrating, to our knowledge, the first attempts to measure MFM on complete nanofiber mats at remanence 
, the problems mentioned before regarding the optimization of the lift height were also found, resulting in the problem that at too small lift heights, the nanofiber morphology was still visible despite the use of contour following mode and double-pass mode, while at too large lift heights, the magnetic information could not be properly visualized.
Due to this lack of sufficient results regarding MFM measurements on electrospun nanofiber mats and other chaotic nanofiber arrangements, the next section discusses approaches reported in the literature for MFM measurements on other rough surfaces and what can be learnt from them.