Customized MFM probes with high lateral resolution

Magnetic force microscopy (MFM) is a widely used technique for magnetic imaging. Besides its advantages such as the high spatial resolution and the easy use in the characterization of relevant applied materials, the main handicaps of the technique are the lack of control over the tip stray field and poor lateral resolution when working under standard conditions. In this work, we present a convenient route to prepare high-performance MFM probes with sub-10 nm (sub-25 nm) topographic (magnetic) lateral resolution by following an easy and quick low-cost approach. This allows one to not only customize the tip stray field, avoiding tip-induced changes in the sample magnetization, but also to optimize MFM imaging in vacuum (or liquid media) by choosing tips mounted on hard (or soft) cantilevers, a technology that is currently not available on the market.


Properties of the thin films as a function of the deposition parameters
Starting from a base pressure of 5·10 −6 mbar, argon gas is introduced into the chamber until the selected working pressure is reached. Inert gases are usually employed as the sputtering gas because they tend not to react with the target material and because of their high molecular weight that causes higher sputtering rates. Plasma is then generated using an AC magnetron sputtering with an input power of 100 W and is confined on the target surface by a permanent magnet located behind the target surface. Positively charged Ar + ions are accelerated toward the negatively biased 99.99% pure Co target, resulting in material being sputtered and deposited onto the side walls of the tips. Table S1 shows the influence of the working pressure in the properties of constantthickness reference samples. As can be observed, the in-plane coercive field (measured by VSM) changes for different working pressures. This parameter is of importance when an in situ magnetic field is applied during the MFM operation.

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The reference samples were characterized by AFM and also by MFM. In every case, the average grain size is below 14 nm, whereas the magnetization of the grown films remains constant with a value of 8·10 2 emu/cm 3 . Figure S1 shows the evolution of the magnetic configuration as a function of the working pressure used during the deposition. The domain configuration evolves from dense stripes domains for the higher pressures to cross-tie domain walls for smaller pressures.  Table S2 show the influence of the magnetic layer thickness on the magnetic behavior. The working pressure was kept around 1.0·10 −2 mbar (the same chosen for the experiments presented in the manuscript). The effect the thickness has on the magnetic properties of a thin film is well known. A critical thickness (t c ) was observed to obtain the so-called dense stripe domains [1], whose value is a function of the saturation magnetization and the perpendicular anisotropy constant, K u . MFM measurements allow us to follow the evolution of the domain configuration as a function of film thickness. The thinnest layers present mainly in-plane magnetization with the presence of cross-tie domain walls (see Figure S1c). As the Co layer thickness increases, the out-of-plane component of the magnetization increases until a dense stripe domain configuration is seen for the layer 60 nm thick ( Figure S2c).

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These MFM results are in good agreement with hysteresis loops measured by VSM.

Characterization of the switching field of the custom-made MFM probes
The resulting custom-coated MFM probes were characterized using an advanced MFM method described elsewhere [2]. As sketched in Figure S3a Using this method, the switching field of different custom-made probes was studied and is shown in Figure S4. As can be seen there, there is a correlation with the inplane coercive field of the corresponding reference thin film, measured by VSM.

Evaluation of the tip radius of the MFM probes
The tip radius was evaluated before and after deposition of the magnetic coating by imaging a carbon nanotube and using the following expression [3], where w and h are the apparent width and height of the nanotube: The results are presented in Figure S5,

Non-standard cantilevers for optimized MFM in liquid and vacuum environments
In scanning probe microscopy, the resonance frequency of the vibrating cantilever shifts, in the presence of a force gradient, inversely proportional to √ 0 : Thus, choosing a cantilever with a smaller spring constant potentially enhances the sensitivity. However, this also reduces its natural resonance frequency, which results in a larger noise level, worsening the frequency shift detection. Such frequency dependent noise varies proportionally to √ 1 • ⁄ , with Q being the quality factor of the resonance. According to this, the measurement noise in liquid media is predicted to be four times larger using a standard cantilever with k ≈ 3 N/m, compared to a typical one designed for this purpose (for instance, Olympus BL-AC40TS-C2) [4]. On the other hand, cantilevers with higher spring constants (20-40 N/m) are mostly used in vacuum environments. Despite them having a sensitivity about three times smaller than the standard ones, the fundamental noise level is improved by a factor of five, resulting in a improvement by a factor of ca. 1.4 in the frequency shift sensitivity (or, in other words, the MFM sensitivity). In addition, these hard levers yield a significantly larger mechanical stability that improves also the imaging quality.
This gives a ways to determine the most advantageous cantilever to optimize MFM imaging for each experiment. However, typical MFM probes currently available are mounted on cantilevers with resonance frequencies and spring constants of about 70 kHz and 1-3 N/m, which are most suitable for ambient pressure conditions. This presents an important limitation for optimized MFM in vacuum and liquid media.

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For this reason, having the possibility to custom-coat tips in a quick and simple way permits to address this problem. Figure   (c) (d) S11

Compositional images acquired with the customcoated MFM probes
In addition to its intrinsic high resolution capability, one of the main features of dynamic AFM is its ability to simultaneously detect different interactions. An example of compositional phase imaging using our custom-made probes is presented here, where an outstanding lateral resolution of 5 nm is achieved. According to the famous Cleveland's formula [5], if one assumes both the PLL and the topographic feedbacks to work ideally, the frequency shift measured during the topographic scan ( Figure S7b,e) yields a map of the energy dissipation during the experiment. Notice that, during the retrace scan, no feedback is used to keep the oscillation amplitude constant so this assumption does not hold during MFM imaging. In general, different materials are expected to interact and dissipate energy in different ways; therefore, these images give an idea of the compositional distribution. S12  The frequency shift image ( Figure S7b) recorded during the topographic scan ( Figure S7a) reveals a well-defined dark stain covering a big part of the epitaxial Co nanostripes, whereas no remarkable feature is observed in the topographic image.
Eventual electrostatic effects are unlikely to be responsible for it, as no relevant frequency shifts are recorded during the retrace scan in the MFM image ( Figure S7c).
In fact, this contrast can be associated to the adsorption of certain species in that region. A zoom-in image of the compositional map is displayed in Figure S7e, where a remarkable lateral resolution of 5 nm is achieved with a signal-to-noise ratio around 400. Notice that the corresponding magnified topography ( Figure S7d) lacks such

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outstanding detailed information; in fact, it is customary in scanning probe experiments to find better resolutions in the dissipation images.