Understanding electrostatic and magnetic forces in magnetic force microscopy: towards single superparamagnetic nanoparticle resolution

Abstract

The detection of superparamagnetic nanoparticles by magnetic force microscopy (MFM) at the single particle level faces difficulties such as superposition of nonmagnetic signals caused by electrostatic interactions as well as reaching the resolution limits due to small magnetic interactions. In MFM the magnetic force is measured at a certain distance to the substrate following the topography measured in a first scan to avoid an influence of short range forces (lift mode). In this work we showed that performing MFM on superparamagnetic nanoparticles the increase of the tip-substrate distance above the nanoparticle in lift mode scans leads to a reduction of the electrostatic forces resulting in a positive phase shift in contrast to the negative phase shift of the attractive magnetic force. Identifying the electrostatic force in MFM on nanoparticles as a capacitive coupling effect between tip and substrate the origin of often seen topography mirroring in phase images of nanoparticles in general is theoretically explained and experimentally proved. Minimization of the capacitive coupling by adjusting the work function difference between tip and substrate as well as using an optimized tip allows the magnetic visualization of single 10 nm superparamagnetic iron oxide nanoparticles (SPIONs) at ambient conditions with and without an external magnetic field.

Magnetic Force Microscopy of in a Polymer Matrix Embedded Single Magnetic Nanoparticles

“…The black squares represent maximal measured phase shift above the nanoparticle at certain lift height. The dotted line represents calculated phase shifts including capacitive coupling effects as described in 3.2 . The magnetic parameters of the MFM tip, r tip.mag and m tip are fitted to r t ip.mag = 80 nm and m tip = 3 × 10 −16 Am 2 with a pre‐factor of 10.…”

“…Mirroring of the topography (Figure a) is observed in the corresponding phase image (Figure b) due to the capacitive coupling of the MFM tip with the substrate. We discussed the origins of this effect and possibilities to reduce the capacitive coupling in our previous work . One of the possibilities to minimize the capacitive coupling is the reduction of the distance changes d (Eq. )…”

“…In our previous work we proposed a theory to the additional disturbing forces during the interleave mode measurement . The effect of disturbing electro static force was as well observed as discussed by other authors.…”

“…Gomez et al observe the effect of electro static interaction for piezo response force microscopy demonstrating the extent of this effect to other AFM variations . Decreasing capacitive coupling between substrate and tip above a relief equal or smaller than the tip area causes a positive phase shift and vice versa resulting in topography mirroring in the phase image . Equation describes the phase shift above the nanoparticles due to the changes in capacitive coupling.…”

“…Equation describes the phase shift above the nanoparticles due to the changes in capacitive coupling. with A effective capacitive area, z lift height, d height of the relief, V CPD contact potential difference between tip and substrate, V tip applied tip voltage . It is possible to minimize Δ φ el by reducing the relief d .…”