Fig. 4: Validation of the point monopole approximation.

Normalized force transfer function \({{{{{\rm{FTF}}}}}}/{q}_{{{{{{\rm{t}}}}}}}\) for nanowire (NW) probes with circular cross-sections. a NW dimensions are: diameter \(d=20\) \({{{{{\rm{nm}}}}}}\) and length \(=5\) \({{{{{\rm{\mu m}}}}}}\). The red line refers to a calculation based on a circular NW cross-section. For comparison, results for a square-shaped NW are also shown (dotted line; note that a side of the square is aligned parallel to \({{{{{{\bf{k}}}}}}}_{{xy}}\)). Purple and reddish-colored areas indicate the \(\lambda\) ranges in which \({{{{{\rm{FTF}}}}}}(\lambda )/{q}_{{{{{{\rm{t}}}}}}}\) is >99% or >90%, respectively. \({{{{{{\bf{k}}}}}}}_{{xy}}\) and \(\lambda =2{{{{{\rm{\pi }}}}}}/{k}_{{xy}}\) are the wavevector and the wavelength of the spatial magnetic field distribution, respectively. b, c The impact of varying \(l\) is shown while \(d=20\) \({{{{{\rm{nm}}}}}}\) is kept constant. d, e The impact of varying \(d\) is shown while \(l=5\) \({{{{{\rm{\mu m}}}}}}\) is kept constant. c, e \(\lambda -l\) and \(\lambda -d\) phase diagrams showing calculated areas with \({{{{{\rm{FTF}}}}}}/{q}_{{{{{{\rm{t}}}}}}}\) ratios exceeding 99%, 95%, and 90%.