Quantitative Magnetic Force Microscopy: Tip Transfer Function Method Revisited with High-Quality Data

Abstract

Magnetic force microscopy (MFM) is a versatile technique used to image the micromagnetic state of a sample and its dependence on an applied magnetic field and/or on the sample temperature with a spatial resolution down to about 10 nm. The high resolution and the ease of implementation in existing atomic force microscopy (AFM) tools make the MFM technique particularly desirable for the investigation of magnetic thin films and nanoscale devices. The measured signal in MFM is a change of the dynamic properties of the imaging cantilever arising from the interaction of the magnetic cantilever tip with the stray field emanating from the sample surface. The obtained MFM images are therefore only indirectly connected to the micromagnetic state of the sample. However, if the perturbations to the micromagnetic states of the tip and sample are negligible during the measurement process, the measured MFM signal can be described as the convolution of the magnetic moment of the tip with the stray field of the sample. This allows for a quantitative analysis of the stray field by the deconvolution of MFM data. Such a deconvolution of the stray field from the measured MFM signal requires the calibration of the imaging properties of the tip. The latter can be achieved by fitting multipole moments to the tip in order to fit MFM data obtained on samples with a known stray field. Nevertheless, the success of such procedures remained limited: the size and position of the tip monopole and dipole moments were found to be dependent on the size of the imaged sample structures.A concept of tip transfer function (TF) was proposed two decades ago by van Schendel et al. [1]. This approach is used to specify the imaging properties of the probe and thus to access the quantitative information about the stray field emanating from the sample surface. More precisely, the method calibrates the response of the MFM tip on different spatial wavelengths of the stray field. This calibration method was then used by our group for the determination of the closure domain structure in thick Cu/Ni/Cu trilayer samples [2], for the measurement of the local density of pinned uncompensated spins in exchange-biased thin films [3], for the measurement of stray fields arising from skyrmions and the determination of the chirality in thin film systems with DMI [4], and for the detailed analysis of the complex dependence of the micromagnetic state on the external field in exchange-coupled Co/Pt-TbFe [5].Despite these successes, the tip calibration method presented by van Schendel et al. has only been taken up slowly. Examples include the reconstruction of magnetic vortex state at the end of FeCo nanowires [6] and the characterization of the 3D stray field landscape above a Ir17Mn83/Co70Fe30 exchange-biased multilayer system with engineered domain walls [7]. However, more recently, quantitative MFM methods have gained renewed interest. Hu et al. have for example analyzed the reproducibility of the tip calibration methods following the TF approach in round robin tests [8]. The results presented by different groups were however based on data acquired with MFM instruments operated under ambient conditions. The limited sensitivity of these instruments and consequently the low signal-to-noise ratio largely affect the final results obtained by the quantitative procedure. Moreover, the tip-sample distance control in most of the existing work was achieved by lift-mode operation, where the sample topography is first scanned with the tip in intermittent contact with the sample. Although the reproducibility of the measurements can be ensured to some extent, tip wear is almost unavoidable as also pointed out in Ref. [8].To exploit all the advantages of quantitative MFM in the investigation of magnetic thin films and nanostructures, the instrument is preferably operated under vacuum conditions. Furthermore, a noncontact technique for tip-sample distance control should be applied to avoid the tip wear.In this work, we present a state-of-the-art MFM tip calibration procedure based on measurements performed in vacuum and with high-quality factor (Q) cantilevers. We also discuss the subtleties in data treatment specifically during tip calibration procedure, which have been largely overlooked in the past. In addition, the advantages and the limits of this TF-method are addressed. **