Numerical Characterization of Magnetic Vortex Probe Imaging for Magnetic Force Microscopy

We theoretically study the performance and limitations of the magnetic vortex probe for magnetic force microscopy (MFM). In the ideal case, the only magnetically active part of the probe is the magnetic vortex core (VC) existing in the center of a Permalloy (Py) disk located at the apex of a nonmagnetic tip. Such VC can be effectively characterized as a point dipole with the magnetic moment of the order of $10^{-17}\text {Am}^{2}$ embedded about 20 nm inside the disk, which is similar to the commercial text low-momentum MFM probes. In addition to the standard probes, the ideal VC probe offers high durability and a text well-controlled magnetic moment suitable for quantitative MFM. However, since the VC probe is made of magnetically soft material its magnetization profile and the resulting MFM image can be deformed by the stray field of the sample. Therefore, the VC probe is suited for imaging the samples with small domain sizes which generate low stray fields. We numerically examine VC imaging of typical magnetic samples, i.e., domain arranged as a single circular dot, stripe patterns, and the chessboard. We determine the limiting dimensions of the domains that can be correctly imaged by the VC tip of optimal parameters. In general, we can conclude that MFM imaging by VC probes gives reasonable results for the samples with domains with lateral dimensions up to 100 nm.