Magnetic force microscopy contrast formation and field sensitivity

Tuning the Coexistence Regime of Incomplete and Tubular Skyrmions in Ferromagnetic/Ferrimagnetic/Ferromagnetic Trilayers

“…This conclusion is reached by noting the relationship between the MFM contrast and skyrmion size and is explained as follows. The MFM contrast depends on the effective magnetic surface charge, the spatial wavelengths of the imaged features, the tip−sample distance, and the tip transfer function (i.e., the decay of the measured frequency shift signal with decreasing spatial wavelength of the stray field at the location of the tip 23 ). Note that the stray field decays exponentially with the spatial wavelength and increasing tip− sample distance.…”

Quantitative Magnetic Force Microscopy: Transfer-Function Method Revisited

“…The cantilevers used in our work have a stiffness c = 0.3 N/m, and are typically operated with an oscillation amplitude A = 5 nm. In vacuum-operation environment and with customized coatings, the Q factor of such cantilevers may exceed Q = 200 000 [25]. The energy that is required to keep such a cantilever oscillating at a constant amplitude per oscillation is much smaller ( E ≈ 0.1 meV).…”

“…In demagnetized state, this sample shows micrometer-size domains separated by narrow Bloch-type domain walls of approximately equal to 10 nm and therefore covers a large range of spatial wavelengths. The substantially increased sensitivity of the MFM [25] helps to image the relatively low signals from the sample, as well as to capture the stray field of the rapidly decaying small spatial wavelengths arising from the sharp domain walls. As such, the calibrated wavelengths' spectrum is expected to have a large spread.…”

“…Conversely, the micromagnetic structure of the tip * yaoxuan.feng@empa.ch may be influenced by the stray field of the sample. Consequently, the design of the magnetic tip must be optimized, such that sufficient signal is generated but the influence of the tip stray field on the sample magnetic structure remains negligible [25]. In this case, the measured signal in an MFM can be described as the convolution of the magnetic moment of the tip with the stray field of the sample.…”

“…To take full advantage of the existing TF method and to push the limits of QMFM in investigating the stray fields of technologically relevant magnetic thin films and nanostructures, the MFM measurements-both for tip calibration and for the application of the obtained TF-have to be performed under optimized conditions. In this paper, we present the state-of-the-art MFM tip calibration based on measurements carried out in vacuum and with highquality-factor (Q-factor) cantilevers [25]. Furthermore, we implement a noncontact operation mode [37] to avoid the tip wear, such that the same tip can be used for the measurements of either various areas of the same sample or several different samples, all under the same conditions [12].…”