Calibration of multi-layered probes with low/high magnetic moments

Abstract

We present a comprehensive method for visualisation and quantification of the magnetic stray field of magnetic force microscopy (MFM) probes, applied to the particular case of custom-made multi-layered probes with controllable high/low magnetic moment states. The probes consist of two decoupled magnetic layers separated by a non-magnetic interlayer, which results in four stable magnetic states: ±ferromagnetic (FM) and ±antiferromagnetic (A-FM). Direct visualisation of the stray field surrounding the probe apex using electron holography convincingly demonstrates a striking difference in the spatial distribution and strength of the magnetic flux in FM and A-FM states. In situ MFM studies of reference samples are used to determine the probe switching fields and spatial resolution. Furthermore, quantitative values of the probe magnetic moments are obtained by determining their real space tip transfer function (RSTTF). We also map the local Hall voltage in graphene Hall nanosensors induced by the probes in different states. The measured transport properties of nanosensors and RSTTF outcomes are introduced as an input in a numerical model of Hall devices to verify the probe magnetic moments. The modelling results fully match the experimental measurements, outlining an all-inclusive method for the calibration of complex magnetic probes with a controllable low/high magnetic moment.

Comparison and Validation of Different Magnetic Force Microscopy Calibration Schemes

“…To guarantee that the best electrical compensation parameters were used, trace and retrace signals were compared and the parameters were adjusted until both signals matched each other (surface potential shown in Figure 3b2). When the electrical compensation was optimized the Hall signal takes the shape of a circular spot at the center of the cross, as previously reported18,17,10 and shown in Figure 3b3. If the electrostatic field was not fully compensated, dark and bright lobes will appear at the edges/corners of the cross, due to capacitive coupling between the probe and the device 17…”

“…To compensate the effect of the electrostatic field the Kelvin‐probe force microscopy uses an AC voltage to probe interaction and then applies a voltage V DC to the probe to null it (see ref. 10 for further details of how the Kelvin‐probe feedback loop operates). During the second pass (Figure 1b Pass II), the Z ‐piezo reproduces the topography measured during the first pass adding a constant height h lift .…”

“…Topography of the sample is shown in , whereas surface potential and the amplitude of the Hall signal are shown in and in , respectively. A good agreement between the trace and retrace surface potential scans, and an absence of dark and bright lobes at the corners of the Hall cross10,17 are both clear indicators of a good electrostatic compensation.…”

“…The second mode, phase modulated‐MFM‐Kelvin‐probe force microscopy (PM‐MFM‐KPFM), was adopted to image the micrometer‐size embedded coils. When imaging the embedded microcoils electrostatic interaction became a major issue due to the insulating layer used for the embedding together with the amplitude of the electrical current passing through the coil and required to generate the magnetic field, thus electrostatic compensation (i.e., Kelvin‐probe force microscopy) was needed 10. In this mode, the probe also oscillates close to its resonant frequency f 0 .…”

“…Other approached use nanostructures, one employs a nanosized Hall cross to measure the stray field from the tip,10 while the other uses nanopatterned coils to generate known magnetic fields and then estimates the tip's field from the resulting image 11,12. Nevertheless, none of these calibration techniques has been fully implemented as a standard operation procedure.…”