Quantitative Magnetic Force Microscopy Study of the Diameter Evolution of Bubble Domains in a $(\hbox{Co/Pd})_{80}$ Multilayer

Bidirectional quantitative force gradient microscopy

“…In the zero field state, where the sample shows a band domain configuration the domain structure, as shown in figure 3(a), it is usually not affected by MFM probe stray-fields and therefore constitutes an ideal reference as shown for similar multilayers in previous work [29]. Vibrating sample magnetometry measurements revealed an uniaxial anisotropy constant of …”

“…In the simple case of a magnetic point charge tip, a multiplication of equation (16) by the tip charge−q and by μ 0 leads to: x y , which can be fully determined by a calibration measurement of an appropriate reference sample [29,31]. Although the TTF now depends on the spatial frequencies k k ( , )…”

“…For the utilized Co/Pt multilayer this pattern can be constructed from a qualitative MFM measurement and independent knowledge of the saturation polarization μ M s 0 , film thickness and domain wall width [29]. A deconvolution of the measured perpendicular force gradient ∂ ∂ F z z with the constructed effective surface charge pattern by means of a Wiener invert filter leads to the spatially resolved stray field gradient of the tip ∂ ∂ ( ) where δ accounts for the distance of the monopole away from the carbon nanotube end and z scan for the scan height in the MFM experiment, i.e.…”

Stray fields above artificial magnetic in-plane domains

“…As this study should quantify magnetic fields for possible applications at room temperature, techniques requiring cryogenic temperatures like SQUID measurements are excluded. Methods fulfilling these conditions are quantitative magnetic force microscopy (qMFM) [9], nitrogen vacancy (NV) center magnetometry [10,11], scanning magnetoresistive microscopy [12] and m-Hall probe microscopy [13]. Here we present a quantitative determination of the stray field z-component (perpendicular to the sample surface) strength as a function of lateral position and height over the surface by m-Hall probe microscopy.…”

Magnetic interactions in 2D and 3D arrays

“…The exp (−kz) transfer function may also be used to compute images at lower scan height [Che et al, 1993] or, ultimately, to infer the magnetic state of the sample or tip from the MFM data [Van Schendel et al, 2000;Vock et al, 2011]. However, this boosts high frequency noise [Saito et al, 1999].…”