Stray Field Components

Because the MFM scans a space devoid of sources of magnetic field, in practice we can write the latter as the gradient of a magnetic potential, , where  satisfies the Laplace equation. For definiteness we assume the sources of the stray field (provided by the sample) are described by a boundary condition on the xy-plane, parallel to the scan plane located at distance z from the top surface of the sample. In the 2D Fourier space utilized in the previous section, this leads to the convenient expression


(3)

and therefore also to


(4)
Consequently, the measurement of the z-component of the stray field provides the remaining components as well, and implies that if ICF(k,z) is known the MFM can measure the stray field vector.
Stray+field+components.jpg
a MFM data of a skyrmion in a [Ir1/Co0.6/Pt]x6 multilayer thin film. b Hz at z = 12nm obtained from the deconvolution of a using qMFM methods. d, e Hx, and Hy components obtained from Hz, and c color wheel representation of the in-plane stray field components.
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