Fig. 3: Fourier analysis of MFM images.

a Typical Fourier transform (here from 0.22 T), indicating the satellite peaks present during the periodic magnetic phase, with pairs of peaks labelled. b Normalised integration of the Fourier peak areas for the satellite peaks, plotted at each field, with the modulus of the Hall resistivity plotted for direct comparison. c, d MFM signals extracted by isolating the relevant respective peaks from the Fourier transform acquired from the 0.22 T scan. Line scan marked with a blue bar in c is plotted in f. e MFM signals extracted by isolating signals responsible for both peaks (convolution of c and d), resulting rectangular lattice is rotated ~28° to the scan direction. f Line scans extracted from raw data in Fig. 2b, and FFT extracted data in c fitted with a sine curve. g Schematic of a cycloidal phase, and how the z component of such a phase appears to vary. h 3D magnetisation simulation of a cycloidal phase with a single propagation vector. i 3D magnetisation simulation of an anisotropic incommensurate (IC) spin crystal, a cycloidal phase with two in plane perpendicular propagation vectors.