Figure 3. Experimental determination of the topological winding number.

(a–c) Resonant soft X-ray magnetic diffraction from Cu₂OSeO₃ for three different azimuthal angles: Ψ=5.95°, 29.56° and 50.17°, respectively. The photon energy is tuned to 931.25 eV and the magnetic satellites are observed around the (001) structural peak. The figures show the reciprocal space maps within the (hk1)-plane, obtained by integrating the scattering intensities for left- and right-circularly polarized incident light. The coordinate system is defined in Fig. 1d. The temperature was 57 K and the applied magnetic field of 32 mT along the z direction, which is also parallel to the [001] crystallographic direction. (d) CD signal as a function of Ψ. The black dots are the measured data, while the red line is a fit using equation (3). (e) Measured PAM, and (f) interpolation obtained by fitting equation (4). The interpolated PAM shows excellent agreement with the calculated result shown in Fig. 2i, in which two humps of equal height can be observed at β≈90°.