Direct experimental determination of the topological winding number of skyrmions in Cu(2)OSeO(3)

The mathematical concept of topology has brought about significant advantages that allow for a fundamental understanding of the underlying physics of a system. In magnetism, the topology of spin order manifests itself in the topological winding number which plays a pivotal role for the determination of the emergent properties of a system. However, the direct experimental determination of the topological winding number of a magnetically ordered system remains elusive. Here, we present a direct relationship between the topological winding number of the spin texture and the polarized resonant X-ray scattering process. This relationship provides a one-to-one correspondence between the measured scattering signal and the winding number. We demonstrate that the exact topological quantities of the skyrmion material Cu(2)OSeO(3) can be directly experimentally determined this way. This technique has the potential to be applicable to a wide range of materials, allowing for a direct determination of their topological properties.