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Skyrmions are topologically protected quantum objects at the nanometre scale.They form perpendicular to an applied magnetic field at a certain temperatureand arrange themselves in a typically hexagonal lattice. Using small angleneutron scattering we have determined the magnetic field versus temperaturephase diagrams of the stability range of the different magnetic phases, thehelical as well as the skyrmion phases in the multiferroic skyrmion materialCu$_2$OSeO$_3$. Therefore, a single crystal was mounted in different crystalorientations, i.e. unoriented and with the crystallographic $\langle1 10\rangle$ and $\langle1 0 0\rangle$ axis aligned parallel to the magneticfield. Furthermore, different cooling procedures were tested, cooling from theparamagnetic phase at zero magnetic field and field cooling through theskyrmion phase where metastable skyrmions are nucleated. From this, not onlywere the stability ranges of both the helical and skyrmion phases in thismultiferroic skyrmion material determined, but the length of the spin helix andthe skyrmion distances at different conditions was also determined throughdetailed analysis of the positions of the observed Bragg peaks. The obtaineddata provide valuable information about the scaling of the skyrmion distancesand therefore their packing density. The knowledge about this tunability willserve as an important input for the theoretical understanding of the formationof skyrmions. Concerning technological applications, for example ashigh-density data storage devices in information technology, the temperatureand magnetic field dependence of the packing density of skyrmions is ofcritical importance for their design. Therefore, the obtained knowledge is anessential input for future skyrmionics applications in high-density datastorage, in low-energy spintronics or in skyrmionics quantum computation.

Scaling behaviour of the helical and skyrmion phases of Cu2OSeO3 determined by single crystal small angle neutron scattering