  The Skyrme-particle, the $skyrmion$, was introduced over half a century ago
and used to construct field theories for dense nuclear matter. But with
skyrmions being mathematical objects - special types of topological solitons -
they can emerge in much broader contexts. Recently skyrmions were observed in
helimagnets, forming nanoscale spin-textures that hold promise as information
carriers. Extending over length-scales much larger than the inter-atomic
spacing, these skyrmions behave as large, classical objects, yet deep inside
they are of quantum origin. Penetrating into their microscopic roots requires a
multi-scale approach, spanning the full quantum to classical domain. By
exploiting a natural separation of exchange energy scales, we achieve this for
the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab
initio calculations reveal that its magnetic building blocks are strongly
fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic
texture that agrees well with reported experiments. It also brings to light a
decay of skyrmions into half-skyrmions in a specific temperature and magnetic
field range. The theoretical multiscale approach explains the strong
renormalization of the local moments and predicts further fingerprints of the
quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$,
like weakly dispersive high-energy excitations associated with the Cu$_4$
tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic
order, and a fractionalized skyrmion phase.
