The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3

The Skyrme-particle, the skyrmion, was introduced over half a century ago in the context of 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. Extending over length scales much larger than the interatomic spacing, they behave as large, classical objects, yet deep inside they are of quantum nature. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. We performed such an approach for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. We show that its magnetic building blocks are strongly fluctuating Cu4 tetrahedra, spawning a continuum theory that culminates in 51 nm large skyrmions, in striking agreement with experiment [1]. Another consequence is the presence of two distinct types of modes: a low-energy manifold that includes a gapless Goldstone mode and a set of weakly dispersive high-energy magnons [2]. Using high-field electron spin resonance with a terahertz free-electron laser and pulsed magnetic fields up to 64 T we identified these modes [3], corroborating the presence of fluctuating Cu4 tetrahedra. We also show that the emerging electric polarization \textbf{P} is governed by quadrupolar spin contributions from symmetry inequivalent bonds and calculate the induced \textbf{P} in different crystallographic directions as a function of the orientation of an applied magnetic field, which are confirmed by experiment [2]. One so far untested prediction that ensues is the temperature-dependent decay of skyrmions into half-skyrmions. \\[4pt] [1] Nature Comm. 5, 5376 (2014)\\[0pt] [2] PRB 90, 140404(R) (2014)\\[0pt] [3] PRL 113, 157205 (2014)