Entangled tetrahedron ground state and excitations of the   magneto-electric skyrmion material Cu$_2$OSeO$_3$
  The strongly correlated cuprate Cu$_2$OSeO$_3$ has recently been identified as the first insulating system exhibiting a skyrmion lattice phase. Using a microscopic multi-boson theory for its magnetic ground state and excitations, we establish 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. These spectral features are the most direct signatures of the fact that the essential magnetic building blocks of Cu$_2$OSeO$_3$ are not individual Cu spins, but rather weakly-coupled Cu$_4$ tetrahedra. Several of the calculated excitation energies are in nearly perfect agreement with reported Raman and far-infrared absorption data, while the magneto-electric effect determined within the present quantum-mechanical framework is also fully consistent with experiments, giving strong evidence in the entangled Cu$_4$ tetrahedra picture of Cu$_2$OSeO$_3$. The predicted dispersions along with the dynamical dipole and quadrupole spin structure factors call for further experimental tests of this picture. 
Judit Romh\'anyi, Jeroen van den Brink, and Ioannis Rousochatzakis
cond-mat.str-el