Figure 6: Exchange couplings between effective tetrahedral entities.
From: The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3
(a) Illustration of how the bare couplings 
and 
of the S=1/2 model give rise to an effective nearest-neighbour (NN) coupling J1 between tetrahedra. The constants l1 and l2 are given in the text and depend on whether one includes the spin-mixing effect or not. The spins of the two effective tetrahedra involved in this coupling are denoted by 
and 
. In the S=1/2 model, different microscopic couplings are denoted by different line styles, while blue (red) colour generally refers to ferromagnetic (antiferromagnetic) exchange. The coupling 
involves a longer-range O-Se-O super-exchange path along the diagonals of hexagonal loops (here only half of such a loop is visible), which are formed by alternating 
bonds (the Se sites reside at the centre of these loops). (b) Similarly for the NNN coupling J2, where the two tetrahedra are connected via a single bare coupling, 
.
