Figure 5: Phase diagram from the continuum description of Cu₂OSeO₃.

(a) H_c1 denotes the reorientation transition from the helical phase (green region) into the conical state (blue region, indicated by a cone traced by the spins along the propagation direction). Without additional anisotropies, the cone angle closes continuously at H_c2 and the system reaches the ferrimagnetic plateau phase. A cubic anisotropy makes H_c2 direction dependent. H_p(111) denotes the continuous transition for fields along [111]. For fields along [100] direction, the conical helix collapses by a first-order process at H_p(100). (b) The high-temperature regime of the phase diagram has a narrow precursor region where skyrmionic phases are found numerically for two-dimensional models. Blue circles show the region of stable densely packed ‘’-skyrmion lattices while red squares mark the region of stable ‘’-skyrmion lattices. (c) Magnetization profile of skyrmions. The colouring of the arrows tracks the longitudinal magnetization M_z. The latter is also shown in the projected contour plot with the colouring scheme indicated on the left. (d) Similar to c but for a half-skyrmion texture. (e) The longitudinal magnetization M_z and the absolute magnetization |M| across two nearest-neighbour (NN) skyrmions of c. (f) Similar to e, but now we cut across the diagonal of a half-skyrmion texture.