Skyrmion clusters and conical droplets in bulk helimagnets with cubic anisotropy

Recent experimental findings in the bulk cubic helimagnet and Mott insulator Cu2OSeO3 highlight the paramount role of cubic anisotropy in stabilizing novel chiral and skyrmion phases. It was indeed found that if a magnetic field is applied along the easy 001 crystallographic direction, competing cubic and
exchange anisotropies tilt the wave vector of the conical spiral away from the magnetic field [Qian et al., Sci. Adv. 4, eaat7323 (2018)]. Furthermore, in this configuration skyrmions have been observed in a broad range of temperatures and magnetic fields [Chacon et al., Nat. Phys. 14, 936 (2018)]. Starting from these
experimental observations and on the basis of a phenomenological Dzyaloshinskii theory, we investigate additional implications of the cubic anisotropy for this specified field direction. By including cubic anisotropy we show that the phase transition between the conical and field-polarized or homogeneous states becomes first order. Furthermore, we show that this transition is accompanied by the formation of conical droplets—domains of the conical phase in the homogeneous state. We investigate the internal structure of these droplets, which at their boundaries encompass alternating regions of positive and negative energy densities with respect to
the homogeneous state. We thus deduce that these droplets may be zipped and unzipped in phase during the first-order phase transition that occurs by either increasing or decreasing the magnetic field. On the other hand, we show that in the conical phase skyrmions may form clusters due to their attractive mutual interaction. However, in
the homogeneous state, the skyrmion-skyrmion interaction becomes repulsive, and the skyrmion clusters expand and disperse isolated skyrmions. This mutual skyrmion repulsion prevents the stabilization of skyrmion clusters even if the energy of isolated skyrmions is lower than that of the homogeneous state. Yet this skyrmion dispersal
may be prevented if skyrmions are surrounded by the circular spiral state and form skyrmion bags. Such a scenario could explain the existence of skyrmions in the field-polarized state reported experimentally.