We discuss thermally activated switching between micromagnetic states in nanodisks with perpendicular anisotropy and a large strength of the interfacial Dzyaloshinskii-Moriya interaction, D. For large D, the magnetization on infinite planes acquires a cycloidal configuration in the ground state. However, Isolated singularities that are analogous to disclinations of cholerestic phases 1 are topologically protected and prevent the system from reaching the cycloidal phase (for examples see Fig. 1). In confined geometries, a rich variety of possible configurations with complex magnetization textures that are also energy minima of the energy landscape 2 has been observed.
We argue that characterizing these different states as arrangements of disclinations is an effective way for understanding them. We support this statement on results of String Method 3 calculations done using OOMMF to examine the energy landscape of nanodisks (Fig. 2). We found that the transition states correspond to motion of individual merons across the device's edge (first maximum in Fig. 2), and to merging of disclinations inside the structure (2nd, 3rd and 4th maxima in Fig. 2).

An additional advantage of emphasizing the importance of these magnetic singularities is the possibility of adopting them for collective coordinate descriptions which can be treated using low-dimensional stochastic methods to study their dynamics in the presence of thermal noise.

References
1 Phys. Rev. B 99, 214408 (2019) 2 The Philosophical Magazine. 22:178, 739-749 3 J. Chem. Phys. 126, 164103 (2007) This research was supported in part by the National Science Centre Poland under OPUS funding Grant No. 2019/33/B/ST5/02013 (GDC, PK) and U.S. National Science Foundation Grant DMR 1610416 (DLS).

Examples of disclinations on the cycloidal phase of a ferromagnet with large DMI. (a) cycloidal phase without singularities. Disclinations occur when the helical axis rotates by a multiple of π. (b,c,e,f) Examples of disclinations, respectively their values are: (π,2π,-π,-2π). (d) a skyrmion shown as a 2π disclination embedded in a cycloidal background, (g) a meron shown as a π disclination embedded in a cycloidad background.

Results of String Method calculations on nanodisks with high DMi for thermally activated switching between two different micromagnetic configurations. The highest maxima occurs when a meron reaches the in-plane edge. The other maxima are the result of -π disclinations merging briefly into a +2π disclination resulting on re-acommodation of adjacent skyrmionic domains.