Precursor skyrmion states near the ordering temperatures of chiral magnets

In noncentrosymmetric magnets, chiral Dzyaloshinskii-Moriya interactions (DMI) provide a distinctive mechanism for the stabilization of localized skyrmion states in two and three dimensions with a fixed sense of rotation. Near the ordering transition, the skyrmion strings develop attractive skyrmion-skyrmion interactions and ultimately become confined in extended clusters or textures [A. O. Leonov and U. K. Rößler, Nanomaterials, 2023, 13, 891], which is a consequence of the coupling between the magnitude and the angular part of the order parameter. Multi-skyrmionic states built from isolated skyrmions (IS) can form multiple modulated magnetic phases that may underlie the exotic magnetic phenomena of "partial order" or the field-driven "A-phase" observed in MnSi and other cubic helimagnets. Based on the standard phenomenological Dzyaloshinskii model, we obtain numerically exact solutions for skyrmion lattices (SkL), formulate their basic properties, and elucidate physical mechanisms of their formation and stability. Our detailed numerical studies show that the bound skyrmion states arise as hexagonal lattices of ±π-skyrmions (with the magnetization in the center along or opposite to the magnetic field) or square staggered lattices of π/2-skyrmions, which contain defect lines with zero modulus value and thus may form thermodynamically stable states only near the ordering temperature. In the simplest case of a two-dimensional (2D) skyrmionic texture, the structure is homogeneous in the third dimension (3D). The skyrmions preserve an ideal axisymmetric "double twist" core in condensed phases, while continuation into a space-filling texture is frustrated. The evolution of skyrmion lattices in an increasing magnetic field leads to a succession of phase transitions of first or second kind between diverse textures and finally ends due to the formation of isolated skyrmion-filaments with fixed radius and shape embedded in a homogeneously magnetized matrix. In the framework of the phenomenological model including only isotropic interactions (exchange, Zeeman, and DM energy contributions), the considered skyrmion lattices are only metastable states as the competing conical one-dimensional spiral forms the equilibrium state. But due to the weak couplings between skyrmions, secondary effects like anisotropies can stabilize skyrmionic textures as compared to simple helices. Also the topological nature of skyrmion condensates makes the magnetization processes in chiral magnets history-dependent and hysteretic.