The bulk helimagnet Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets exhibiting a tilted spiral and skyrmion phase at low temperatures when the magnetic field is applied along the easy (001) crystallographic direction. Here we present a systematic study of the stability and ordering of these low-temperature magnetic states. We focus our attention on the temperature and field dependencies of the tilted spiral state that we observe persisting up to above T=35 K, i.e., up to higher temperatures than reported so far. We discuss these results in the frame of the phenomenological theory introduced by Dzyaloshinskii in an attempt to reach a quantitative description of the experimental findings. We find that the anisotropy constants, which are the drivers behind the observed behavior, exhibit a pronounced temperature dependence. This explains the differences in the behavior observed at high temperatures (above T=18 K), where the cubic anisotropy is weak, and at low temperatures (below T=18 K), where a strong cubic anisotropy induces an abrupt appearance of the tilted spirals out of the conical state and enhances the stability of skyrmions.

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We present a systematic study of tilted spiral states obtained theoretically within the classical Dzyaloshinskii model for magnetic states in cubic non-centrosymmetric ferromagnets. Such tilted spirals are shown to stabilize under the competing effect of cubic and exchange anisotropies inherent to cubic helimagnets. By focusing on the internal structure of these spirals and their field-driven behaviour for different aspect ratios of the anisotropy coefficients, we are able to capture the main features of the experimental findings in a bulk cubic helimagnet Cu₂OSeO₃ and to make a step further towards a complete quantitative model of this chiral magnet. In particular, we show that for strong anisotropy values (which experimentally correspond to low temperatures near zero) there exist an angular separation between the conical and tilted spirals, i.e., the conical spiral flips into a tilted state and immediately composes some finite angle with respect to the field direction. As the anisotropy ratio decreases, such a transition between two spiral states becomes almost continuous and corresponds to higher temperatures at the experiments. In addition, we investigate the field-driven reorientation of metastable skyrmion lattices induced by the competing anisotropies, which may be responsible for some peculiarities at the experimental phase diagrams of Cu₂OSeO₃.

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Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets with a tilted spiral and a low-temperature skyrmion phase arising for magnetic fields applied along the easy crystallographic (100) axes. Although the stabilization mechanism of these phases can be accounted for by cubic magnetic anisotropy, the skyrmion nucleation process is still an open question, since the stability region of the skyrmion phase displays strongly hysteretic behavior with different phase boundaries for increasing and decreasing magnetic fields. Here, we address this important point using micromagnetic simulations and come to the conclusion that skyrmion nucleation is underpinned by the reorientation of spiral domains occurring near the critical magnetic fields of the phase diagrams: HC1, the critical field of the transition between the helical and conical/tiled spiral phase, and HC2, the critical field between the conical/tiled spiral and the homogenous phase. By studying a wide variety of cases we show that domain walls may have a 3D structure. Moreover, they can carry a finite topological charge stemming from half-skyrmions (merons) also permitting along-the-field and perpendicular-to-the-field orientation. Thus, domain walls may be envisioned as nucleation source of skyrmions that can form thermodynamically stable and metastable lattices as well as skyrmion networks with misaligned skyrmion tubes. The results of numerical simulations are discussed in view of recent experimental data on chiral magnets, in particular, for the bulk cubic helimagnet Cu2OSeO3.

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Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. Deep physical relations and common physical features of a large variety of very different solitonic states in these systems arise from the mathematical similarity of phenomenological equations.
During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for the experimental investigation of topological solitons and the understanding of their nonsingular field configurations. This is directly related to the discovery of particle-like chiral skyrmions, which are also considered as promising
ingredients for technological applications. Here we introduce a paradigm of facile skyrmionic networks with mutually orthogonal orientations of constituent isolated skyrmions. On the one hand, such networks are envisioned as a novel concept of spintronic devices based, e.g., on gapless skyrmion motion along each other, and are presumably responsible for precursor phenomena near the ordering temperatures of bulk cubic helimagnets. In particular, we demonstrate an interconversion between mutually orthogonal skyrmions: horizontal skyrmions may swirl into an intermediate spring-like state and subsequently squeeze into vertical skyrmions with both polarities. On the other hand, skyrmion tubes are considered as building blocks for particle-like states with more involved internal structure. A family of target-skyrmions, which includes a so far overlooked type with a multiple topological charge, is formed owing to the tendency to minimize the interaction energy between vertical
and horizontal skyrmions. The conical phase serves as a suitable background for considered skyrmion evolution.
It substantializes the attracting skyrmion-skyrmion interaction in the skyrmionic networks, shapes their internal
structure, and guides the nucleation processes. Alternatively, intricate textural changes of isolated skyrmions
result not only in the structural deformations of a host conical state, but may lead to the formation of an exotic
skyrmion order with pairs of merons being the core of the game. Generically, the fundamental insights provided
by this work emphasize a three-dimensional character of skyrmion metamorphoses and can also be extended to
three-dimensional solitons, such as hopfions@en

The lack of inversion symmetry in the crystal lattice of magnetic materials gives rise to complex noncollinear spin orders through interactions of a relativistic nature, resulting in interesting physical phenomena, such as emergent electromagnetism. Studies of cubic chiral magnets revealed a universal magnetic phase diagram composed of helical spiral, conical spiral, and skyrmion crystal phases. We report a remarkable deviation from this universal behavior. By combining neutron diffraction with magnetization measurements, we observe a new multidomain state in Cu₂OSeO₃. Just below the upper critical field at which the conical spiral state disappears, the spiral wave vector rotates away from the magnetic field direction. This transition gives rise to large magnetic fluctuations. We clarify the physical origin of the new state and discuss its multiferroic properties.

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