A magnetic skyrmion is a spin whirl with topological protection and high mobility to electric current. Intrinsic magnetoelastic coupling in chiral magnets permits manipulation of magnetic skyrmions and their lattice using mechanical loads, which is essential for developing future spintronics devices. It is found in experiments that the stability and deformation of skyrmions are sensitive to stresses, while the appearance of magnetic skyrmions in turn has a significant effect on the mechanical properties of the underlying material. However, a theory which explains these related phenomena within a unified framework is not seen. Here we construct a thermodynamic model for B20 helimagnets incorporating a magnetoelastic functional with necessary higher order interactions derived by group theory. Within the model, we establish the methodology to calculate the phase diagram and equilibrium properties of helimagnets under coupled temperature-magneto-elastic field. Applying the model to bulk MnSi, we calculate the temperature-magnetic field phase diagram under stress-free condition and its variation when uniaxial compression is applied. We also calculate the variation of all the elastic constants with magnetic field. The results obtained agree quantitatively with corresponding experiments. Our model provides a reliable basis for further theoretical studies concerning any magnetoelastic related phenomena in chiral magnets.

Topological spin textures emerging in magnetic materials usually appear in crystalline states. A long-standing dilemma is whether we should understand these emergent crystals as gathering "particles" or coupling waves, the answer of which affects almost every aspect of our understanding on the subject. Here we prove that 2-D emergent crystals with long-range order in helimagnets, such as skyrmion crystals and dipole skyrmion crystals, have a wave nature. We systematically study their equilibrium properties, metastability, and phase transition path when unstable. We show that the robustness of a skyrmion crystal derives from its metastability, and that its phase transition dynamics at low (high) magnetic field is mediated by a soft mode which breaks (maintains) its hexagonal symmetry. Different from ordinary crystals which are formed by. and breaks into atoms, emergent crystals have a new formation (destruction) mechanism: they appear from (turn to) "single-Q" spin-density-wave states through nonlinear mode-mode interactions.

No abstract

through a skyrmion, its twisted spins endow these electrons with an emergent electromagnetic field, yielding a variety of unconventional magnetoelectronic phenomena, such as topological Hall effect [12] and ultralow current density for skyrmion motion. [23][24][25][26] These properties together with the nanoscale size and topological stability, make magnetic skyrmion promising potential for future highdensity, low-power-consuming magnetic memory devices. [1][2][3] Like many quasiparticles in condensed matter physics, magnetic skyrmion also has a particle-like characteristic. [1][2][3] Owing to this feature, multiple skyrmions can aggregate and dissipate in a defined geometry, which holds promise for applications beyond conventional binary memories, such as multi-level memories, [1,28,29] neuromorphic computing, [28][29][30] probabilistic computing, [31] and nano-oscillators. [32,33] In previous work, the experiment demonstrated an accumulation and dissipation of isolated skyrmions in micrometer-sized geometries using the spin-polarized pulse current. [30] However, since the skyrmion-skyrmion interaction between different Magnetic skyrmions are topological swirling spin configurations that hold promise for building future magnetic memories and logic circuits. Skyrmionic devices typically rely on the electrical manipulation of a single skyrmion, but controllably manipulating a group of skyrmions can lead to more compact and memory-efficient devices. Here, an electric-field-driven cascading transition of skyrmion clusters in a nanostructured ferromagnetic/ferroelectric multiferroic heterostructure is reported, which allows a continuous multilevel transition of the number of skyrmions in a one-by-one manner. Most notably, the transition is non-volatile and reversible, which is crucial for multi-bit memory applications. Combined experiments and theoretical simulations reveal that the switching of skyrmion clusters is induced by the strain-mediated modification of both the interfacial Dzyaloshinskii-Moriya interaction and effective uniaxial anisotropy. The results not only open up a new direction for constructing low-power-consuming, non-volatile, and multi-bit skyrmionic devices, but also offer valuable insights into the fundamental physics underlying the voltage manipulation of skyrmion clusters.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.202107908.

Emergent crystals are periodic alignment of "emergent particles", i.e., localized collective behavior of atoms or their charges/spins/orbits. These novel states of matter, widely observed in various systems, may deform under mechanical forces with elasticity strikingly different from that of the underlying material. However, their nonlinear and critical behaviors under strong fields are hitherto unclear. Here we theoretically study the nonlinear elasticity and structural transitions of skyrmion crystals (SkX) suffering uniaxial distortion by using three different methods. Under moderate tension, SkX behaves like a ductile material, with a negative crossover elastic stiffness and a negative emergent Poisson's ratio at appropriate conditions of magnetic field. Under strong straining, we observe at most six phase transitions, leading to appearance of four novel emergent crystals that are thermodynamically metastable. When subject to external loads, emergent crystals rotate globally, and their composing "particles" have unlimited deformability, which render their exotic polymorphism.