Axisymmetric solitonic states (chiral skyrmions) were first predicted theoretically more than two decades ago. However, until recently they have been observed in a form of skyrmionic condensates (hexagonal lattices and other mesophases). In this paper we report experimental and theoretical investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers two years ago by Romming et al (2013 Science 341 636). The results of spin-polarized scanning tunneling microscopy analyzed within the continuum and discrete models provide a consistent description of isolated skyrmions in thin layers. The existence region of chiral skyrmions is restricted by strip-out instabilities at low fields and a collapse at high fields. We demonstrate that the same equations describe axisymmetric localized states in all condensed matter systems with broken mirror symmetry, and thus our findings establish basic properties of isolated skyrmions common for chiral liquid crystals, different classes of noncentrosymmetric magnets, ferroelectrics, and multiferroics.

This paper reports on magnetometry and magnetoresistance measurements of MnSi epilayers performed in out-of-plane magnetic fields. We present a theoretical analysis of the chiral modulations that arise in confined cubic helimagnets where the uniaxial anisotropy axis and magnetic field are both out-of-plane. In contrast to in-plane field measurements (Wilson et al., Phys. Rev. B 86, 144420 (2012)), the hard-axis uniaxial anisotropy in MnSi/Si(111) increases the energy of (111)oriented skyrmions and in-plane helicoids relative to the cone phase, and makes the cone phase the only stable magnetic texture below the saturation field. While induced uniaxial anisotropy is important in stabilizing skyrmion lattices and helicoids in other confined cubic helimagnets, the particular anisotropy in MnSi/Si(111) entirely suppresses these states in an out-of-plane magnetic field. However, it is predicted that isolated skyrmions with enlarged sizes exist in MnSi/Si(111) epilayers in a broad range of out-of-plane magnetic fields. These results reveal the importance of the symmetry of the anisotropies in bulk and confined cubic helimagnets in the formation of chiral modulations and they provide additional evidence of the physical nature of the A-phase states in other B20-compounds. 75.70.Ak

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purposedesign broad-band spin dynamic and logic devices. arXiv:2001.00026v3 [cond-mat.str-el]

We present an experimental and theoretical investigation of the influence of a uniaxial magnetocrystalline anisotropy on the magnetic textures that are formed in a chiral magnetic system. We show that the epitaxially induced tensile stress in MnSi thin films grown on Si (111) creates an easy-plane uniaxial anisotropy. The magnetoelastic shear stress coefficient is derived from SQUID magnetometry measurements in combination with transmission electron microscopy and x-ray diffraction data. Density functional calculations of the magnetoelastic coefficient support the conclusion that the uniaxial anisotropy originates from the magnetoelastic coupling. Theoretical calculations based on a Dzyaloshinskii model that includes an easy-plane anisotropy predict a variety of modulations to the magnetic order that are not observed in bulk MnSi crystals. Evidence for these states is found in the magnetic hysteresis and polarized neutron reflectometry measurements.

Theoretical analysis and Lorentz transmission electron microscopy (LTEM) investigations in an FeGe wedge demonstrate that chiral twists arising near the surfaces of noncentrosymmetric ferromagnets [Meynell et al., Phys. Rev. B 90, 014406 (2014)] provide a stabilization mechanism for magnetic Skyrmion lattices and helicoids in cubic helimagnet nanolayers. The magnetic phase diagram obtained for freestanding cubic helimagnet nanolayers shows that magnetization processes differ fundamentally from those in bulk cubic helimagnets and are characterized by the first-order transitions between modulated phases. LTEM investigations exhibit a series of hysteretic transformation processes among the modulated phases, which results in the formation of the multidomain patterns.

Magnetometry and magnetoresistance measurements in MnSi thin films and rigorous analytical solutions of the micromagnetic equations show that the field-induced unwinding of confined helicoids occurs via discrete steps. A comparison between the magnetometry data and theoretical results shows that finite size effects confine the wavelength and lead to a quantization of the number of turns in the helicoid. We demonstrate a prototypical spintronic device where the magnetic field can push or pull individual turns into a magnetic spring that can be read by electrical means

A detailed investigation of the magnetization processes in epitaxial MnSi thin film reveals the existence of elliptically distorted skyrmion strings that lie in the plane of the film. We provide proof that the uniaxial anisotropy stabilizes this state over extended regions of the magnetic phase diagram. Theoretical analysis of an observed cascade of first-order phase transitions is based on rig- orous numerical calculations of competing chiral modulations, which shows the existence of helicoids, elliptic skyrmions, and cone phases

In epitaxial MnSi/Si(111) films, the in-plane magnetization saturation is never reached due to the formation of specific surface chiral modulations with the propagation direction perpendicular to the film surfaces [Wilson et al. Phys. Rev. B 88, 214420 (2013)]. In this paper we show that the occurrence of such chiral surface twists is a general effect attributed to all bulk and con- fined magnetic crystals lacking inversion symmetry. We present experimental investigations of this phenomenon in nanolayers of MnSi/Si(111) supported by detailed theoretical analysis within the standard phenomenological model. In magnetic nanolayers with intrinsic or induced chirality, such surface induced instabilities become sizeable effects and play a crucial role in the formation of skyrmion lattices and other nontrivial chiral modulations