A. N. Bogdanov

Stabilization of skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets

In cubic noncentrosymmetric ferromagnets, uniaxial distortions suppress the helical states and stabilize skyrmion lattices in a broad range of thermodynamical parameters. Using a phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the skyrmion and helical states are derived as functions of the applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field, skyrmion lattices can be formed as thermodynamically stable states in large intervals of magnetic field and temperatures in cubic helimagnets, e.g., in intermetallic compounds MnSi, FeGe, (Fe,Co)Si. We argue that this mechanism is responsible for the formation of skyrmion states recently observed in thin layers of

Chiral skyrmions in cubic helimagnet films: The role of uniaxial anisotropy

{\text{Fe}}_{0.5}{\text{Co}}_{0.5}\text{Si}

The properties of isolated chiral skyrmions in thin magnetic films

[X. Z. Yu et al., Nature (London) 465, 901 (2010)].

Chiral Skyrmionic matter in non-centrosymmetric magnets

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.

Three-dimensional chiral skyrmions with attractive interparticle interactions

Axisymmetric solitonic states (chiral skyrmions) have been 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 (Science 341 , 636 (2013)). 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.

Spintronics via non-axisymmetric chiral skyrmions

Axisymmetric magnetic strings with a xed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non- centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical ndings to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-eld-dri ven evolution of Skyrmions and helicoids in chiral helimagnets.

Skyrmionic textures in chiral magnets

We introduce a new class of isolated three-dimensional skyrmion that can occur within the cone phase of chiral magnetic materials. These novel solitonic states consist of an axisymmetric core separated from the host phase by an asymmetric shell. These skyrmions attract one another. We derive regular solutions for isolated skyrmions arising in the cone phase of cubic helimagnets and investigate their bound states.

Exchange shift of stripe domains in antiferromagnetically coupled multilayers

Micromagnetic calculations demonstrate a peculiar evolution of non-axisymmetric skyrmions driven by an applied magnetic field in confined helimagnets with longitudinal modulations. We argue that these specific solitonic states can be employed in nanoelectronic devices as an effective alternative to the common axisymmetric skyrmions that occur in magnetically saturated states.

Magnetic remanent states in antiferromagnetically coupled multilayers

In non-centrosymmetric magnets, the chiral Dzyaloshinskii-Moriya exchange stabilizes Skyrmion-strings as excitations which may condense into multiply modulated phases. Such extended Skyrmionic textures are determined by the stability of the localized solitonic Skyrmion cores and their geometrical incompatibility which frustrates regular space-filling. We present numerically exact solutions for Skyrmion lattices and formulate basic properties of the Skyrmionic states.

Crossover of skyrmion and helical modulations in noncentrosymmetric ferromagnets

Antiferromagnetically coupled multilayers with perpendicular anisotropy, such as [CoPt]∕Ru, Co∕Ir, and Fe∕Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This “exchange shift” is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of the so-called “tiger-tail” patterns, and a “mixed state” of antiferromagnetic and ferromagnetic domains in [CoPt]∕Ru multilayers. The derived analytical relations between the values of the shift and the strength of antiferromagnetic coupling provide an effective method for a quantitative determination of the interlayer exchange interactions.