Chiral Magnetic Skyrmions with Arbitrary Topological Charge ("skyrmionic sacks")

We show that continuous and spin-lattice models of chiral ferro- and antiferromagnets provide the existence of an infinite number of stable soliton solutions of any integer topological charge. A detailed description of the morphology of new skyrmions and the corresponding energy dependencies are provided. The considered model is general, and is expected to predict a plethora of particle-like states which may occur in various chiral magnets including atomic layers, e.g., PdFe/Ir(111), rhombohedral GaV$_4$S$_8$ semiconductor, B20-type alloys as Mn$_{1-x}$Fe$_x$Ge, Mn$_{1-x}$Fe$_x$Si, Fe$_{1-x}$Co$_x$Si, Cu$_2$OSeO$_3$, acentric tetragonal Heusler compounds

New type of stable particle like states in chiral magnets (Chiral bobbers)

We present a new type of a thermodynamically stable magnetic state at interfaces and surfaces of chiral magnets. The state is a soliton solution of micromagnetic equations localized in all three dimensions near a boundary and contains a singularity, but nevertheless has a finite energy. Both features combine to a quasi-particle state for which we expect unusual transport and dynamical properties. It exhibits high thermal stability and thereby can be considered as promising object for fundamental research and practical applications in spintronic devices. We provide arguments that such a state can be found in different B20-type alloys e.g. Mn$_{1-x}$Fe$_x$Ge, Mn$_{1-x}$Fe$_x$Si, Fe$_{1-x}$Co$_x$Si.Comment: accepted in PR

Interaction of Individual Skyrmions in Nanostructured Cubic Chiral Magnet

We report the direct evidence of field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of external magnetic field the character of such long-range skyrmion interactions change from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skrymion-edge distances as function of applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. Important role of demagnetizing fields and internal symmetry of three-dimensional magnetic skyrmions are discussed in details.Comment: accepted in PR

Exact Self-consistent Particle-like Solutions to the Equations of Nonlinear Scalar Electrodynamics in General Relativity

Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is shown that the equations of motion admit a special kind of solutions with sharp boundary known as droplets. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero.Comment: 17 pages, Submitted to the International Journal of Theoretical Physic

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Coexistence of type-I and type-II superconductivity signatures in ZrB12 probed by muon spin rotation measurements

Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example, at different temperatures, is rare in nature. We employed the muon spin rotation (μSR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most important, we found a region showing unusual behavior where the usually mutually exclusive μSR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modeling that required taking into account multiple bands and multiple coherence lengths, which suggests that material has one coherence length larger and another smaller than the magnetic field penetration length (the type-1.5 regime). At stronger fields, a footprint of the type-II mixed state showing square flux-line lattice was also obtained using neutron diffraction