F. N. Rybakov

Three-dimensional skyrmion states in thin films of cubic helimagnets

A direct three-dimensional minimization of the standard energy functional shows that in thin films of cubic helimagnets chiral skyrmions are modulated along three spatial directions. The structure of such 3D skyrmions can be thought of as a superposition of conical modulations along the skyrmion axis and double-twist rotation in the perpendicular plane. Numerical solutions for chiral modulations demonstrate that 3D skyrmion lattices and helicoids are thermodynamically stable in a broad range of applied magnetic fields. Our results disclose a basic physical mechanism underlying the formation of skyrmion states recently observed in nanolayers of cubic helimagnets.

New type of stable particlelike states in chiral magnets.

We present a new type of 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 it contains a singularity but nevertheless has finite energy. Both features combine to form a quasiparticle state for which we expect unusual transport and dynamical properties. It exhibits high thermal stability and thereby can be considered as a promising object for fundamental research and practical applications in spintronic devices. We identified the range of existence of such particlelike states in the thickness dependent magnetic phase diagram for helimagnet films and analyzed its stability in comparison with the isolated skyrmion within the conical phase. 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.

Control of morphology and formation of highly geometrically confined magnetic skyrmions

The ability to controllably manipulate magnetic skyrmions, small magnetic whirls with particle-like properties, in nanostructured elements is a prerequisite for incorporating them into spintronic devices. Here, we use state-of-the-art electron holographic imaging to directly visualize the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in the range of 45–150 nm. We find that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticities in a nanostripe that are absent in both thin films and bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We perform a theoretical analysis based on a three-dimensional general model of isotropic chiral magnets to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices.

New spiral state and skyrmion lattice in 3D model of chiral magnets

We present the phase diagram of magnetic states for films of isotropic chiral magnets calculated as function of applied magnetic field and thickness of the film. We have found a novel magnetic state driven by the natural confinement of the crystal, localized at the surface and stacked on top of the conical bulk phase. This magnetic surface state has a three-dimensional (3D) chiral spin-texture described by the superposition of helical and cycloidal spin spirals. This surface state exists for a large range of applied magnetic fields and for any film thickness beyond a critical one. We also identified the whole thickness and field range for which the skyrmion lattice becomes the ground state of the system. Below a certain critical thickness the surface state and bulk conical phase are suppressed in favor of the skyrmion lattice. Unraveling of those phases and the construction of the phase diagram became possible using advanced computational techniques for direct energy minimization applied to a basic 3D model for chiral magnets. Presented results provide a comprehensive theoretical description for those effects already observed in experiments on thin films of chiral magnets, predict new effects important for applications and open perspectives for experimental studies of such systems.

Experimental observation of chiral magnetic bobbers in B20-type FeGe

Chiral magnetic skyrmions1,2 are nanoscale vortex-like spin textures that form in the presence of an applied magnetic field in ferromagnets that support the Dzyaloshinskii–Moriya interaction (DMI) because of strong spin–orbit coupling and broken inversion symmetry of the crystal3,4. In sharp contrast to other systems5,6 that allow for the formation of a variety of two-dimensional (2D) skyrmions, in chiral magnets the presence of the DMI commonly prevents the stability and coexistence of topological excitations of different types7. Recently, a new type of localized particle-like object—the chiral bobber (ChB)—was predicted theoretically in such materials8. However, its existence has not yet been verified experimentally. Here, we report the direct observation of ChBs in thin films of B20-type FeGe by means of quantitative off-axis electron holography (EH). We identify the part of the temperature–magnetic field phase diagram in which ChBs exist and distinguish two mechanisms for their nucleation. Furthermore, we show that ChBs are able to coexist with skyrmions over a wide range of parameters, which suggests their possible practical applications in novel magnetic solid-state memory devices, in which a stream of binary data bits can be encoded by a sequence of skyrmions and bobbers.Electron holography enables direct experimental verification of the existence of chiral bobbers in thin films of chiral magnets.The use of chiral skyrmions, which are nanoscale vortex-like spin textures, as movable data bit carriers forms the basis of a recently proposed concept for magnetic solid-state memory. In this concept, skyrmions are considered to be unique localized spin textures, which are used to encode data through the quantization of different distances between identical skyrmions on a guiding nanostripe. However, the conservation of distances between highly mobile and interacting skyrmions is difficult to implement in practice. Here, we report the direct observation of another type of theoretically-predicted localized magnetic state, which is referred to as a chiral bobber (ChB), using quantitative off-axis electron holography. We show that ChBs can coexist together with skyrmions. Our results suggest a novel approach for data encoding, whereby a stream of binary data representing a sequence of ones and zeros can be encoded via a sequence of skyrmions and bobbers. The need to maintain defined distances between data bit carriers is then not required. The proposed concept of data encoding promises to expedite the realization of a new generation of magnetic solid-state memory.

Lifetime of racetrack skyrmions

The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.

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.

Stationary precession topological solitons with nonzero Hopf invariant in a uniaxial ferromagnet

Three-dimensional stationary precession solitons with nonzero Hopf indices are found numerically by solving the Landau-Lifshitz equation. The structure and existence domain of the solitons are found.

Charge order–superfluidity transition in a two-dimensional system of hard-core bosons and emerging domain structures

We have used high-performance parallel computations by NVIDIA graphics cards applying the method of nonlinear conjugate gradients and Monte Carlo method to observe directly the developing ground state configuration of a two-dimensional hard-core boson system with decrease in temperature, and its evolution with deviation from a half-filling. This has allowed us to explore unconventional features of a charge order—superfluidity phase transition, specifically, formation of an irregular domain structure, emergence of a filamentary superfluid structure that condenses within of the charge-ordered phase domain antiphase boundaries, and formation and evolution of various topological structures.

Spiral Structures in Helicoidal Magnets

The structure and properties of two-dimensional spiral textures in helical ferromagnets are studied. The existence of novel types of periodic structures, namely, of spiral lattices, is predicted for these magnetic systems.