This work studies the resonance excitations of the three-dimensional skyrmions lattice in the finite thickness plate of an isotropic chiral magnet using spin dynamics simulations. We found that the absorption spectra and resonance modes differ from those predicted by the two-dimensional model and the model of the unconfined bulk crystal. The features observed on the spectra can be explained by the formation of chiral standing spin waves, which, contrary to conventional standing spin waves, are characterized by the helical profile of dynamic magnetization of fixed chirality that is defined by the Dzyaloshinskii-Moriya interaction. In this case, the dynamic susceptibility becomes a function of the plate thickness, which gives rise to an interesting effect that manifests itself in periodical fading of the intensity of corresponding modes and makes excitation of these modes impossible at specific thicknesses.

Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search for hopfions in real physical systems has been ongoing for nearly half a century, starting with the seminal work of Faddeev. However, so far, realizations in bulk solids are missing. Here, we show that hopfions appear as emergent particles of the classical Heisenberg model with competing exchange interactions. This requires going beyond the model approach used in prior work and deriving a general micromagnetic energy functional directly from a spin-lattice Hamiltonian. We present a definite parameter space in which the existence of hopfions is possible. This opens a concrete vista to combine computational approaches such as density functional theory with material informatics to find magnetic crystals that can host hopfions. As proof of principle, we show how zero-field hopfions can be visualized by the means of off-axis electron holography in a transmission electron microscope.

A fundamental property of particles and antiparticles (such as electrons and positrons, respectively) is their ability to annihilate one another. A similar behaviour is predicted for magnetic solitons1—localized spin textures that can be distinguished by their topological index Q. Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions2 and their antiparticles (namely, antiskyrmions), are expected to be able to continuously merge and annihilate3. However, experimental verification of such particle–antiparticle pair production and annihilation processes has been lacking. Here we report the creation and annihilation of skyrmion–antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet of B20-type FeGe observed using transmission electron microscopy. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Our findings provide a new platform for the fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets. 

Here, by combining a symmetry-based analysis with numerical computations, we predict a different kind of magnetic ordering-antichiral ferromagnetism. This term aims to reflect that spontaneous modulation of the magnetization direction m(r) appears in a way that both types of chirality (handedness) exist simultaneously, and alternate in space. Without loss of generality, we focus our investigation on crystals with full tetrahedral symmetry where chiral interaction terms-Lifshitz invariants-are forbidden by symmetry. However, we demonstrate that the leading chirality-related term leads to nontrivial smooth magnetic textures exhibiting antichirality. In addition to the unconventional ground state, the revealed ordering gives rise to rich phenomena such as unique magnetic domains and skyrmions.

The uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's equation. Our results provide a universal geometrical understanding of the dependence of the skyrmion's velocity and Hall angle on the skyrmion's topological charge, shape, and orientation. The generality of our approach suggests the validity of our results for exchange-frustrated magnets, bubble materials, and other materials.

Skyrmions are vortex-like spin textures that form strings in magnetic crystals. Due to the analogy to elastic strings, skyrmion strings are naturally expected to braid and form complex three-dimensional patterns, but this phenomenon has not been explored yet. We found that skyrmion strings can form braids in cubic crystals of chiral magnets. This finding is confirmed by direct observations of skyrmion braids in B20-type FeGe using transmission electron microscopy. The theoretical analysis predicts that the discovered phenomenon is general for a wide family of chiral magnets. These findings have important implications for skyrmionics and propose a solid-state framework for applications of the mathematical theory of braids.

Shortly after the Gor'kov microscopic derivation of the Ginzburg-Landau (GL) model via a small order parameter expansion in Bardeen-Cooper-Schrieffer theory of superconductivity, the derivation was carried to next-to-leading order in that parameter and its spatial derivatives. The aim was to obtain a generalized GL free energy that approximates the microscopic model better. Since 1960s, multiple works have claimed or implicitly assumed that this extended GL model corresponds to the free energy and has solutions in the form of local minima describing superconductivity, such as vortex solutions. In contrast to this, we prove that this extended GL functional does not represent free energy since it does not have any solutions in the form of minima. Accordingly, it cannot be used to describe superconducting states.& nbsp;

Topological excitations are subjects of intensive studies in physics and mathematics. In solid-state and soft matter physics, topological excitations can largely determine the thermodynamic and electromagnetic properties of materials, while in high energy physics they were theorized as particles. The corresponding theories are based on field models, which are among the pillars of theoretical physics.

Field theory models of superconductivity and magnetism are the theoretical basis for this work. Topological excitations in superconductors and magnets have been studied since the middle of the last century. Since then, a huge amount of work has been accumulated on vortices, Bloch points and skyrmions. In this popular topic, we discovered new phenomena. The main results are:

Discovery and theory of skyrmion braids in cubic chiral magnets. 

Coexistence of type-I and type-II superconductivity signatures in muon spin rotation measurements on ZrB_{12} explained by theoretical modeling of vortex states giving qualitative agreement. 

Theory and experimental evidence of magnetic field controlled pairwise interaction of skyrmions in cubic chiral magnets. 

Experimental observation of chiral bobbers predicted in theory by Rybakov et al. (2015). 

Theory of a new type of magnetic ordering - antichiral ferromagnetism - giving rise to unique skyrmions.  

Generalization of the Bogdanov-Yablonskii solution (1989) for classical models of magnets from the case of a skyrmion with a topological charge of -1 (+1) to the case of all integer charges. 

Positive answer to the Babaev-Faddeev-Niemi hypothesis (2002) on the existence of knot excitations in the superconducting state by demonstrating stable solutions in a model that takes into account the Andreev-Bashkin effect. 

Topologiska excitationer har fått stor uppmärksamhet inom både fysik och matematik. I den kondenserade materiens fysik kan topologiska excitationer ha en avgörande roll för termodynamiska och elektromagnetiska egenskaper av material, medan dessa excitationer i högenergifysik var teoretisk betraktade som partiklar. De motsvarande teorierna är baserade på fältmodeller, vilka är av fundamental vikt för teoretisk fysik. Fältteoretiska modeller för supraledning och magnetism är de teoretiska utgångspunkterna för denna avhandling. 

Topologiska excitationer i supraledare och magneter har studerats sedan 50-talet. Sedan dess har en stor mängd arbete ägnats åt att studera virvlar, Bloch-punkter och skyrmioner. I detta populära forskningsområde har vår forskning lett till upptäckten av nya fenomen, de huvudsakliga resultaten är: 

Upptäckten av skyrmionflätor i kirala kubiska magneter och formuleringen av teorin rörande dessa.

Förklaring av samexisterande typ-1 och typ-2 supraledande signaturer i muon-spin-rotationsmätningar i ZrB_{12} genom teoretisk modellering av virveltillstånd som uppvisar kvalitativa överenstämmelser. 

Teoretiskt och experimentellt bevis för magnetisk justerbar skyrmion-skyrmion interaktion i kirala kubiska magneter. 

Experimentell observation av kirala flötesstrukturer förutspådd av Rybakov et el. (2015). 

Teori rörande anti-chiral ferromagnetism, en ny typ av magnetisk ordning som ger upphov till unika skyrmioner. 

Generalisering av Bogdanov-Yablonskii lösningen (1989) för klassiska modeller av magneter från fallet av en skyrmion med topologisk laddning-1 (+1) till alla heltalsladdningar.

Positivt besvarat Babaev-Faddeev-Niemi hypotesen (2002) rörande existensen av knutexcitationer i supraledare genom att ha demonstrerat stabila lösningar i en modell som tar i beaktande Andreev-Bashkin effekten.

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 (mu SR) 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 mu SR 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.

Magnetic singularities, also known as magnetic monopoles or Bloch points, represent intriguing phenomena in nanomagnetism. We show that a pair of coupled Bloch points-a dipole string-may appear as a stable state in cubic chiral magnets. Analysis of the thermodynamic stability of such objects in the interior of crystals and in geometrically confined systems is presented. Employing advanced Monte Carlo simulations, we reveal an effect of spontaneous nucleation of dipole strings with characteristic size on the order of the helix pitch at temperature close to the paramagnetic phase transition. Such behavior of chiral magnets at elevated temperature drastically distinguishes them from ordinary ferromagnets and may provide a significant contribution to the topological Hall effect even in the absence of skyrmions.