Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of crystalline order composed of topologically stable spin states. 1 arXiv: 0902.1968v1 [cond-mat.str-el]

1Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations [1]. As an exception Skyrme's model succeeded to describe nuclear particles as localized states, so-called 'skyrmions', within a non-linear field theory [2]. Skyrmions are a characteristic of non-linear continuum models ranging from microscopic to cosmological scales [3,4,5,6]. Skyrmionic states have been found under non-equilibrium conditions, or when stabilised by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids [7], spin textures in quantum Hall magnets [8], or the blue phases in liquid crystals [9], respectively. However, it is believed that skyrmions cannot form spontaneous ground states like ferromagnetic or antiferromagnetic order in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model, that is based on a few material-specific parameters that may be determined from experiment. As a new condition not considered before, we allow for softened amplitude variations of the magnetisation -a key property of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist quite generally in a large number of materials, notably at surfaces and in thin films as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.The possibility that particle-like states may form spontaneously in continuous fields has motivated intense theoretical efforts in the past. Derrick and Hobart established by rather general arguments that particle-like configurations are not stable in the majority of nonlinear field models [10,11]. However, a few exceptions have been found. Skyrme showed that particle-like excitations of continuous fields exist in the presence of certain non-linear interactions [2]. As a drawback, the interactions considered by Skyrme are physically not transparent, because they involve higher order derivative terms that are technically intractable. Therefore, Skyrme's approach is not viable in the context of ordered states in condensed matter that are ruled by short range interactions. In contrast, a physically transparent exception to the Derrick-Hobart theorem has been recognized in systems with bro-2 ken inversion symmetry, where chiral interactions lead to skyrmion excitations in condensed matter systems [12,14,16]. Chiral interactions exist in many different systems, e.g., (i) spin-orbit interactions in non-centrosymmetric materials, also referred to as DzyaloshinskyMoriya (DM) interactions [13], (ii) in non-centrosymmetric ferroelectrics, (iii) for certain structural phase transitions, (iv) in chiral liquid crystals, and (v) in the form of Che...

Spin manipulation using electric currents is one of the most promising directions in the field of spintronics. We used neutron scattering to observe the influence of an electric current on the magnetic structure in a bulk material.In the skyrmion lattice of MnSi, where the spins form a lattice of magnetic vortices similar to the vortex lattice in type II superconductors, we observe the rotation of the diffraction pattern in response to currents which are over five orders of magnitude smaller than those typically applied in experimental studies on current-driven magnetization dynamics in nanostructures. We attribute our observations to an extremely efficient coupling of inhomogeneous spin currents to topologically stable knots in spin structures. 1 arXiv:1012.3496v1 [cond-mat.str-el]

When an electron moves in a smoothly varying non-collinear magnetic structure, its spin-orientation adapts constantly, thereby inducing forces that act on both the magnetic structure and the electron. These forces may be described by electric and magnetic fields of an emergent electrodynamics. The topologically quantized winding number of so-called skyrmions, i.e., certain magnetic whirls, discovered recently in chiral magnets are theoretically predicted to induce exactly one quantum of emergent magnetic flux per skyrmion. A moving skyrmion is therefore expected to induce an emergent electric field following Faraday's law of induction, which inherits this topological quantization. Here we report Hall effect measurements, which establish quantitatively the predicted emergent electrodynamics. This allows to obtain quantitative evidence of the depinning of skyrmions from impurities at ultra-low current densities of only 10^6 A/m^2 and their subsequent motion. The combination of exceptionally small current densities and simple transport measurements offers fundamental insights into the connection between emergent and real electrodynamics of skyrmions in chiral magnets, and promises to be important for applications in the long-term.Comment: 24 pages, supplementary information file include

Recent small angle neutron scattering suggests, that the spin structure in the A-phase of MnSi is a so-called triple-Q state, i.e., a superposition of three helices under 120 degrees. Model calculations suggest that this structure in fact is a lattice of so-called skyrmions, i.e., a lattice of topologically stable knots in the spin structure. We report a distinct additional contribution to the Hall effect in the temperature and magnetic field range of the proposed skyrmion lattice, where such a contribution is neither seen nor expected for a normal helical state. Our Hall effect measurements constitute a direct observation of a topologically quantized Berry phase that identifies the spin structure seen in neutron scattering as the proposed skyrmion lattice.PACS numbers: 72.80. Ga, Many years ago Skyrme showed that topologically stable objects of a nonlinear field theory for pions can be interpreted as protons or neutrons [1,2]. This seminal paper inspired the search for topological stable particlelike objects in a broad range of fields ranging from highenergy to many areas of condensed matter physics. For instance, twenty years ago it has been predicted that skyrmions exist in anisotropic spin systems with chiral spin-orbit interactions, where they are expected to form crystalline structures [3,4]. Lattices of skyrmions have also been suggested to occur in dense nuclear matter [5] or in quantum Hall systems near Landau level filling factor ν = 1 [6]. However, thus far the experimental evidence is only indirect [7,8].Recently we reported microscopic evidence of a skyrmion lattice in the A-phase of the transition metal compound MnSi using small angle neutron scattering (SANS) [9]. The SANS data shows magnetic Bragg peaks with a hexagonal symmetry consistent with the superposition of three helices under an angle of 120 degrees -a so-called triple-Q structure. The three helices are thereby confined to a plane strictly perpendicular to the applied magnetic field. A detailed theoretical analysis [9] of an appropriate Ginzburg-Landau model suggested that a lattice of anti-skyrmion lines forms in the A-phase of MnSi, similar to the vortex lattice in superconductors.However, whether the spin structure in the A-phase indeed represents a skyrmion lattice depends crucially on the phase relationship of the helices that are superimposed. This phase information could not be extracted from the SANS data. In contrast to neutron scattering the phase relationship of the helices, and thus existence of topologically nontrivial spin structures, may be established directly by means of the so-called topological Hall effect (THE) [10]. The perhaps most convincing example of a topological Hall effect has been reported for 3D pyrochlore lattices [11,12]. However, in these systems the non-coplanar spin structure is due to frustration on short length scales, i.e., the spin structure is not a continuous field for which topological properties may be defined in a strict sense. The topological Hall effect has also been considered, e.g., in La 1...

Intermetallic compounds containing f-electron elements display a wealth of superconducting phases, that are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferro-and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconductivity near valence transitions, or in the vicinity of magneto-polar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of f-electron compounds is reviewed.

We report a comprehensive small angle neutron scattering study (SANS) of the magnetic phase diagram of the doped semiconductor Fe1−xCoxSi for x = 0.2 and 0.25. For magnetic field parallel to the neutron beam we observe a six-fold intensity pattern under field-cooling, which identifies the A-phase of Fe1−xCoxSi as a skyrmion lattice. The regime of the skyrmion lattice is highly hysteretic and extents over a wide temperature range, consistent with the site disorder of the Fe and Co atoms. Our study identifies Fe1−xCoxSi is a second material after MnSi in which a skyrmion lattice forms and establishes that skyrmion lattices may also occur in strongly doped semiconductors.PACS numbers: 72.80. Ga, Recently a skyrmion lattice was identified in the cubic B20 system MnSi [1,2], that is, magnetic order representing a crystallization of topologically stable, particle-like knots of the spin structure originally anticipated to occur in anisotropic materials [3]. This raises the question for further magnetic materials with skyrmion lattices and if they are a general phenomenon in cubic magnets without inversion symmetry as suggested by our theoretical treatment in [1]. Because MnSi is a pure metal, an additional question concerns if skyrmion lattices are sensitive to disorder and whether they also exist in semiconductors and insulators. More generally, the microscopic identification of a skyrmion lattice in MnSi represents also a showcase for similar lattice structures considered in nuclear physics [4,5], quantum Hall systems [6,7], and liquid crystals [8].

Skyrmion crystals are regular arrangements of magnetic whirls that exist in a wide range of chiral magnets. Because of their topology, they cannot be created or destroyed by smooth rearrangements of the direction of the local magnetization. Using magnetic force microscopy, we tracked the destruction of the skyrmion lattice on the surface of a bulk crystal of Fe(1-x)Co(x)Si (x = 0.5). Our study revealed that skyrmions vanish by a coalescence, forming elongated structures. Numerical simulations showed that changes of topology are controlled by singular magnetic point defects. They can be viewed as quantized magnetic monopoles and antimonopoles, which provide sources and sinks of one flux quantum of emergent magnetic flux, respectively.