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
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].
High pressure studies in MnSi suggest the existence of a non-Fermi liquid state without quantum criticality. The observation of partial magnetic order in a small pocket of the pressure versus temperature phase diagram of MnSi has additionally inspired several proposals of complex spin textures in chiral magnets. We used neutron scattering to observe the formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, under applied magnetic fields in metallic and semiconducting B20 compounds. In strongly disordered systems the skyrmion lattice is hysteretic and extends over a large temperature range. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of spin order composed of topologically stable spin textures.
We report an experimental and computational study of the Hall effect in Mn1−xFexSi, as complemented by measurements in Mn1−xCoxSi, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of ten. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification, that while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.PACS numbers: 71.15.Mb, 71.20.Be Measurements of the Hall effect in chiral magnets with B20 crystal structure have recently attracted great interest [1][2][3][4][5][6][7]. Due to a hierarchy of energy scales [8], comprising in decreasing strength ferromagnetic exchange, Dzyaloshinsky-Moriya (DM) spin-orbit interactions, and higher order spin-orbit coupling terms, magnetic order in these systems displays generically long-wavelength helical modulations. Under a small applied magnetic field this hierarchy of energy scales stabilizes a skyrmion lattice phase (SLP) in the vicinity of the magnetic transition temperature, i.e., a lattice composed of topologically non-trivial whirls of the magnetization [9-16]. The Hall effect, which has been studied most extensively in MnSi [1][2][3][17][18][19], displays thereby three contributions, notably an ordinary Hall effect (OHE), an anomalous Hall effect (AHE) related to the uniform magnetization, and an additional topological Hall effect (THE) in the SLP due to the non-trivial topology of the spin order.It was only recently noticed that the THE and AHE represent the real-and reciprocal-space limits of generalised phase-space Berry phases of the conduction electrons, respectively. First principles calculations in MnSi suggest that these phase-space Berry phases account quantitatively for the DM interaction and may even give rise to an electric charge of the skyrmions [20,21]. However, so far perhaps most spectacular because of the experimental evidence is the notion that the non-trivial topological winding of skyrmions gives rise to Berry phases in real space that may be viewed as an emergent magnetic field B eff = Φ 0 Φ of one flux quantum (Φ 0 = h/e) times the winding number Φ = −1 per skyrmion [1]. The same mechanism also leads to large spin transfer torques in MnSi [22,23] and FeGe at ultralow current densities. In turn, a very large THE in MnGe [4] and SrFeO 3 [5] has fuelled speculations that the emergent fields may even approach the quantum limit.Despite this wide range of interest, the account of Berry phases in the Hall effect has been essentially phenomenological, in particular for the THE, while a material-specific microscopic justification has been missing. This situation is aggravated by the microscopic sensitivity of the TH...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.