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Register a new userMagnetic skyrmions, chiral kinks and holomorphic functions
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We present a novel approach to understanding the extraordinary diversity of magnetic skyrmion solutions. Our approach combines a new classification scheme with efficient analytical and numerical methods. We introduce the concept of chiral kinks to account for regions of disfavoured chirality in spin textures, and classify two-dimensional magnetic skyrmions in terms of closed domain walls carrying such chiral kinks. In particular, we show that the topological charge of magnetic skyrmions can be expressed in terms of the constituent closed domain walls and chiral kinks. Guided by our classification scheme, we propose a method for creating hitherto unknown magnetic skyrmions which involves initial spin configurations formulated in terms of holomorphic functions and subsequent numerical energy minimization. We numerically study the stability of the resulting magnetic skyrmions for a range of external fields and anisotropy parameters, and provide quantitative estimates of the stability range for the whole variety of skyrmions with kinks. We show that the parameters limiting this range can be well described in terms of the relative energies of particular skyrmion solutions and isolated stripes with and without chiral kinks.
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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 Faradays 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.
We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the 2+1 dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data, and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.
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.
Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $beta$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K. The magnetic field-induced redistribution of the SANS intensity showed that the helical structure transforms to a lattice of skyrmions at $sim$13~mT at temperatures just below $T_{text C}$. Our key observation is that the skyrmion state in FePtMo$_3$N is robust against field cooling down to the lowest temperatures. Moreover, once the metastable state is prepared by field cooling, the skyrmion lattice exists even in zero field. Furthermore, we show that the skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample temperature and can be continuously tuned between 120 and 210~nm. This offers new prospects in the control of topological properties of chiral magnets.
The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for dense nuclear matter. But with skyrmions being mathematical objects - special types of topological solitons - they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. By exploiting a natural separation of exchange energy scales, we achieve this for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab initio calculations reveal that its magnetic building blocks are strongly fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic texture that agrees well with reported experiments. It also brings to light a decay of skyrmions into half-skyrmions in a specific temperature and magnetic field range. The theoretical multiscale approach explains the strong renormalization of the local moments and predicts further fingerprints of the quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$, like weakly dispersive high-energy excitations associated with the Cu$_4$ tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic order, and a fractionalized skyrmion phase.
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