Abstract
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Highlights
Unusual spin textures, identified as magnetic Skyrmions of topological origin, were observed in helimagnetic crystals like Mn Si and FexCo1−xSi, in a series of recent experiments QHexperim,nutronScattExp,LorentzExp
The recent experimental observation of Skyrmions in helimagnetic materials on a 2d plane, is a triumph of the theoretical prediction of such exact topological solitons in a ferromagnetic model proposed 40 years ago by Belavin and Polyakov (BP) BP, though due to the metastable states they could not be detected in the original model
On the other hand, during all these years, there was hardly any proposal which could generalize the idea of BP for constructing novel exact solitons of topological origin in other 2d models, which could be tested experimentally
Summary
Unusual spin textures, identified as magnetic Skyrmions of topological origin, were observed in helimagnetic crystals like Mn Si and FexCo1−xSi, in a series of recent experiments QHexperim,nutronScattExp,LorentzExp. The possibility of such a phenomenon to occur on a two-dimensional (2d) plane in ferromagnetic model was predicted by Belavin and Polyakov 40 years back, in a pioneering work, where they found exact Skyrmions in a general framework with topological charge Q = N, linked to any analytic functions [4] Problem with this beautiful theoretical result was, that due to scale invariance of the solution it could give only metastable states, where for stabilizing the Skyrmions one needs to bring in coupling parameters through additional interactions. A natural application of such asymmetric solitons to the helimagnetic model, through their stabilization under DM interaction might be a promising perspective to be verified in a precision experiment
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