Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons

By H. Braun. 2012

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Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. (2016, background): “e their magnetisation texture cannot be continuously transformed into the uniform magnetic state without causing a singularity [8].”
Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications (2019, background): “In the context of 2D and quasi-2D systems, the topological structure of a spin texture is generally characterized by the topological charge [55-57], which is also referred to as the Pontryagin number [2, 3]: Q = ∫ d(2)r ρ(r), (1)”
Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet (2018, background): “. A topological number of spin configurations, which remains intact under local deformation or weak fluctuations, offers another unique parameter to capture the characteristic nature of spin textures (11). This concept has recently attracted growing interest since the discovery of magnetic skyrmion ”
Skyrmions in magnetic multilayers (2017, background): “As a result, they belong to the same topological class [59].”
Cavity magnonics (2021, background): “Since the exchange energy cost of changes of its modulus is very high, it may taken to be constant |Ms(r)| = Ms (Braun, 2012).”