The algebraic topology of Bloch points

Kotiuga, P. Robert

doi:10.1109/20.42340

Cited by 27 publications

(16 citation statements)

References 13 publications

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“…It can be seen that the points with M ( r )= 0 correspond to the hedgehog or antihedgehog of n ( r ) with the effective magnetic charge ( S is the surface enclosing the singularity), namely the emergent magnetic monopole and antimonople (see Fig. 1c and also Supplementary Note 1 ) 6 7 8 9 10 11 12 21 22 23 . Therefore, the strong correlation limit produces the non-trivial topological classification of the spin configurations and the topological phase transition as well.…”

Section: Resultsmentioning

confidence: 99%

“…A real-space geometric arrangement of spins affects charge transport by exerting an additional quantum phase on the itinerant electrons, called Berry phase 5 , which acts as the effective magnetic field. Among topological spin orders, hedgehogs and antihedgehogs play the roles of sources or sinks of emergent field, that is, emergent monopoles or antimonopoles 6 7 . These hedgehog spin structures have been indeed realized as topological defects such as Bloch points 8 9 10 11 and singular points where magnetic skyrmions coalesce with or split from one another 12 .…”

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confidence: 99%

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Critical phenomena of emergent magnetic monopoles in a chiral magnet

et al. 2016

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Second-order continuous phase transitions are characterized by symmetry breaking with order parameters. Topological orders of electrons, characterized by the topological index defined in momentum space, provide a distinct perspective for phase transitions, which are categorized as quantum phase transitions not being accompanied by symmetry breaking. However, there are still limited observations of counterparts in real space. Here we show a real-space topological phase transition in a chiral magnet MnGe, hosting a periodic array of hedgehog and antihedgehog topological spin singularities. This transition is driven by the pair annihilation of the hedgehogs and antihedgehogs acting as monopoles and antimonopoles of the emergent electromagnetic field. Observed anomalies in the magnetoresistivity and phonon softening are consistent with the theoretical prediction of critical phenomena associated with enhanced fluctuations of emergent field near the transition. This finding reveals a vital role of topology of the spins in strongly correlated systems.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Critical phenomena of emergent magnetic monopoles in a chiral magnet

et al. 2016

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“…In the present paper, we use the word, (anti) monopole, to express the topological defect on the skyrmion string. Kotiuga 31,32 described the topological nature of (anti)monopole by the Hopf extension theorem of algebraic topology. (The references 33,34 give a more extensive discussion on the group theoretical description of topological matters.)…”

Section: Openmentioning

confidence: 99%

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

Koshibae

Nagaosa

2020

Sci Rep

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The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

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“…Thus, a BP cannot appear alone within a continuous structure: either it is created in a pair, or it enters into the sample from the boundary. 3 Experimental proofs of the existence of BP's are not numerous, but exist. Lorentz imaging of nickel thin films with an asymmetric Bloch-wall structure showed polarity reversals that imply the presence of a BP.…”

Section: Introductionmentioning

confidence: 99%

Micromagnetic study of Bloch-point-mediated vortex core reversal

et al. 2003

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We study how micromagnetic calculations can be applied to processes that involve a singularity of the magnetization field, namely, the Bloch point. In order to allow for comparison with recent experiments, we consider Permalloy thin-film disks supporting a vortex magnetic configuration. The structure of the Bloch point at rest in the middle of the core of the vortex is studied first, comparing the evolution of the calculation results under decreasing mesh size to analytical results. The reversal of the core of the vortex under a field applied perpendicularly to the disk plane is then investigated. We apply two different procedures to evaluate switching fields and processes: direct micromagnetic time-dependent calculation, and the evaluation of the energy barrier that separates the two orientations of the vortex core in the configuration space, using a path method. Both methods show the occurrence of Bloch points during reversal. Special attention is paid to the extrapolation towards zero mesh size of the numerical results. The calculations are confronted to experimental values from Okuno et al. ͓J. Magn. Magn. Mater. 240, 1 ͑2002͔͒. We conclude that defects and thermal agitation are likely to assist Bloch-point injection, hence lowering the switching fields.

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The algebraic topology of Bloch points

Cited by 27 publications

References 13 publications

Critical phenomena of emergent magnetic monopoles in a chiral magnet

Critical phenomena of emergent magnetic monopoles in a chiral magnet

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

Micromagnetic study of Bloch-point-mediated vortex core reversal

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