A theory of skyrmion crystal formation

Hu, X. C.; Wu, H. T.; Wang, Xiangrong

doi:10.1039/d2nr01300b

Cited by 11 publications

(7 citation statements)

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“…[165] The nature of skyrmion entropy is also an interesting issue. [165,166] Moreover, skyrmion qubits can be constructed by using the energy-level quantization of the helicity degree of freedom. [167] Quantum computing using chiral spin textures is worth of exploring further.…”

Section: Discussionmentioning

confidence: 99%

Progress and challenges in magnetic skyrmionics

Wang

2022

Chinese Phys. B

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Magnetic skyrmions are two-dimensional localized topological spin-structures characterized by the skyrmion number that measures the number of times of spins wrapping the Bloch sphere. Skyrmions behave like particles under an external stimulus and are promising information carriers. Skyrmions can exist as an isolated object as well as skyrmion condensates in crystal structures, helical/conical states, mazes or irregular stripy states with emergent electromagnetic fields. Thus, skyrmions provide a nice platform for studying fundamental physics, other than its applications in spintronics. In this perspective, we briefly review some recent progress in the field and present an outlook of the fundamental challenges in device applications.

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Section: Discussionmentioning

confidence: 99%

Progress and challenges in magnetic skyrmionics

Wang

2022

Chinese Phys. B

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“…Previous studies − showed that the stripe skyrmion structure follows m z ( x ) = for – L /2 < x < L /2 and m z ( x ) = for L /2 < x < 3 L /2, where L and w are the stripe width and wall thickness. x = 0 refers to stripe center where m z = 1.…”

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confidence: 98%

“…Testing this belief motivates current study. For a perpendicularly magnetized chiral film described by magnetization M , the Heisenberg exchange stiffness constant A , anisotropic coefficient K , and the Dzyaloshinskii–Moriya interaction (DMI) coefficient D , κ ≡ (π 2 D 2 )/(16 AK ) = 1, an important quantity, separates isolated skyrmions (κ < 1) from condensed stripe skyrmions (κ > 1) in the absence of a magnetic field. − In this Letter, we study how the morphology of a collection of stripe skyrmions changes as the stripe widths gradually increase. Our results show the topological equivalence of stripy states and SkXs and raise the question about the notion of the first-order phase transition in SkX formations.…”

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confidence: 99%

“…Previous studies − showed that the stripe skyrmion structure follows m z ( x ) = sinh 2 ( L / 2 w ) − sinh 2 ( x / w ) sinh 2 ( L / 2 w ) + sinh 2 ( x / w ) for – L /2 < x < L /2 and m z ( x ) = prefix− sinh 2 ( L / 2 w ) − sinh 2 ( x / w − L / w ) sinh 2 ( L / 2 w ) + sinh 2 ( x / w − L / w ) for L /2 < x < 3 L /2, where L and w are the stripe width and wall thickness. x = 0 refers to stripe center where m z = 1.…”

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confidence: 99%

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Topological Equivalence of Stripy States and Skyrmion Crystals

Wang

Zhen

2023

Nano Lett.

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Stripy states, consisting of a collection of stripy spin textures, are the precursors of skyrmion crystals (SkXs). The common belief is that stripy states and SkXs are topologically unconnected and that transitions between SkXs and stripy states are phase transitions. Here, we show that both stripy states and SkXs are skyrmion condensates and they are topologically equivalent. By gradually tuning the stripe whose width goes from smaller than to larger than skyrmion–skyrmion separation, the structure of a skyrmion condensate transforms smoothly and continuously from various stripy phases, including helical states and mazes, to crystals, showing that stripy states are topologically connected to SkXs.

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“…The magnetic moments in these multi-q structures can be noncollinear and noncoplanar. In general, multi-q has also been used to define the spin texture as superpositions of multiple spin helices or spin density waves, mostly incommensurate, such as skyrmions [33][34][35][36][37][38][39][40][41][42] in 2D thin films or layered structures, and hedgehog 43,44 in 3D structures, with a real space non-trivial topology and also a periodicity much larger than the underlying crystal lattice. Although magnetic space groups (MSG) give all the symmetry operations for Wyckoff positions with breaking time-reversal symmetry due to magnetism, multi-q as a superposition of multiple propagating vectors can include the orientation of the magnetic moments to describe both commensurate and incommensurate magnetic structures with noncollinear and noncoplanar components.…”

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Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding

et al. 2023

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Many complex magnetic structures in a high-symmetry lattice can arise from a superposition of well-defined magnetic wave vectors. These “multi-q” structures have garnered much attention because of interesting real-space spin textures such as skyrmions. However, the role multi-q structures play in the topology of electronic bands in momentum space has remained rather elusive. Here we show that the type-I anti-ferromagnetic 1q, 2q and 3q structures in an face-centered cubic sublattice with band inversion, such as NdBi, can induce unconventional surface state pairs inside the band-folding hybridization bulk gap. Our density functional theory calculations match well with the recent experimental observation of unconventional surface states with hole Fermi arc-like features and electron pockets below the Neel temperature. We further show that these multi-q structures have Dirac and Weyl nodes. Our work reveals the special role that band-folding from anti-ferromagnetism and multi-q structures can play in developing new types of surface states.

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A theory of skyrmion crystal formation

Abstract: A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with...

Cited by 11 publications

References 55 publications

Progress and challenges in magnetic skyrmionics

Progress and challenges in magnetic skyrmionics

Topological Equivalence of Stripy States and Skyrmion Crystals

Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding

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