Magnetic skyrmions, chiral kinks, and holomorphic functions

Kuchkin, Vladyslav M.; Barton-Singer, Bruno; Rybakov, Filipp N.; Blügel, Stefan; Schroers, Bernd J.; Kiselev, Nikolai S.

doi:10.1103/physrevb.102.144422

Cited by 63 publications

(63 citation statements)

References 27 publications

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“…This class of solutions has skyrmions acting as noninteracting particles with the energy of 4π each. A diverse array of multi-skyrmion configurations was constructed analytically and confirmed numerically [25]. The absolute ground states of the model are, unfortunately, not among these special states.…”

Section: Historical Notementioning

confidence: 86%

Chiral magnetism: a geometric perspective

2021

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We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

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Section: Historical Notementioning

confidence: 86%

Chiral magnetism: a geometric perspective

2021

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“…It had been theoretically proposed in chiral magnets that the skyrmions, antiskyrmions, and other magnetic configurations can be naturally interpreted in terms of chiral kinks. These kinks carry a topological charge and allow to construct new topological particle-like states [15,31,32]. In addition, the previous studies demonstrated that some special magnetic textures often appear in the corners of the polygon geometries like triangles, squares, rectangles, in which the corners may also act as pinning sites for the domain wall motion [33][34][35][36].…”

Section: Introductionmentioning

confidence: 97%

“…Generally, the presence of edges and corners in nanostructures can be utilized to tailor the magnetic textures and modify their dynamics behaviors. For the skyrmion confined in ultrathin film nanostructures with Dzyaloshinskii-Moriya (DM) interaction, the boundary constrictions naturally make the magnetization orientation undergo the 180°rotation at the edges, forming the so-called kink or π domain wall configurations [2,15,[29][30][31][32]. Depending on the crystal symmetry of chiral magnets, two distinct types of chiral kinks, namely, Néel-type and Blochtype kinks, are favorable in interfacial and bulk DM interaction systems respectively [29,30].…”

Section: Introductionmentioning

confidence: 99%

Control of Néel-type Magnetic Kinks Confined in a Square Nanostructure by Spin-Polarized Currents

et al. 2021

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Magnetic skyrmion in chiral magnet exhibits a variety of unique topological properties associated with its innate topological structure. This inspires a number of ongoing searching for new topological magnetic textures. In this work, we used micromagnetic simulations and Monte Carlo simulations to investigate an exotic Néel-type magnetic kinks in square-shaped nanostructures of chiral magnets, which performs rather stably in the absence of magnetic field. The individual magnetic kink can reside in one of the four possible corners, and carry possibly upward or downward core polarity, constituting eight degenerate states. In addition, these kinks also exhibit unique behaviors of generation, stability and dynamics, as revealed by micromagnetic simulations. It was found that such kinks can be created, annihilated, displaced, and polarity-reversed on demand by applying a spin-polarized current pulse, and are easily switchable among the eight degenerate states. In particularly, the kinks can be switched toward the ferromagnetic-like states and backward reversibly by applying two successive current pulses, indicating the capability of writing and deleting the kink structures. These findings predict the existence of Néel-type magnetic kinks in the square-shaped nanostructures, as well as provide us a promising approach to tailor the kinks by utilizing the corners of the nanostructures, and control these states by spin-polarized currents. The present work also suggests a theoretical guide to explore other chiral magnetic textures in nanostructures of polygon geometries.

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“…Loosely speaking, topological stability does not imply energetic stability, as topologically distinct vacua are always separated by finite action barriers 5. For a recent discussion of stable soliton solutions of arbitrary topological charge in chiral magnets, see[50][51][52] 6. In principle, this would work similar to the previous section, by adding the Hopf charge to the loss function, L = S + λ H (H − H 0 ) 2 .…”

mentioning

confidence: 95%

Exploring instantons in nonlinear sigma models with spin-lattice systems

Schenk

Spannowsky

2021

Phys. Rev. B

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Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features often remain elusive due to the complicated computational treatment. Here, we address this problem by studying topological as well as nontopological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in O(3) nonlinear sigma models with a Dzyaloshinskii-Moriya interaction in (1 + 1) and (1 + 2) dimensions, thereby resembling an example of a chiral magnet. We demonstrate that, due to their close correspondence, Monte Carlo techniques in spin-lattice systems are well suited to describe topologically nontrivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons, and critical instanton solutions.

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Magnetic skyrmions, chiral kinks, and holomorphic functions

Cited by 63 publications

References 27 publications

Chiral magnetism: a geometric perspective

Chiral magnetism: a geometric perspective

Control of Néel-type Magnetic Kinks Confined in a Square Nanostructure by Spin-Polarized Currents

Exploring instantons in nonlinear sigma models with spin-lattice systems

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