Coupling of Chiralities in Spin and Physical Spaces: The Möbius Ring as a Case Study

Pylypovskyi, Oleksandr V.; Kravchuk, Volodymyr P.; Sheka, Denis D.; Makarov, Denys; Schmidt, Oliver G.; Gaididei, Yuri

doi:10.1103/physrevlett.114.197204

Cited by 83 publications

(61 citation statements)

References 40 publications

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“…The effective Dzyaloshinskii interaction coefficients D αβγ are linear with respect to the b µν components. This effective interaction is a source of possible magnetochiral effects, such as the vortex polarity-chirality coupling [6], and interrelation between chiralities of the sample and its magnetisation subsystem for Möbius rings [20]. The effects of curvature induced magnetochirality were reviewed recently in Ref.…”

Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

“…[11]. It is instructive to establish a link between the 2D energy (22) and the 1D expression (13). For this purpose we define the surface ς(ξ 1 , ξ 2 ) as a local extension of the curve γ(s) in the following way…”

Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

“…Assuming now that the magnetisation on the surface (24) depends on s only, one obtains ∇θ = θ (s)e 1 and ∇φ = φ (s)e 1 , and finally the 2D energy (22) takes the form (13). Let us take into account the anisotropy term, starting from the energy functional (5) and choosing the anisotropy axis n = e 3 , i.e.…”

Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

“…Examples are magnetic vortices in easy-surface spherical shells [6], magnetic domains in Möbius rings with easy-normal anisotropy [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Curvature effects in statics and dynamics of low dimensional magnets

Sheka

Kravchuk

Gaididei

2015

J. Phys. A: Math. Theor.

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122

162

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Abstract. We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.

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Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

Section: Energy and The Curvature Induced Effective Fields For A Curvmentioning

confidence: 99%

“…Examples are magnetic vortices in easy-surface spherical shells [6], magnetic domains in Möbius rings with easy-normal anisotropy [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Curvature effects in statics and dynamics of low dimensional magnets

Sheka

Kravchuk

Gaididei

2015

J. Phys. A: Math. Theor.

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122

162

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“…Since a Möbius ring is a nonorientable surface, its topology forces a discontinuity in any nonvanishing normal vector field. Recently we proposed that magnetic nanostructures shaped as Möbius strips possess non-volatility in their magneto-electric response due to the presence of topologically protected magnetic domain walls in materials with an out-of-plane orientation of the easy axis of magnetization [21]. In both of these examples, the link between surface topology and magnetization is a consequence of geometry-dependent anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Magnetization in narrow ribbons: curvature effects

Gaididei¹,

Goussev²,

Kravchuk³

et al. 2017

J. Phys. A: Math. Theor.

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Abstract.A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Möbius ribbon, for which the central curve is a circle about which the line segment executes a 180 • twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Möbius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

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New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

et al. 2021

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condensed matter physics, including cell membranes, [1] nematic crystals, [2,3] superfluids, [4] semiconductors, [5][6][7][8] ferromagnets, [9] and superconductors. [10,11] Currently, much attention is paid to strongly correlated electronic systems, for example, ferromagnets and superconductors, as they provide a unique tool to manipulate the topology of coexisting vector and scalar fields, associated with geometries of conventional systems.Until recently, in the case of magnetism, the influence of the geometry on the spin vector fields was addressed primarily by the design of the sample boundaries. This approach naturally brings the shape anisotropy to the system and leads to the formation of specific spin textures, for example, magnetic vortices [12] and antivortices [13] as well as provides control over the dynamics of the topologically nontrivial magnetic solitons. [14][15][16][17][18] This discussion also tackles the state of the art in modern experimental antiferromagnetism, where the design of the sample topography and boundaries allows to control the domain wall states. [19][20][21][22] With the development of novel fabrication techniques allowing to realize complex 3D architectures, not only the boundary effects but also the extrinsic geometrical properties (e.g., local curvatures) can be addressed rigorously for the case of ferromagnets [23][24][25][26][27] as well as superconductors. [28][29][30] The explored effects are directly related to the interplay between the Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro-and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-...

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Coupling of Chiralities in Spin and Physical Spaces: The Möbius Ring as a Case Study

Cited by 83 publications

References 40 publications

Curvature effects in statics and dynamics of low dimensional magnets

Curvature effects in statics and dynamics of low dimensional magnets

Magnetization in narrow ribbons: curvature effects

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

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