Heisenberg spins on an infinite cylinder: a geometrical effect of anisotropy

Villain-Guillot, Simon; Dandoloff, Rossen; Saxena, Avadh

doi:10.1016/0375-9601(94)90473-1

Cited by 12 publications

(23 citation statements)

References 5 publications

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“…The mapping of this sphere to S 2 , the order parameter manifold, gives π 2 (S 2 )= Z. Thus the spin distributions on the infinite cylinder can be classified in different classes of topologically non-trivial spin distributions [2,5]. Inside each class, the spin distributions are topologically equivalent: they belong to the same homotopy class.…”

Section: Rigid Circular Cylindermentioning

confidence: 95%

“…The EL equations resulting from the variation of H isotropic + H el with respect to θ and ρ are highly nonlinear differential equations [8]. A trivial solution of these equations, compatible with the boundary conditions, is ρ = ρ 0 and θ given by (5). Obviously, the system does not exploit the "new degree of freedom" ρ = ρ(x).…”

Section: Rigid Circular Cylindermentioning

confidence: 97%

“…Then, in cylindrical coordinates (ρ,x,ϕ) we write the Hamiltonian as [5] H isotropic = J cylinder [(∂ x θ) 2 + sin 2 θ (∂ x Φ) 2…”

Section: Rigid Circular Cylindermentioning

confidence: 99%

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Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Dandoloff

Saxena

1997

Zeitschrift für Physik B Condensed Matter

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Classical Heisenberg spins considered on an elastic two-dimensional curved manifold in the continuum limit correspond to the nonlinear σ model. If the corresponding Euler-Lagrange (EL) equations support a soliton solution, a mismatch of length scales induces geometrical frustration in the region of the soliton which is relieved by a deformation of the manifold in the region of the soliton. We illustrate the origin of this elastic effect in four different cases: (i) A single soliton on a circular cylinder with anisotropic spinspin coupling, (ii) a soliton lattice on a circular cylinder with isotropic spin-spin coupling, (iii) a single soliton on an elliptic cylinder, and (iv) a circular cylinder in an external axial magnetic field. For the first three cases the EL equation is the sine-Gordon equation while for the last case it is the double sine-Gordon equation. Geometrical frustration results whenever the solution of the EL equation does not satisfy the self-dual equations of Bogomol'nyi which are a necessary condition to reach the minimum energy configuration in each homotopy class.

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Section: Rigid Circular Cylindermentioning

confidence: 95%

Section: Rigid Circular Cylindermentioning

confidence: 97%

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Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Dandoloff

Saxena

1997

Zeitschrift für Physik B Condensed Matter

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“…In these cases, a number of new phenomena have been described, like the geometrical frustration on spin textures induced by curvature and/or by non-trivial topological aspects of the space manifold, say, angular deficit in cones, area deficit in planes with a disk cut out, and so forth (see, for example, Refs. [15,13,14,16]). Actually, the study of such systems may be of considerable importance for practical applications, for example, in connection to soft condensed matter materials [15] (deformable vesicles, membranes, etc), and also to artificially nanostructured curved objects (nanocones, nanocylinders, etc) in high storage data devices [17,18].…”

Section: Introductionmentioning

confidence: 99%

“…where we have taken into account the type of the excitation, according to (13)(14). Now, looking only for the harmonic potential (say, the quadractic term) it is easy to show (we refer the reader to Ref.…”

Section: Introductionmentioning

confidence: 99%

Heisenberg spins on a cone: an interplay between geometry and magnetism

Freitas

Moura-Melo²,

Pereira

2005

Physics Letters A

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This work is devoted to the study of how spin texture excitations are affected by the presence of a static nonmagnetic impurity whenever they lie on a conical support. We realize a number of novelties as compared to the flat plane case. Indeed, by virtue of the conical shape, the interaction potential between a soliton and an impurity appears to become stronger as long as the cone is tighten. As a consequence, a new kind of solitonic excitation shows up exhibiting lower energy than in the absence of such impurity. In addition, we conclude that such an energy is also dependent upon conical aperture, getting lower values as the latter is decreased. We also discuss how an external magnetic field (Zeeman coupling) affects static solitonic textures, providing instability to their structure.

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Nonlinearity and Topology

Saxena

Kevrekidis

Cuevas–Maraver

2020

Nonlinear Systems and Complexity

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The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated.

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Heisenberg spins on an infinite cylinder: a geometrical effect of anisotropy

Cited by 12 publications

References 5 publications

Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Heisenberg spins on a cone: an interplay between geometry and magnetism

Nonlinearity and Topology

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