Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry |
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Authors: | Vagson L Carvalho-Santos Rossen Dandoloff |
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Institution: | 1. Instituto Federal de Educação, Ciência e Tecnologia Baiano, Campus Senhor do Bonfim, 48970-000 Senhor do Bonfim, Bahia, Brazil;2. Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France |
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Abstract: | We study the nonlinear σ-model in an external magnetic field applied on curved surfaces with rotational symmetry. The Euler–Lagrange equations derived from the Hamiltonian yield the double sine-Gordon equation (DSG) provided the magnetic field is tuned with the curvature of the surface. A 2π skyrmion appears like a solution for this model and surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. We also study some specific examples by applying the model on three rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. |
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Keywords: | Classical spin models Skyrmions Curvature Heisenberg Hamiltonian |
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