Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry

Abstract

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler-Lagrange static equations, derived from the Hamiltonian lead to the inhomogeneous double sine-Gordon equation (DSG). However, if the magnetic field is coupled with the metric elements of the surface, and consequently, its curvature, the homogeneous DSG appears and a 2π-soliton is obtained as a solution for this model. In order to obey the self-dual equations, surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. The model was used to particularize the characteristic lenght of the 2π-soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. Fractional 2π-solitons must appear on finite surfaces, as the sphere, torus and barrels, for example.

Topological magnetic solitons on a paraboloidal shell

“…The Heisenberg model on a curved surface in the presence of an external field has been studied before on non-simply connected surfaces. It has been shown that tuning the magnetic field to the surface curvature in the form B ∝ 1/r 2 yields the homogeneous double sine-Gordon equation (DSGE) [30,31,32]. The associated solutions are 2π-skyrmions, whose widths depend on a second length scale, introduced into the system by the magnetic field.…”

“…[29], provided the magnetic field is tuned to the surface curvature in the form B(r) = B ′ 0 /r 2 , with B ′ 0 ≡ gµB 0 constant. [30,31,32] However, the studied cases refer to non-simply connected manifolds and no considerations have been made about simply-connected surfaces for which the proposed magnetic field presents a divergence at the origin. In this context we present some arguments that ensure that the solutions discussed above are also valid on simply-connected surfaces, in particular, on a paraboloid.…”

“…With the introduction of the cut-off, the punctured paraboloid becomes a nonsimply-connected surface and the solutions discussed in Refs. [30,31,32] are recovered. In this case, Eqs.…”

Manipulating the shape of flexible magnetoelastic nanodiscs with meron-like magnetic states

“…Theoretical works have considered magnetic subsystems where the short-range exchange interaction determines the magnetic properties of the particle, and stretching and bending are responsible for describing the energetic cost to deform the elastic subsystem. In this case, the nucleation of periodic solitons in the magnetic system induces the appearance of periodic shrinking of the membrane [26], and curvature-induced geometrical frustration in magnetic systems in both cases under the absence and presence of external magnetic fields [27][28][29][30]. Additionally, Yershov et al [31] showed that a unidimensional magnetoelastic ring presents a shape depending on the magnetic configuration.…”

On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

“…Furthermore, the interaction of an external magnetic field with Heisenberg spins on a cylindrical surface yields a 2π soliton-like solution, inducing a deformation at the sector where the spins are pointing in the opposite direction to the magnetic field [16]. A 2π soliton has also been predicted to appear on curved surfaces with cylindrical symmetry, provided the magnetic field is coupled with the curvature of the substrate [17,18].…”