Deformable curved magnetic surfaces

We study curved magnetic surfaces in the context of soft condensed matter. Specifically, we consider classical Heisenberg spins on elastically deformable curved geometries in orthogonal curvilinear coordinates such as a cylinder, a torus, etc. We find that a mismatch of length scales (geometrical frustration) in the presence of magnetic solitons leads to an elastic soliton (deformation) on the magnetic surfaces. We illustrate the results on (i) a circular cylinder with either spin anisotropy or external magnetic field or multiple solitons, (ii) an elliptic cylinder and (iii) a torus section. Our results are applicable to microtubules and vesicles (spheroidal or toroidal) comprised of magnetic organic materials such as magnetic polymers.