Heisenberg spins on a cylinder in an axial magnetic field

Abstract

For classical Heisenberg spins in the continuum limit ~i.e., the nonlinear s model! on an elastic cylinder in an external axial magnetic field we find that the corresponding Euler-Lagrange equation is the double sineGordon ~DSG! equation. The DSG soliton adopts a characteristic length j which is smaller than the radius of the cylinder. This mismatch of length scales results in a geometric frustration in the region of the soliton and is relieved by the deformation of the cylinder. We also find the DSG kink soliton lattice and pulse soliton lattice solutions and show that they cause a periodic deformation of the cylinder. @S0163-1829~98!51126-5# Cylindrical structures, in particular microtubules, 1 abound in nature. They may either be made out of magnetic materials or may enclose magnetorheological fluids. 2 To study their magnetoelastic properties, one may treat their surfaces as a continuum of classical spins. Along this line of thinking, here we explore the elastic consequences of classical Heisenberg-coupled spins on a deformable cylinder in the presence of topological spin solitons and an external magnetic field. Recently, it has become possible to fabricate magnetic thin films in a cylindrical shape. 3 The continuum limit of the Heisenberg Hamiltonian for classical ferromagnets or antiferromagnets for isotropic spinspin coupling is the nonlinear s model. 4‐8 The total Hamiltonian for a deformable, magnetoelastically coupled manifold is given by H5Hmagn1Hel1Hm2el , where Hmagn, Hel and Hm2el represent the magnetic, elastic, and magnetoelastic energy, respectively. In this paper we will focus mainly on the magnetic part. The magnetic part ~a variant of the nonlinear s model! on a circular cylinder in an external axial magnetic field is given by