Quantized Topological Solitons in Antiferromagnets on an Infinite Cylinder

Abstract

We semiclassically quantize static topological solitons which exist within a continuum Heisenberg model of an antiferromagnet on an infinite rigid cylinder. It is shown that the energy of a quantized fundamental soliton and the spin‐wave spectrum are strongly dependent on the geometry of isotropic spin systems. This dependence implies that the spin‐wave gap increases and the energy of a quantized soliton decreases as the radius of the cylinder decreases. Our calculations may have relevance for the recently synthesized carbon nanotubes or cylindrically wrapped thin films of magnetic materials with antiferromagnetic order.

Heisenberg spin textures on a cylinder with topological defects

“…Keywords: Heisenberg's spins -nanomagnetism The nonlinear sigma model is the continuous limit of Heisenberg's hamiltonian for spins and has gained interest recently. It allows the study of equilibrium configurations of spins on non-trivial geometries such as cylinders, tori, ellipsoids, surfaces with negative curvature and so on [1][2][3][4]. The study of the stability of spin configurations and geometric frustration on different kinds of geometry are the two effects most explored with this model [5][6][7][8].…”

“…For isotropic interaction we have h ab = diag (1,1,1). The parameter g is the gyromagnetic factor of the spins in the material medium, µ is their magnetic momentum and B a is the a-th component of the external magnetic field.…”