Bessel function descriptions of magneto-chiral interactions (DMI)-magnetic and spin flexoelectric skyrmions

In this work we present an exact Bessel function solution to the variation equations for a ground state of the chiral Hamiltonians in the continuum limit for cylindrical symmetry. The solution imposes no constraints on the magnetic spin moment magnitude. The formulation is consistent with the generalized view of U. K. Roessler et al. Nature 442, 797-801 (2006) that both the magnetic moment amplitude and magnetic stiffness ratio are micromagnetic properties and variations in amplitude may be allowed. With the exact solutions, we reveal that the added stabilization energy of the 2D skyrmion relative to the 1D solution is the result of the cylindrical symmetry rather than specifics of the chiral interactions. The methods can be employed to understand Bloch type magnetic spin textures observed in MnSi and FeGe and Ne ' el type magnetization textures in antiferromagnetic dielectrics and ferrimagnetic thin sheets with the application of an electric field.