Radiality and antisymmetry of bilayer skyrmion minimizers for all parameter values

Establish that, for the thin‑film micromagnetic energy \bar E_2(m_1,m_2) of exchange‑decoupled antisymmetric ferromagnetic bilayers (two layers with opposite interfacial Dzyaloshinskii–Moriya interaction) defined in equation (E2b), every locally energy‑minimizing skyrmion solution is radially symmetric and satisfies the antisymmetry ansatz m_1=(m^\perp,m^\|), m_2=(−m^\perp,m^\|) for all values of the reduced DMI strength \bar\kappa and reduced film thickness \bar\delta at which skyrmions exist.

Background

The paper studies skyrmion states in antisymmetric ultrathin ferromagnetic bilayers using a reduced thin‑film micromagnetic energy \bar E_2 that depends on two nondimensional parameters: the reduced Dzyaloshinskii–Moriya interaction strength \bar\kappa and the reduced film thickness \bar\delta. A natural antisymmetry ansatz aligns the in‑plane magnetization antiparallel and the out‑of‑plane magnetization parallel across the two layers, which simplifies the analysis and energetically favors skyrmion configurations.

The authors rigorously prove the existence of skyrmion minimizers in a small‑parameter regime and show that, there, the solutions are asymptotically radial and obey the antisymmetry ansatz. They then conjecture that these structural properties persist for all values of \bar\kappa and \bar\delta within the skyrmion existence region, beyond the proven asymptotic regime.