Three-Dimensional Shankar Skyrmions in Frustrated Antiferromagnets

We formulate a continuum theory for three-dimensional (3D) Shankar skyrmions in frustrated chiral antiferromagnets (AFs) and derive the conditions for metastable finite-size ${\pi }_3(SO(3))$ solitons. A Derrick–Hobart scaling analysis shows that exchange, Dzyaloshinskii–Moriya interaction (DMI), anisotropy, and frustration can balance to set a finite equilibrium size. We identify two microscopic routes to this common topological and stabilization framework: intrinsic rotation-frame order in noncollinear AFs and an ${\mathbb{S}}^3$ extension of an amplitude-softened Néel field. In the latter, the smooth four-component texture projects onto a Néel field containing a spatially separated pair of oppositely charged Bloch points. Numerical minimization yields metastable monopole textures, while the effective dynamics identifies coherent breathing oscillations as their characteristic finite-frequency collective mode. Our results provide a microscopic framework for the statics and dynamics of Shankar skyrmions and identify frustrated chiral AFs as promising hosts of 3D non-Abelian topological textures.