Spin-current-controlled anisotropic deformation of magnetic lump solitons

Abstract

We investigate a (2+1)-dimensional nonlinear spin system containing an effective spin-current transport term. Based on its integrable structure, exact magnetic lump solutions are constructed on a rotating spin background, including both fundamental and higher-order configurations generated via the Darboux transformation. The obtained excitations are doubly localized in spatial directions, while their temporal evolution is characterized by intrinsic spin precession rather than translational motion of the localized envelope. It is shown that the effective spin-current contribution enters the localization coordinate and acts as a geometric control parameter for the spatial structure of the solutions. In particular, different values of the effective spin-current contribution correspond to anisotropically deformed localized profiles, with the exact-solution family approaching a quasi-one-dimensional soliton-like limiting state under specific parameter regimes. More importantly, this deformation mechanism is found to be universal across different hierarchical lump structures, including both fundamental and higher-order solutions, indicating that spin current governs a unified structural modulation law for the entire family of localized spin excitations. These results provide an analytically tractable example of spin-current-controlled anisotropic deformation and dimensional crossover in nonlinear spin systems, and further reveal a universal mechanism for geometric control of localized spin textures beyond individual solution types.