Curvature-controlled stability and growth of dipolar chains on spherical surfaces

We investigate the structural stability and growth limits of magnetic dipolar particle chains confined to a spherical surface, using theoretical analysis and Monte Carlo simulations. We show that curvature leading to a direct geometric mapping between the bulk magic angle γc=54.7∘, and a critical polar angular separation on the sphere θc=2γc, which separates attractive and repulsive regimes. This geometrical criterion is obtained by considering the dipole-dipole interaction in the plane where the first chain develops for systems containing a small particles number. This curvature-induced constraint imposes a geometrically determined limit on chain growth: the angular configuration at the endpoints controls the stability of linear aggregates where dipolar interactions vanish. As a result, we identify a maximum chain length governed by the interplay between dipolar anisotropy and spherical geometry. Furthermore, we find that inter-chain interactions are repulsive across the spherical surface and are enhanced when interacting chains are comparable in size. This collective effect drives the system toward equilibrium configurations in which chains localise at opposite poles. These results reveal a simple physical mechanism by which curvature and symmetry jointly control self-assembly in dipolar systems.