It is shown that an external electron current gradient in a nonuniform magnetized plasma can drive a purely growing instability involving coupled convective cells and magnetostatic modes. Accounting for the mode coupling, it is demonstrated that the quasistationary state of the unstable flute modes can lead to a spatially ordered dipolar vortex structure. The latter could alter the transport properties and it may also be responsible for a relaxed state in a force‐free magnetized plasma.